EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

CERN-PH-EP-2014ndash20412 August 2014

Odd and Even Partial Waves of ηπminus and ηprimeπminus in πminusprarr η(prime)πminusp at191GeVc

The COMPASS Collaboration

Abstract

Exclusive production of ηπminus and ηprimeπminus has been studied with a 191 GeVc πminus beam impinging ona hydrogen target at COMPASS (CERN) Partial-wave analyses reveal different oddeven angularmomentum (L) characteristics in the inspected invariant mass range up to 3 GeVc2 A strikingsimilarity between the two systems is observed for the L = 2 4 6 intensities (scaled by kinematicalfactors) and the relative phases The known resonances a2(1320) and a4(2040) are in line with thissimilarity In contrast a strong enhancement of ηprimeπminus over ηπminus is found for the L = 1 3 5 waveswhich carry non-qq quantum numbers The L = 1 intensity peaks at 17 GeVc2 in ηprimeπminus and at14 GeVc2 in ηπminus the corresponding phase motions with respect to L = 2 are different

(to be submitted to Phys Lett B)

arX

iv1

408

4286

v1 [

hep-

ex]

19

Aug

201

4

The COMPASS Collaboration

C Adolph8 R Akhunzyanov7 MG Alexeev27 GD Alexeev7 A Amoroso2729 V Andrieux22V Anosov7 A Austregesilo1017 B Badełek31 F Balestra2729 J Barth4 G Baum1 R Beck3Y Bedfer22 A Berlin2 J Bernhard13 K Bicker1017 E R Bielert10 J Bieling4 R Birsa25J Bisplinghoff3 M Bodlak19 M Boer22 P Bordalo12a F Bradamante2425 C Braun8A Bressan2425 M Buumlchele9 E Burtin22 L Capozza22 M Chiosso2729 SU Chung17bA Cicuttin2625 ML Crespo2625 Q Curiel22 S Dalla Torre25 SS Dasgupta6 S Dasgupta25OYu Denisov29 SV Donskov21 N Doshita33 V Duic24 W Duumlnnweber16 M Dziewiecki32A Efremov7 C Elia2425 PD Eversheim3 W Eyrich8 M Faessler16 A Ferrero22 M Finger19M Finger jr19 H Fischer9 C Franco12 N du Fresne von Hohenesche1310 JM Friedrich17V Frolov10 F Gautheron2 OP Gavrichtchouk7 S Gerassimov1517 R Geyer16 I Gnesi2729B Gobbo25 S Goertz4 M Gorzellik9 S Grabmuumlller17 A Grasso2729 B Grube17 T Grussenmeyer9A Guskov7 F Haas17 D von Harrach13 D Hahne4 R Hashimoto33 FH Heinsius9 F Herrmann9F Hinterberger3 Ch Houmlppner17 N Horikawa18d N drsquoHose22 S Huber17 S Ishimoto33eA Ivanov7 Yu Ivanshin7 T Iwata33 R Jahn3 V Jary20 P Jasinski13 P Joumlrg9 R Joosten3E Kabuszlig13 B Ketzer17f GV Khaustov21 YuA Khokhlov21g Yu Kisselev7 F Klein4K Klimaszewski30 JH Koivuniemi2 VN Kolosov21 K Kondo33 K Koumlnigsmann9 I Konorov1517VF Konstantinov21 AM Kotzinian2729 O Kouznetsov7 M Kraumlmer17 ZV Kroumchtein7N Kuchinski7 F Kunne22 K Kurek30 RP Kurjata32 AA Lednev21 A Lehmann8 M Levillain22S Levorato25 J Lichtenstadt23 A Maggiora29 A Magnon22 N Makke2425 GK Mallot10C Marchand22 A Martin2425 J Marzec32 J Matousek19 H Matsuda33 T Matsuda14G Meshcheryakov7 W Meyer2 T Michigami33 YuV Mikhailov21 Y Miyachi33 A Nagaytsev7T Nagel17 F Nerling13 S Neubert17 D Neyret22 J Novy20 W-D Nowak9 AS Nunes12AG Olshevsky7 I Orlov7 M Ostrick13 R Panknin4 D Panzieri2829 B Parsamyan2729 S Paul17DV Peshekhonov7 S Platchkov22 J Pochodzalla13 VA Polyakov21 J Pretz4h M Quaresma12C Quintans12 S Ramos12a C Regali9 G Reicherz2 E Rocco10 NS Rossiyskaya7DI Ryabchikov21 A Rychter32 VD Samoylenko21 A Sandacz30 S Sarkar6 IA Savin7G Sbrizzai2425 P Schiavon2425 C Schill9 T Schluumlter16 K Schmidt9c H Schmieden4K Schoumlnning10 S Schopferer9 M Schott10 OYu Shevchenko7 L Silva12 L Sinha6 S Sirtl9M Slunecka7 S Sosio2729 F Sozzi25 A Srnka5 L Steiger25 M Stolarski12 M Sulc11 R Sulej30H Suzuki33d A Szabelski30 T Szameitat9c P Sznajder30 S Takekawa2729 J ter Wolbeek9cS Tessaro25 F Tessarotto25 F Thibaud22 S Uhl17 I Uman16 M Virius20 L Wang2 T Weisrock13M Wilfert13 R Windmolders4 H Wollny22 K Zaremba32 M Zavertyaev15 E Zemlyanichkina7M Ziembicki32 and A Zink8

1 Universitaumlt Bielefeld Fakultaumlt fuumlr Physik 33501 Bielefeld Germanyi

2 Universitaumlt Bochum Institut fuumlr Experimentalphysik 44780 Bochum Germanyip

3 Universitaumlt Bonn Helmholtz-Institut fuumlr Strahlen- und Kernphysik 53115 Bonn Germanyi

4 Universitaumlt Bonn Physikalisches Institut 53115 Bonn Germanyi

5 Institute of Scientific Instruments AS CR 61264 Brno Czech Republicj

6 Matrivani Institute of Experimental Research amp Education Calcutta-700 030 Indiak

7 Joint Institute for Nuclear Research 141980 Dubna Moscow region Russial

8 Universitaumlt ErlangenndashNuumlrnberg Physikalisches Institut 91054 Erlangen Germanyi

9 Universitaumlt Freiburg Physikalisches Institut 79104 Freiburg Germanyip

10 CERN 1211 Geneva 23 Switzerland11 Technical University in Liberec 46117 Liberec Czech Republicj

12 LIP 1000-149 Lisbon Portugalm13 Universitaumlt Mainz Institut fuumlr Kernphysik 55099 Mainz Germanyi

14 University of Miyazaki Miyazaki 889-2192 Japann

15 Lebedev Physical Institute 119991 Moscow Russia16 Ludwig-Maximilians-Universitaumlt Muumlnchen Department fuumlr Physik 80799 Munich Germanyio

17 Technische Universitaumlt Muumlnchen Physik Department 85748 Garching Germanyio

18 Nagoya University 464 Nagoya Japann

19 Charles University in Prague Faculty of Mathematics and Physics 18000 Prague Czech Republicj

20 Czech Technical University in Prague 16636 Prague Czech Republicj

21 State Scientific Center Institute for High Energy Physics of National Research Center lsquoKurchatovInstitutersquo 142281 Protvino Russia

22 CEA IRFUSPhN Saclay 91191 Gif-sur-Yvette Francep

23 Tel Aviv University School of Physics and Astronomy 69978 Tel Aviv Israelq24 University of Trieste Department of Physics 34127 Trieste Italy25 Trieste Section of INFN 34127 Trieste Italy26 Abdus Salam ICTP 34151 Trieste Italy27 University of Turin Department of Physics 10125 Turin Italy28 University of Eastern Piedmont 15100 Alessandria Italy29 Torino Section of INFN 10125 Turin Italy30 National Centre for Nuclear Research 00-681 Warsaw Polandr

31 University of Warsaw Faculty of Physics 00-681 Warsaw Polandr

32 Warsaw University of Technology Institute of Radioelectronics 00-665 Warsaw Polandr

33 Yamagata University Yamagata 992-8510 Japann

a Also at Instituto Superior Teacutecnico Universidade de Lisboa Lisbon Portugalb Also at Department of Physics Pusan National University Busan 609-735 Republic of Korea and

at Physics Department Brookhaven National Laboratory Upton NY 11973 USAc Supported by the DFG Research Training Group Programme 1102 ldquoPhysics at Hadron Accelera-

torsrdquod Also at Chubu University Kasugai Aichi 487-8501 Japann

e Also at KEK 1-1 Oho Tsukuba Ibaraki 305-0801 Japanf Present address Universitaumlt Bonn Helmholtz-Institut fuumlr Strahlen- und Kernphysik 53115 Bonn

Germanyg Also at Moscow Institute of Physics and Technology Moscow Region 141700 Russiah present address RWTH Aachen University III Physikalisches Institut 52056 Aachen Germanyi Supported by the German Bundesministerium fuumlr Bildung und Forschungj Supported by Czech Republic MEYS Grants ME492 and LA242k Supported by SAIL (CSR) Govt of Indial Supported by CERN-RFBR Grants 08-02-91009 and 12-02-91500

m Supported by the Portuguese FCT - Fundaccedilatildeo para a Ciecircncia e Tecnologia COMPETE and QRENGrants CERNFP1093232009 CERNFP1163762010 and CERNFP1236002011

n Supported by the MEXT and the JSPS under the Grants No18002006 No20540299 and No18540281Daiko Foundation and Yamada Foundation

o Supported by the DFG cluster of excellence lsquoOrigin and Structure of the Universersquo (wwwuniverse-clusterde)

p Supported by EU FP7 (HadronPhysics3 Grant Agreement number 283286)q Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Hu-

manitiesr Supported by the Polish NCN Grant DEC-201101MST202350 Deceased

The ηπ and ηprimeπ mesonic systems are attractive for spectroscopic studies because any state with oddangular momentum L which coincides with the total spin J has non-qq (ldquoexoticrdquo) quantum numbersJPC = 1minus+ 3minus+ 5minus+ The 1minus+ state has been the principal case studied so far [1 2]

A comparison of ηπ and ηprimeπ should illuminate the role of flavour symmetry Since η and ηprime are dom-inantly flavour octet and singlet states respectively different SU(3)flavour configurations are formed byηπ and ηprimeπ These configurations are linked to odd or even L by Bose symmetry [3ndash5] Indeed experi-mentally the diffractively produced P -wave (L = J = 1) in ηprimeπminus was found to be more pronounced thanin ηπminus [6] A more systematic study of the two systems in the odd and even partial waves is desirable

Diffractive production of ηπminus and ηprimeπminus was studied by previous experiments with πminus beams in the18 GeVc-37 GeVc range [6ndash9] Apart from the well-known resonances a2(1320) and a4(2040) res-onance features were observed for the exotic P -wave in the 14 GeVc2 minus 17 GeVc2 mass range Ithas quantum numbers JPG = 1minusminus where G-parity is used for the charged system corresponding toC = +1 since the isospin is 1 Results for charge-exchange production of η(prime)π0 are difficult to relateto these observations [1] Critical discussions of the resonance character concern a possible dynamicalorigin of the behaviour of the L = 1 wave in these systems [1 10 11]

The present study is performed with a 191 GeVc πminus beam and in the region 01 (GeVc)2 lt minust lt1 (GeVc)2 where t denotes the squared four-momentum transfer to the proton target This is within therange of Reggeon-exchange processes [12 13] where diffractive excitation and mid-rapidity (ldquocentralrdquo)production coexist The former can induce exclusive resonance production The latter will lead to asystem of the leading and the centrally produced mesons with (almost) no interaction in the final state

In this Letter the behaviour of all partial waves with L = 1 minus 6 in the η(prime)πminus invariant mass range upto 3 GeVc2 is studied A peculiar difference between ηπminus and ηprimeπminus in the even and odd-L waves isobserved

The data were collected with the COMPASS apparatus at CERN COMPASS is a two-stage magneticspectrometer with tracking and calorimetry in both stages [14 15] A beam of negatively charged hadronsat 191 GeVc was impinging on a liquid hydrogen target of 40 cm length and 35 mm diameter Using theinformation from beam particle identifaction detectors it was checked that Kminus and p admixtures to the97 πminus beam are insignificant in the final sample analysed here Recoiling target protons were identifiedby their time of flight and energy loss in a detector (RPD) which consisted of two cylindrical rings ofscintillating counters at distances of 12 cm and 78 cm from the beam axis covering the polar angle rangeabove 50 as seen from the target centre The angular range between the RPD and the opening angleof the spectrometer of about plusmn10 was covered mostly by a large-area photon and charged-particle vetodetector (SW) thus enriching the data recording with kinematically complete events [16] The triggerfor taking the present data required coincidence between beam definition counters and the RPD and noveto from the SW nor from a small counter telescope for non-interacting beam particles far downstream(32 m) from the target A sample of 45times 109 events was recorded with this trigger in 2008

For the analysis of the exclusively produced πminusη and πminusηprime mesonic systems the η was detected by itsdecay η rarr πminusπ+π0 (π0 rarr γγ) and the ηprime by its decay ηprime rarr πminusπ+η (η rarr γγ) The preselection forthe common final state πminusπminusπ+γγ required

(a) three tracks with total charge minus1 reconstructed in the spectrometer

(b) a vertex located inside the target volume with one incoming beam particle track and the threeoutgoing tracks

(c) exactly two ldquoeligiblerdquo clusters in the electromagnetic calorimeters of COMPASS (ECAL1 ECAL2)and

(d) the total energy Etot of the outgoing particles within a 10 GeV wide window centred on the 6 GeVFWHM peak at 191 GeV in the Etot distribution

Clusters were considered ldquoeligiblerdquo if they were not associated with a reconstructed track if the clusterenergy was above 1 GeV and 4 GeV in ECAL1 and ECAL2 respectively and if their timing with respectto the beam was within plusmn4 ns

Sharp η (ηprime) peaks of widths 3 MeVc2-4 MeVc2 were obtained in the πminusπ+π0 and πminusπ+η massspectra after kinematic fitting of the γγ systems within plusmn20 MeVc2 windows about the respective π0

and η masses For the present four-body analyses of the systems πminusπminusπ+π0 and πminusπminusπ+η broadwindows of 50 MeVc2 width about the η and ηprime masses were applied to the three-body πminusπ+π0 andπminusπ+η systems respectively In this way a common treatment of η(prime) and the small number of non-η(prime) events becomes possible in the subsequent likelihood fit No significant deviations from coplanarity(required to hold within 13) are observed for the momentum vectors of beam particle mesonic systemand recoil proton which confirms the exclusivity of the reaction Details are found in Refs [17 18]

In order to account for the acceptance of the spectrometer and the selection procedure Monte Carlosimulations [15 19] were performed for four-body phase-space distributions The latter were weightedwith the experimental t distributions approximated by dσdt prop |t| exp(minusb|t|) with slope parameterb = 80 (GeVc)minus2 and b = 845 (GeVc)minus2 for ηprimeπminus and ηπminus respectively The observed weakmass-dependence of the slope parameter was found not to affect the present results The overall ac-ceptances for ηπminus and ηprimeπminus in the present kinematic range and decay channels amounted to 10 and14 respectively Due to the large coverage of forward solid angle by the COMPASS spectrometerthe acceptances vary smoothly over the relevant regions of phase space see Ref [20] A test of theMonte Carlo description was provided by comparison to a five-charged-track sample where ηprime decaysvia π+πminusη (η rarr π+πminusπ0) The known branching ratio of η decay into γγ and πminusπ+π0 was repro-duced [18] leading to a conservative estimate of 8 for the uncertainty of the relative acceptance of thetwo channels discussed here

To visualize the gross features of the two channels subsamples of events were selected with tightplusmn10 MeVc2 windows on the η and ηprime masses These contain 116 000 and 39 000 events respectivelyincluding 5 background from non-η(prime) events These subsamples are shown as function of the ηπminus andηprimeπminus mass in Figs 1 (a) and (b) and additonally in the scatter plots Figs 2 (a) and (b) as a function ofthese invariant masses and of cosϑGJ where ϑGJ is the angle between the directions of the η(prime) and thebeam as seen in the centre of mass of the η(prime)πminus system (polar angle in the Gottfried-Jackson frame)These distributions are integrated over |t| from 01 (GeVc)2 to 10 (GeVc)2 and over the azimuth ϕGJ

(measured with respect to the reaction plane) The ϕGJ distributions are observed to follow closely asin2 ϕGJ pattern throughout the mass ranges covered in both channels [18 20]

Several salient features of the intensity distributions in Fig 2 are noted before proceeding to the partial-wave analysis In the ηπminus data the a2(1320) with its two-hump D-wave angular distribution is promi-nent see also Fig 1 (a) The D-wave pattern extends to 2 GeVc2 where interference with the a4(2040)can be discerned For higher masses increasingly narrow forwardbackward peaks are observed Thisfeature corresponds to the emergence of a rapidity gap In terms of partial waves it indicates coherentcontributions from larger angular momenta Forwardbackward asymmetries (only weakly affected byacceptance) occur for all masses in both channels which indicates interference of odd and even partialwaves In the ηprimeπminus data the a2(1320) is close to the threshold energy of this channel (11 GeV) andthe signal is not dominant see also Fig 1 (b) A forwardbackward asymmetric interference patternindicating coherent D- and P -wave contributions with mass-dependent relative phase governs the ηprimeπminus

mass range up to 2 GeVc2 In the a4(2040) region well-localised interference is recognised As forηπminus narrow forwardbackward peaking occurs at higher mass but in this case the forwardbackwardasymmetry is visibly larger over the whole mass range of ηprimeπminus

m(ηπminus) [GeVc2]

Entrie

s

4M

eVc2

1 15 2 25 3 35 4 450

400

800

1200

1600

2000

8

10

12

Acceptance

[]

(a) m(ηπminus)

m(ηprimeπminus) [GeVc2]

Entrie

s

20M

eVc2

15 2 25 3 35 4 45 50

100

200

300

400

500

600

121416

Acceptance

[]

(b) m(ηπminus)

Fig 1 Invariant mass spectra (not acceptance corrected) for (a) ηπminus and (b) ηprimeπminus Acceptances (con-tinuous lines) refer to the kinematic ranges of the present analysis

cosϑG

J

m(ηπminus) [GeVc2]

1 15 2 25 3 35 4 45-1

-08-06-04-02

002040608

1

(a) m(ηπminus) vs cosϑGJ

cosϑG

J

m(ηprimeπminus) [GeVc2]

15 2 25 3 35 4 45 5-1

-08-06-04-02

002040608

1

(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

20

40

60

80

100

120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

3000

4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

200

400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

The COMPASS Collaboration

C Adolph8 R Akhunzyanov7 MG Alexeev27 GD Alexeev7 A Amoroso2729 V Andrieux22V Anosov7 A Austregesilo1017 B Badełek31 F Balestra2729 J Barth4 G Baum1 R Beck3Y Bedfer22 A Berlin2 J Bernhard13 K Bicker1017 E R Bielert10 J Bieling4 R Birsa25J Bisplinghoff3 M Bodlak19 M Boer22 P Bordalo12a F Bradamante2425 C Braun8A Bressan2425 M Buumlchele9 E Burtin22 L Capozza22 M Chiosso2729 SU Chung17bA Cicuttin2625 ML Crespo2625 Q Curiel22 S Dalla Torre25 SS Dasgupta6 S Dasgupta25OYu Denisov29 SV Donskov21 N Doshita33 V Duic24 W Duumlnnweber16 M Dziewiecki32A Efremov7 C Elia2425 PD Eversheim3 W Eyrich8 M Faessler16 A Ferrero22 M Finger19M Finger jr19 H Fischer9 C Franco12 N du Fresne von Hohenesche1310 JM Friedrich17V Frolov10 F Gautheron2 OP Gavrichtchouk7 S Gerassimov1517 R Geyer16 I Gnesi2729B Gobbo25 S Goertz4 M Gorzellik9 S Grabmuumlller17 A Grasso2729 B Grube17 T Grussenmeyer9A Guskov7 F Haas17 D von Harrach13 D Hahne4 R Hashimoto33 FH Heinsius9 F Herrmann9F Hinterberger3 Ch Houmlppner17 N Horikawa18d N drsquoHose22 S Huber17 S Ishimoto33eA Ivanov7 Yu Ivanshin7 T Iwata33 R Jahn3 V Jary20 P Jasinski13 P Joumlrg9 R Joosten3E Kabuszlig13 B Ketzer17f GV Khaustov21 YuA Khokhlov21g Yu Kisselev7 F Klein4K Klimaszewski30 JH Koivuniemi2 VN Kolosov21 K Kondo33 K Koumlnigsmann9 I Konorov1517VF Konstantinov21 AM Kotzinian2729 O Kouznetsov7 M Kraumlmer17 ZV Kroumchtein7N Kuchinski7 F Kunne22 K Kurek30 RP Kurjata32 AA Lednev21 A Lehmann8 M Levillain22S Levorato25 J Lichtenstadt23 A Maggiora29 A Magnon22 N Makke2425 GK Mallot10C Marchand22 A Martin2425 J Marzec32 J Matousek19 H Matsuda33 T Matsuda14G Meshcheryakov7 W Meyer2 T Michigami33 YuV Mikhailov21 Y Miyachi33 A Nagaytsev7T Nagel17 F Nerling13 S Neubert17 D Neyret22 J Novy20 W-D Nowak9 AS Nunes12AG Olshevsky7 I Orlov7 M Ostrick13 R Panknin4 D Panzieri2829 B Parsamyan2729 S Paul17DV Peshekhonov7 S Platchkov22 J Pochodzalla13 VA Polyakov21 J Pretz4h M Quaresma12C Quintans12 S Ramos12a C Regali9 G Reicherz2 E Rocco10 NS Rossiyskaya7DI Ryabchikov21 A Rychter32 VD Samoylenko21 A Sandacz30 S Sarkar6 IA Savin7G Sbrizzai2425 P Schiavon2425 C Schill9 T Schluumlter16 K Schmidt9c H Schmieden4K Schoumlnning10 S Schopferer9 M Schott10 OYu Shevchenko7 L Silva12 L Sinha6 S Sirtl9M Slunecka7 S Sosio2729 F Sozzi25 A Srnka5 L Steiger25 M Stolarski12 M Sulc11 R Sulej30H Suzuki33d A Szabelski30 T Szameitat9c P Sznajder30 S Takekawa2729 J ter Wolbeek9cS Tessaro25 F Tessarotto25 F Thibaud22 S Uhl17 I Uman16 M Virius20 L Wang2 T Weisrock13M Wilfert13 R Windmolders4 H Wollny22 K Zaremba32 M Zavertyaev15 E Zemlyanichkina7M Ziembicki32 and A Zink8

1 Universitaumlt Bielefeld Fakultaumlt fuumlr Physik 33501 Bielefeld Germanyi

2 Universitaumlt Bochum Institut fuumlr Experimentalphysik 44780 Bochum Germanyip

3 Universitaumlt Bonn Helmholtz-Institut fuumlr Strahlen- und Kernphysik 53115 Bonn Germanyi

4 Universitaumlt Bonn Physikalisches Institut 53115 Bonn Germanyi

5 Institute of Scientific Instruments AS CR 61264 Brno Czech Republicj

6 Matrivani Institute of Experimental Research amp Education Calcutta-700 030 Indiak

7 Joint Institute for Nuclear Research 141980 Dubna Moscow region Russial

8 Universitaumlt ErlangenndashNuumlrnberg Physikalisches Institut 91054 Erlangen Germanyi

9 Universitaumlt Freiburg Physikalisches Institut 79104 Freiburg Germanyip

10 CERN 1211 Geneva 23 Switzerland11 Technical University in Liberec 46117 Liberec Czech Republicj

12 LIP 1000-149 Lisbon Portugalm13 Universitaumlt Mainz Institut fuumlr Kernphysik 55099 Mainz Germanyi

14 University of Miyazaki Miyazaki 889-2192 Japann

15 Lebedev Physical Institute 119991 Moscow Russia16 Ludwig-Maximilians-Universitaumlt Muumlnchen Department fuumlr Physik 80799 Munich Germanyio

17 Technische Universitaumlt Muumlnchen Physik Department 85748 Garching Germanyio

18 Nagoya University 464 Nagoya Japann

19 Charles University in Prague Faculty of Mathematics and Physics 18000 Prague Czech Republicj

20 Czech Technical University in Prague 16636 Prague Czech Republicj

21 State Scientific Center Institute for High Energy Physics of National Research Center lsquoKurchatovInstitutersquo 142281 Protvino Russia

22 CEA IRFUSPhN Saclay 91191 Gif-sur-Yvette Francep

23 Tel Aviv University School of Physics and Astronomy 69978 Tel Aviv Israelq24 University of Trieste Department of Physics 34127 Trieste Italy25 Trieste Section of INFN 34127 Trieste Italy26 Abdus Salam ICTP 34151 Trieste Italy27 University of Turin Department of Physics 10125 Turin Italy28 University of Eastern Piedmont 15100 Alessandria Italy29 Torino Section of INFN 10125 Turin Italy30 National Centre for Nuclear Research 00-681 Warsaw Polandr

31 University of Warsaw Faculty of Physics 00-681 Warsaw Polandr

32 Warsaw University of Technology Institute of Radioelectronics 00-665 Warsaw Polandr

33 Yamagata University Yamagata 992-8510 Japann

a Also at Instituto Superior Teacutecnico Universidade de Lisboa Lisbon Portugalb Also at Department of Physics Pusan National University Busan 609-735 Republic of Korea and

at Physics Department Brookhaven National Laboratory Upton NY 11973 USAc Supported by the DFG Research Training Group Programme 1102 ldquoPhysics at Hadron Accelera-

torsrdquod Also at Chubu University Kasugai Aichi 487-8501 Japann

e Also at KEK 1-1 Oho Tsukuba Ibaraki 305-0801 Japanf Present address Universitaumlt Bonn Helmholtz-Institut fuumlr Strahlen- und Kernphysik 53115 Bonn

Germanyg Also at Moscow Institute of Physics and Technology Moscow Region 141700 Russiah present address RWTH Aachen University III Physikalisches Institut 52056 Aachen Germanyi Supported by the German Bundesministerium fuumlr Bildung und Forschungj Supported by Czech Republic MEYS Grants ME492 and LA242k Supported by SAIL (CSR) Govt of Indial Supported by CERN-RFBR Grants 08-02-91009 and 12-02-91500

m Supported by the Portuguese FCT - Fundaccedilatildeo para a Ciecircncia e Tecnologia COMPETE and QRENGrants CERNFP1093232009 CERNFP1163762010 and CERNFP1236002011

n Supported by the MEXT and the JSPS under the Grants No18002006 No20540299 and No18540281Daiko Foundation and Yamada Foundation

o Supported by the DFG cluster of excellence lsquoOrigin and Structure of the Universersquo (wwwuniverse-clusterde)

p Supported by EU FP7 (HadronPhysics3 Grant Agreement number 283286)q Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Hu-

manitiesr Supported by the Polish NCN Grant DEC-201101MST202350 Deceased

The ηπ and ηprimeπ mesonic systems are attractive for spectroscopic studies because any state with oddangular momentum L which coincides with the total spin J has non-qq (ldquoexoticrdquo) quantum numbersJPC = 1minus+ 3minus+ 5minus+ The 1minus+ state has been the principal case studied so far [1 2]

A comparison of ηπ and ηprimeπ should illuminate the role of flavour symmetry Since η and ηprime are dom-inantly flavour octet and singlet states respectively different SU(3)flavour configurations are formed byηπ and ηprimeπ These configurations are linked to odd or even L by Bose symmetry [3ndash5] Indeed experi-mentally the diffractively produced P -wave (L = J = 1) in ηprimeπminus was found to be more pronounced thanin ηπminus [6] A more systematic study of the two systems in the odd and even partial waves is desirable

Diffractive production of ηπminus and ηprimeπminus was studied by previous experiments with πminus beams in the18 GeVc-37 GeVc range [6ndash9] Apart from the well-known resonances a2(1320) and a4(2040) res-onance features were observed for the exotic P -wave in the 14 GeVc2 minus 17 GeVc2 mass range Ithas quantum numbers JPG = 1minusminus where G-parity is used for the charged system corresponding toC = +1 since the isospin is 1 Results for charge-exchange production of η(prime)π0 are difficult to relateto these observations [1] Critical discussions of the resonance character concern a possible dynamicalorigin of the behaviour of the L = 1 wave in these systems [1 10 11]

The present study is performed with a 191 GeVc πminus beam and in the region 01 (GeVc)2 lt minust lt1 (GeVc)2 where t denotes the squared four-momentum transfer to the proton target This is within therange of Reggeon-exchange processes [12 13] where diffractive excitation and mid-rapidity (ldquocentralrdquo)production coexist The former can induce exclusive resonance production The latter will lead to asystem of the leading and the centrally produced mesons with (almost) no interaction in the final state

In this Letter the behaviour of all partial waves with L = 1 minus 6 in the η(prime)πminus invariant mass range upto 3 GeVc2 is studied A peculiar difference between ηπminus and ηprimeπminus in the even and odd-L waves isobserved

The data were collected with the COMPASS apparatus at CERN COMPASS is a two-stage magneticspectrometer with tracking and calorimetry in both stages [14 15] A beam of negatively charged hadronsat 191 GeVc was impinging on a liquid hydrogen target of 40 cm length and 35 mm diameter Using theinformation from beam particle identifaction detectors it was checked that Kminus and p admixtures to the97 πminus beam are insignificant in the final sample analysed here Recoiling target protons were identifiedby their time of flight and energy loss in a detector (RPD) which consisted of two cylindrical rings ofscintillating counters at distances of 12 cm and 78 cm from the beam axis covering the polar angle rangeabove 50 as seen from the target centre The angular range between the RPD and the opening angleof the spectrometer of about plusmn10 was covered mostly by a large-area photon and charged-particle vetodetector (SW) thus enriching the data recording with kinematically complete events [16] The triggerfor taking the present data required coincidence between beam definition counters and the RPD and noveto from the SW nor from a small counter telescope for non-interacting beam particles far downstream(32 m) from the target A sample of 45times 109 events was recorded with this trigger in 2008

For the analysis of the exclusively produced πminusη and πminusηprime mesonic systems the η was detected by itsdecay η rarr πminusπ+π0 (π0 rarr γγ) and the ηprime by its decay ηprime rarr πminusπ+η (η rarr γγ) The preselection forthe common final state πminusπminusπ+γγ required

(a) three tracks with total charge minus1 reconstructed in the spectrometer

(b) a vertex located inside the target volume with one incoming beam particle track and the threeoutgoing tracks

(c) exactly two ldquoeligiblerdquo clusters in the electromagnetic calorimeters of COMPASS (ECAL1 ECAL2)and

(d) the total energy Etot of the outgoing particles within a 10 GeV wide window centred on the 6 GeVFWHM peak at 191 GeV in the Etot distribution

Clusters were considered ldquoeligiblerdquo if they were not associated with a reconstructed track if the clusterenergy was above 1 GeV and 4 GeV in ECAL1 and ECAL2 respectively and if their timing with respectto the beam was within plusmn4 ns

Sharp η (ηprime) peaks of widths 3 MeVc2-4 MeVc2 were obtained in the πminusπ+π0 and πminusπ+η massspectra after kinematic fitting of the γγ systems within plusmn20 MeVc2 windows about the respective π0

and η masses For the present four-body analyses of the systems πminusπminusπ+π0 and πminusπminusπ+η broadwindows of 50 MeVc2 width about the η and ηprime masses were applied to the three-body πminusπ+π0 andπminusπ+η systems respectively In this way a common treatment of η(prime) and the small number of non-η(prime) events becomes possible in the subsequent likelihood fit No significant deviations from coplanarity(required to hold within 13) are observed for the momentum vectors of beam particle mesonic systemand recoil proton which confirms the exclusivity of the reaction Details are found in Refs [17 18]

In order to account for the acceptance of the spectrometer and the selection procedure Monte Carlosimulations [15 19] were performed for four-body phase-space distributions The latter were weightedwith the experimental t distributions approximated by dσdt prop |t| exp(minusb|t|) with slope parameterb = 80 (GeVc)minus2 and b = 845 (GeVc)minus2 for ηprimeπminus and ηπminus respectively The observed weakmass-dependence of the slope parameter was found not to affect the present results The overall ac-ceptances for ηπminus and ηprimeπminus in the present kinematic range and decay channels amounted to 10 and14 respectively Due to the large coverage of forward solid angle by the COMPASS spectrometerthe acceptances vary smoothly over the relevant regions of phase space see Ref [20] A test of theMonte Carlo description was provided by comparison to a five-charged-track sample where ηprime decaysvia π+πminusη (η rarr π+πminusπ0) The known branching ratio of η decay into γγ and πminusπ+π0 was repro-duced [18] leading to a conservative estimate of 8 for the uncertainty of the relative acceptance of thetwo channels discussed here

To visualize the gross features of the two channels subsamples of events were selected with tightplusmn10 MeVc2 windows on the η and ηprime masses These contain 116 000 and 39 000 events respectivelyincluding 5 background from non-η(prime) events These subsamples are shown as function of the ηπminus andηprimeπminus mass in Figs 1 (a) and (b) and additonally in the scatter plots Figs 2 (a) and (b) as a function ofthese invariant masses and of cosϑGJ where ϑGJ is the angle between the directions of the η(prime) and thebeam as seen in the centre of mass of the η(prime)πminus system (polar angle in the Gottfried-Jackson frame)These distributions are integrated over |t| from 01 (GeVc)2 to 10 (GeVc)2 and over the azimuth ϕGJ

(measured with respect to the reaction plane) The ϕGJ distributions are observed to follow closely asin2 ϕGJ pattern throughout the mass ranges covered in both channels [18 20]

Several salient features of the intensity distributions in Fig 2 are noted before proceeding to the partial-wave analysis In the ηπminus data the a2(1320) with its two-hump D-wave angular distribution is promi-nent see also Fig 1 (a) The D-wave pattern extends to 2 GeVc2 where interference with the a4(2040)can be discerned For higher masses increasingly narrow forwardbackward peaks are observed Thisfeature corresponds to the emergence of a rapidity gap In terms of partial waves it indicates coherentcontributions from larger angular momenta Forwardbackward asymmetries (only weakly affected byacceptance) occur for all masses in both channels which indicates interference of odd and even partialwaves In the ηprimeπminus data the a2(1320) is close to the threshold energy of this channel (11 GeV) andthe signal is not dominant see also Fig 1 (b) A forwardbackward asymmetric interference patternindicating coherent D- and P -wave contributions with mass-dependent relative phase governs the ηprimeπminus

mass range up to 2 GeVc2 In the a4(2040) region well-localised interference is recognised As forηπminus narrow forwardbackward peaking occurs at higher mass but in this case the forwardbackwardasymmetry is visibly larger over the whole mass range of ηprimeπminus

m(ηπminus) [GeVc2]

Entrie

s

4M

eVc2

1 15 2 25 3 35 4 450

400

800

1200

1600

2000

8

10

12

Acceptance

[]

(a) m(ηπminus)

m(ηprimeπminus) [GeVc2]

Entrie

s

20M

eVc2

15 2 25 3 35 4 45 50

100

200

300

400

500

600

121416

Acceptance

[]

(b) m(ηπminus)

Fig 1 Invariant mass spectra (not acceptance corrected) for (a) ηπminus and (b) ηprimeπminus Acceptances (con-tinuous lines) refer to the kinematic ranges of the present analysis

cosϑG

J

m(ηπminus) [GeVc2]

1 15 2 25 3 35 4 45-1

-08-06-04-02

002040608

1

(a) m(ηπminus) vs cosϑGJ

cosϑG

J

m(ηprimeπminus) [GeVc2]

15 2 25 3 35 4 45 5-1

-08-06-04-02

002040608

1

(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

20

40

60

80

100

120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

3000

4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

200

400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

15 Lebedev Physical Institute 119991 Moscow Russia16 Ludwig-Maximilians-Universitaumlt Muumlnchen Department fuumlr Physik 80799 Munich Germanyio

17 Technische Universitaumlt Muumlnchen Physik Department 85748 Garching Germanyio

18 Nagoya University 464 Nagoya Japann

19 Charles University in Prague Faculty of Mathematics and Physics 18000 Prague Czech Republicj

20 Czech Technical University in Prague 16636 Prague Czech Republicj

21 State Scientific Center Institute for High Energy Physics of National Research Center lsquoKurchatovInstitutersquo 142281 Protvino Russia

22 CEA IRFUSPhN Saclay 91191 Gif-sur-Yvette Francep

23 Tel Aviv University School of Physics and Astronomy 69978 Tel Aviv Israelq24 University of Trieste Department of Physics 34127 Trieste Italy25 Trieste Section of INFN 34127 Trieste Italy26 Abdus Salam ICTP 34151 Trieste Italy27 University of Turin Department of Physics 10125 Turin Italy28 University of Eastern Piedmont 15100 Alessandria Italy29 Torino Section of INFN 10125 Turin Italy30 National Centre for Nuclear Research 00-681 Warsaw Polandr

31 University of Warsaw Faculty of Physics 00-681 Warsaw Polandr

32 Warsaw University of Technology Institute of Radioelectronics 00-665 Warsaw Polandr

33 Yamagata University Yamagata 992-8510 Japann

a Also at Instituto Superior Teacutecnico Universidade de Lisboa Lisbon Portugalb Also at Department of Physics Pusan National University Busan 609-735 Republic of Korea and

at Physics Department Brookhaven National Laboratory Upton NY 11973 USAc Supported by the DFG Research Training Group Programme 1102 ldquoPhysics at Hadron Accelera-

torsrdquod Also at Chubu University Kasugai Aichi 487-8501 Japann

e Also at KEK 1-1 Oho Tsukuba Ibaraki 305-0801 Japanf Present address Universitaumlt Bonn Helmholtz-Institut fuumlr Strahlen- und Kernphysik 53115 Bonn

Germanyg Also at Moscow Institute of Physics and Technology Moscow Region 141700 Russiah present address RWTH Aachen University III Physikalisches Institut 52056 Aachen Germanyi Supported by the German Bundesministerium fuumlr Bildung und Forschungj Supported by Czech Republic MEYS Grants ME492 and LA242k Supported by SAIL (CSR) Govt of Indial Supported by CERN-RFBR Grants 08-02-91009 and 12-02-91500

m Supported by the Portuguese FCT - Fundaccedilatildeo para a Ciecircncia e Tecnologia COMPETE and QRENGrants CERNFP1093232009 CERNFP1163762010 and CERNFP1236002011

n Supported by the MEXT and the JSPS under the Grants No18002006 No20540299 and No18540281Daiko Foundation and Yamada Foundation

o Supported by the DFG cluster of excellence lsquoOrigin and Structure of the Universersquo (wwwuniverse-clusterde)

p Supported by EU FP7 (HadronPhysics3 Grant Agreement number 283286)q Supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Hu-

manitiesr Supported by the Polish NCN Grant DEC-201101MST202350 Deceased

The ηπ and ηprimeπ mesonic systems are attractive for spectroscopic studies because any state with oddangular momentum L which coincides with the total spin J has non-qq (ldquoexoticrdquo) quantum numbersJPC = 1minus+ 3minus+ 5minus+ The 1minus+ state has been the principal case studied so far [1 2]

A comparison of ηπ and ηprimeπ should illuminate the role of flavour symmetry Since η and ηprime are dom-inantly flavour octet and singlet states respectively different SU(3)flavour configurations are formed byηπ and ηprimeπ These configurations are linked to odd or even L by Bose symmetry [3ndash5] Indeed experi-mentally the diffractively produced P -wave (L = J = 1) in ηprimeπminus was found to be more pronounced thanin ηπminus [6] A more systematic study of the two systems in the odd and even partial waves is desirable

Diffractive production of ηπminus and ηprimeπminus was studied by previous experiments with πminus beams in the18 GeVc-37 GeVc range [6ndash9] Apart from the well-known resonances a2(1320) and a4(2040) res-onance features were observed for the exotic P -wave in the 14 GeVc2 minus 17 GeVc2 mass range Ithas quantum numbers JPG = 1minusminus where G-parity is used for the charged system corresponding toC = +1 since the isospin is 1 Results for charge-exchange production of η(prime)π0 are difficult to relateto these observations [1] Critical discussions of the resonance character concern a possible dynamicalorigin of the behaviour of the L = 1 wave in these systems [1 10 11]

The present study is performed with a 191 GeVc πminus beam and in the region 01 (GeVc)2 lt minust lt1 (GeVc)2 where t denotes the squared four-momentum transfer to the proton target This is within therange of Reggeon-exchange processes [12 13] where diffractive excitation and mid-rapidity (ldquocentralrdquo)production coexist The former can induce exclusive resonance production The latter will lead to asystem of the leading and the centrally produced mesons with (almost) no interaction in the final state

In this Letter the behaviour of all partial waves with L = 1 minus 6 in the η(prime)πminus invariant mass range upto 3 GeVc2 is studied A peculiar difference between ηπminus and ηprimeπminus in the even and odd-L waves isobserved

The data were collected with the COMPASS apparatus at CERN COMPASS is a two-stage magneticspectrometer with tracking and calorimetry in both stages [14 15] A beam of negatively charged hadronsat 191 GeVc was impinging on a liquid hydrogen target of 40 cm length and 35 mm diameter Using theinformation from beam particle identifaction detectors it was checked that Kminus and p admixtures to the97 πminus beam are insignificant in the final sample analysed here Recoiling target protons were identifiedby their time of flight and energy loss in a detector (RPD) which consisted of two cylindrical rings ofscintillating counters at distances of 12 cm and 78 cm from the beam axis covering the polar angle rangeabove 50 as seen from the target centre The angular range between the RPD and the opening angleof the spectrometer of about plusmn10 was covered mostly by a large-area photon and charged-particle vetodetector (SW) thus enriching the data recording with kinematically complete events [16] The triggerfor taking the present data required coincidence between beam definition counters and the RPD and noveto from the SW nor from a small counter telescope for non-interacting beam particles far downstream(32 m) from the target A sample of 45times 109 events was recorded with this trigger in 2008

For the analysis of the exclusively produced πminusη and πminusηprime mesonic systems the η was detected by itsdecay η rarr πminusπ+π0 (π0 rarr γγ) and the ηprime by its decay ηprime rarr πminusπ+η (η rarr γγ) The preselection forthe common final state πminusπminusπ+γγ required

(a) three tracks with total charge minus1 reconstructed in the spectrometer

(b) a vertex located inside the target volume with one incoming beam particle track and the threeoutgoing tracks

(c) exactly two ldquoeligiblerdquo clusters in the electromagnetic calorimeters of COMPASS (ECAL1 ECAL2)and

(d) the total energy Etot of the outgoing particles within a 10 GeV wide window centred on the 6 GeVFWHM peak at 191 GeV in the Etot distribution

Clusters were considered ldquoeligiblerdquo if they were not associated with a reconstructed track if the clusterenergy was above 1 GeV and 4 GeV in ECAL1 and ECAL2 respectively and if their timing with respectto the beam was within plusmn4 ns

Sharp η (ηprime) peaks of widths 3 MeVc2-4 MeVc2 were obtained in the πminusπ+π0 and πminusπ+η massspectra after kinematic fitting of the γγ systems within plusmn20 MeVc2 windows about the respective π0

and η masses For the present four-body analyses of the systems πminusπminusπ+π0 and πminusπminusπ+η broadwindows of 50 MeVc2 width about the η and ηprime masses were applied to the three-body πminusπ+π0 andπminusπ+η systems respectively In this way a common treatment of η(prime) and the small number of non-η(prime) events becomes possible in the subsequent likelihood fit No significant deviations from coplanarity(required to hold within 13) are observed for the momentum vectors of beam particle mesonic systemand recoil proton which confirms the exclusivity of the reaction Details are found in Refs [17 18]

In order to account for the acceptance of the spectrometer and the selection procedure Monte Carlosimulations [15 19] were performed for four-body phase-space distributions The latter were weightedwith the experimental t distributions approximated by dσdt prop |t| exp(minusb|t|) with slope parameterb = 80 (GeVc)minus2 and b = 845 (GeVc)minus2 for ηprimeπminus and ηπminus respectively The observed weakmass-dependence of the slope parameter was found not to affect the present results The overall ac-ceptances for ηπminus and ηprimeπminus in the present kinematic range and decay channels amounted to 10 and14 respectively Due to the large coverage of forward solid angle by the COMPASS spectrometerthe acceptances vary smoothly over the relevant regions of phase space see Ref [20] A test of theMonte Carlo description was provided by comparison to a five-charged-track sample where ηprime decaysvia π+πminusη (η rarr π+πminusπ0) The known branching ratio of η decay into γγ and πminusπ+π0 was repro-duced [18] leading to a conservative estimate of 8 for the uncertainty of the relative acceptance of thetwo channels discussed here

To visualize the gross features of the two channels subsamples of events were selected with tightplusmn10 MeVc2 windows on the η and ηprime masses These contain 116 000 and 39 000 events respectivelyincluding 5 background from non-η(prime) events These subsamples are shown as function of the ηπminus andηprimeπminus mass in Figs 1 (a) and (b) and additonally in the scatter plots Figs 2 (a) and (b) as a function ofthese invariant masses and of cosϑGJ where ϑGJ is the angle between the directions of the η(prime) and thebeam as seen in the centre of mass of the η(prime)πminus system (polar angle in the Gottfried-Jackson frame)These distributions are integrated over |t| from 01 (GeVc)2 to 10 (GeVc)2 and over the azimuth ϕGJ

(measured with respect to the reaction plane) The ϕGJ distributions are observed to follow closely asin2 ϕGJ pattern throughout the mass ranges covered in both channels [18 20]

Several salient features of the intensity distributions in Fig 2 are noted before proceeding to the partial-wave analysis In the ηπminus data the a2(1320) with its two-hump D-wave angular distribution is promi-nent see also Fig 1 (a) The D-wave pattern extends to 2 GeVc2 where interference with the a4(2040)can be discerned For higher masses increasingly narrow forwardbackward peaks are observed Thisfeature corresponds to the emergence of a rapidity gap In terms of partial waves it indicates coherentcontributions from larger angular momenta Forwardbackward asymmetries (only weakly affected byacceptance) occur for all masses in both channels which indicates interference of odd and even partialwaves In the ηprimeπminus data the a2(1320) is close to the threshold energy of this channel (11 GeV) andthe signal is not dominant see also Fig 1 (b) A forwardbackward asymmetric interference patternindicating coherent D- and P -wave contributions with mass-dependent relative phase governs the ηprimeπminus

mass range up to 2 GeVc2 In the a4(2040) region well-localised interference is recognised As forηπminus narrow forwardbackward peaking occurs at higher mass but in this case the forwardbackwardasymmetry is visibly larger over the whole mass range of ηprimeπminus

m(ηπminus) [GeVc2]

Entrie

s

4M

eVc2

1 15 2 25 3 35 4 450

400

800

1200

1600

2000

8

10

12

Acceptance

[]

(a) m(ηπminus)

m(ηprimeπminus) [GeVc2]

Entrie

s

20M

eVc2

15 2 25 3 35 4 45 50

100

200

300

400

500

600

121416

Acceptance

[]

(b) m(ηπminus)

Fig 1 Invariant mass spectra (not acceptance corrected) for (a) ηπminus and (b) ηprimeπminus Acceptances (con-tinuous lines) refer to the kinematic ranges of the present analysis

cosϑG

J

m(ηπminus) [GeVc2]

1 15 2 25 3 35 4 45-1

-08-06-04-02

002040608

1

(a) m(ηπminus) vs cosϑGJ

cosϑG

J

m(ηprimeπminus) [GeVc2]

15 2 25 3 35 4 45 5-1

-08-06-04-02

002040608

1

(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

20

40

60

80

100

120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

3000

4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

200

400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

The ηπ and ηprimeπ mesonic systems are attractive for spectroscopic studies because any state with oddangular momentum L which coincides with the total spin J has non-qq (ldquoexoticrdquo) quantum numbersJPC = 1minus+ 3minus+ 5minus+ The 1minus+ state has been the principal case studied so far [1 2]

A comparison of ηπ and ηprimeπ should illuminate the role of flavour symmetry Since η and ηprime are dom-inantly flavour octet and singlet states respectively different SU(3)flavour configurations are formed byηπ and ηprimeπ These configurations are linked to odd or even L by Bose symmetry [3ndash5] Indeed experi-mentally the diffractively produced P -wave (L = J = 1) in ηprimeπminus was found to be more pronounced thanin ηπminus [6] A more systematic study of the two systems in the odd and even partial waves is desirable

Diffractive production of ηπminus and ηprimeπminus was studied by previous experiments with πminus beams in the18 GeVc-37 GeVc range [6ndash9] Apart from the well-known resonances a2(1320) and a4(2040) res-onance features were observed for the exotic P -wave in the 14 GeVc2 minus 17 GeVc2 mass range Ithas quantum numbers JPG = 1minusminus where G-parity is used for the charged system corresponding toC = +1 since the isospin is 1 Results for charge-exchange production of η(prime)π0 are difficult to relateto these observations [1] Critical discussions of the resonance character concern a possible dynamicalorigin of the behaviour of the L = 1 wave in these systems [1 10 11]

The present study is performed with a 191 GeVc πminus beam and in the region 01 (GeVc)2 lt minust lt1 (GeVc)2 where t denotes the squared four-momentum transfer to the proton target This is within therange of Reggeon-exchange processes [12 13] where diffractive excitation and mid-rapidity (ldquocentralrdquo)production coexist The former can induce exclusive resonance production The latter will lead to asystem of the leading and the centrally produced mesons with (almost) no interaction in the final state

In this Letter the behaviour of all partial waves with L = 1 minus 6 in the η(prime)πminus invariant mass range upto 3 GeVc2 is studied A peculiar difference between ηπminus and ηprimeπminus in the even and odd-L waves isobserved

The data were collected with the COMPASS apparatus at CERN COMPASS is a two-stage magneticspectrometer with tracking and calorimetry in both stages [14 15] A beam of negatively charged hadronsat 191 GeVc was impinging on a liquid hydrogen target of 40 cm length and 35 mm diameter Using theinformation from beam particle identifaction detectors it was checked that Kminus and p admixtures to the97 πminus beam are insignificant in the final sample analysed here Recoiling target protons were identifiedby their time of flight and energy loss in a detector (RPD) which consisted of two cylindrical rings ofscintillating counters at distances of 12 cm and 78 cm from the beam axis covering the polar angle rangeabove 50 as seen from the target centre The angular range between the RPD and the opening angleof the spectrometer of about plusmn10 was covered mostly by a large-area photon and charged-particle vetodetector (SW) thus enriching the data recording with kinematically complete events [16] The triggerfor taking the present data required coincidence between beam definition counters and the RPD and noveto from the SW nor from a small counter telescope for non-interacting beam particles far downstream(32 m) from the target A sample of 45times 109 events was recorded with this trigger in 2008

For the analysis of the exclusively produced πminusη and πminusηprime mesonic systems the η was detected by itsdecay η rarr πminusπ+π0 (π0 rarr γγ) and the ηprime by its decay ηprime rarr πminusπ+η (η rarr γγ) The preselection forthe common final state πminusπminusπ+γγ required

(a) three tracks with total charge minus1 reconstructed in the spectrometer

(b) a vertex located inside the target volume with one incoming beam particle track and the threeoutgoing tracks

(c) exactly two ldquoeligiblerdquo clusters in the electromagnetic calorimeters of COMPASS (ECAL1 ECAL2)and

(d) the total energy Etot of the outgoing particles within a 10 GeV wide window centred on the 6 GeVFWHM peak at 191 GeV in the Etot distribution

Clusters were considered ldquoeligiblerdquo if they were not associated with a reconstructed track if the clusterenergy was above 1 GeV and 4 GeV in ECAL1 and ECAL2 respectively and if their timing with respectto the beam was within plusmn4 ns

Sharp η (ηprime) peaks of widths 3 MeVc2-4 MeVc2 were obtained in the πminusπ+π0 and πminusπ+η massspectra after kinematic fitting of the γγ systems within plusmn20 MeVc2 windows about the respective π0

and η masses For the present four-body analyses of the systems πminusπminusπ+π0 and πminusπminusπ+η broadwindows of 50 MeVc2 width about the η and ηprime masses were applied to the three-body πminusπ+π0 andπminusπ+η systems respectively In this way a common treatment of η(prime) and the small number of non-η(prime) events becomes possible in the subsequent likelihood fit No significant deviations from coplanarity(required to hold within 13) are observed for the momentum vectors of beam particle mesonic systemand recoil proton which confirms the exclusivity of the reaction Details are found in Refs [17 18]

In order to account for the acceptance of the spectrometer and the selection procedure Monte Carlosimulations [15 19] were performed for four-body phase-space distributions The latter were weightedwith the experimental t distributions approximated by dσdt prop |t| exp(minusb|t|) with slope parameterb = 80 (GeVc)minus2 and b = 845 (GeVc)minus2 for ηprimeπminus and ηπminus respectively The observed weakmass-dependence of the slope parameter was found not to affect the present results The overall ac-ceptances for ηπminus and ηprimeπminus in the present kinematic range and decay channels amounted to 10 and14 respectively Due to the large coverage of forward solid angle by the COMPASS spectrometerthe acceptances vary smoothly over the relevant regions of phase space see Ref [20] A test of theMonte Carlo description was provided by comparison to a five-charged-track sample where ηprime decaysvia π+πminusη (η rarr π+πminusπ0) The known branching ratio of η decay into γγ and πminusπ+π0 was repro-duced [18] leading to a conservative estimate of 8 for the uncertainty of the relative acceptance of thetwo channels discussed here

To visualize the gross features of the two channels subsamples of events were selected with tightplusmn10 MeVc2 windows on the η and ηprime masses These contain 116 000 and 39 000 events respectivelyincluding 5 background from non-η(prime) events These subsamples are shown as function of the ηπminus andηprimeπminus mass in Figs 1 (a) and (b) and additonally in the scatter plots Figs 2 (a) and (b) as a function ofthese invariant masses and of cosϑGJ where ϑGJ is the angle between the directions of the η(prime) and thebeam as seen in the centre of mass of the η(prime)πminus system (polar angle in the Gottfried-Jackson frame)These distributions are integrated over |t| from 01 (GeVc)2 to 10 (GeVc)2 and over the azimuth ϕGJ

(measured with respect to the reaction plane) The ϕGJ distributions are observed to follow closely asin2 ϕGJ pattern throughout the mass ranges covered in both channels [18 20]

Several salient features of the intensity distributions in Fig 2 are noted before proceeding to the partial-wave analysis In the ηπminus data the a2(1320) with its two-hump D-wave angular distribution is promi-nent see also Fig 1 (a) The D-wave pattern extends to 2 GeVc2 where interference with the a4(2040)can be discerned For higher masses increasingly narrow forwardbackward peaks are observed Thisfeature corresponds to the emergence of a rapidity gap In terms of partial waves it indicates coherentcontributions from larger angular momenta Forwardbackward asymmetries (only weakly affected byacceptance) occur for all masses in both channels which indicates interference of odd and even partialwaves In the ηprimeπminus data the a2(1320) is close to the threshold energy of this channel (11 GeV) andthe signal is not dominant see also Fig 1 (b) A forwardbackward asymmetric interference patternindicating coherent D- and P -wave contributions with mass-dependent relative phase governs the ηprimeπminus

mass range up to 2 GeVc2 In the a4(2040) region well-localised interference is recognised As forηπminus narrow forwardbackward peaking occurs at higher mass but in this case the forwardbackwardasymmetry is visibly larger over the whole mass range of ηprimeπminus

m(ηπminus) [GeVc2]

Entrie

s

4M

eVc2

1 15 2 25 3 35 4 450

400

800

1200

1600

2000

8

10

12

Acceptance

[]

(a) m(ηπminus)

m(ηprimeπminus) [GeVc2]

Entrie

s

20M

eVc2

15 2 25 3 35 4 45 50

100

200

300

400

500

600

121416

Acceptance

[]

(b) m(ηπminus)

Fig 1 Invariant mass spectra (not acceptance corrected) for (a) ηπminus and (b) ηprimeπminus Acceptances (con-tinuous lines) refer to the kinematic ranges of the present analysis

cosϑG

J

m(ηπminus) [GeVc2]

1 15 2 25 3 35 4 45-1

-08-06-04-02

002040608

1

(a) m(ηπminus) vs cosϑGJ

cosϑG

J

m(ηprimeπminus) [GeVc2]

15 2 25 3 35 4 45 5-1

-08-06-04-02

002040608

1

(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

20

40

60

80

100

120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

3000

4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

200

400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

(d) the total energy Etot of the outgoing particles within a 10 GeV wide window centred on the 6 GeVFWHM peak at 191 GeV in the Etot distribution

Clusters were considered ldquoeligiblerdquo if they were not associated with a reconstructed track if the clusterenergy was above 1 GeV and 4 GeV in ECAL1 and ECAL2 respectively and if their timing with respectto the beam was within plusmn4 ns

Sharp η (ηprime) peaks of widths 3 MeVc2-4 MeVc2 were obtained in the πminusπ+π0 and πminusπ+η massspectra after kinematic fitting of the γγ systems within plusmn20 MeVc2 windows about the respective π0

and η masses For the present four-body analyses of the systems πminusπminusπ+π0 and πminusπminusπ+η broadwindows of 50 MeVc2 width about the η and ηprime masses were applied to the three-body πminusπ+π0 andπminusπ+η systems respectively In this way a common treatment of η(prime) and the small number of non-η(prime) events becomes possible in the subsequent likelihood fit No significant deviations from coplanarity(required to hold within 13) are observed for the momentum vectors of beam particle mesonic systemand recoil proton which confirms the exclusivity of the reaction Details are found in Refs [17 18]

In order to account for the acceptance of the spectrometer and the selection procedure Monte Carlosimulations [15 19] were performed for four-body phase-space distributions The latter were weightedwith the experimental t distributions approximated by dσdt prop |t| exp(minusb|t|) with slope parameterb = 80 (GeVc)minus2 and b = 845 (GeVc)minus2 for ηprimeπminus and ηπminus respectively The observed weakmass-dependence of the slope parameter was found not to affect the present results The overall ac-ceptances for ηπminus and ηprimeπminus in the present kinematic range and decay channels amounted to 10 and14 respectively Due to the large coverage of forward solid angle by the COMPASS spectrometerthe acceptances vary smoothly over the relevant regions of phase space see Ref [20] A test of theMonte Carlo description was provided by comparison to a five-charged-track sample where ηprime decaysvia π+πminusη (η rarr π+πminusπ0) The known branching ratio of η decay into γγ and πminusπ+π0 was repro-duced [18] leading to a conservative estimate of 8 for the uncertainty of the relative acceptance of thetwo channels discussed here

To visualize the gross features of the two channels subsamples of events were selected with tightplusmn10 MeVc2 windows on the η and ηprime masses These contain 116 000 and 39 000 events respectivelyincluding 5 background from non-η(prime) events These subsamples are shown as function of the ηπminus andηprimeπminus mass in Figs 1 (a) and (b) and additonally in the scatter plots Figs 2 (a) and (b) as a function ofthese invariant masses and of cosϑGJ where ϑGJ is the angle between the directions of the η(prime) and thebeam as seen in the centre of mass of the η(prime)πminus system (polar angle in the Gottfried-Jackson frame)These distributions are integrated over |t| from 01 (GeVc)2 to 10 (GeVc)2 and over the azimuth ϕGJ

(measured with respect to the reaction plane) The ϕGJ distributions are observed to follow closely asin2 ϕGJ pattern throughout the mass ranges covered in both channels [18 20]

Several salient features of the intensity distributions in Fig 2 are noted before proceeding to the partial-wave analysis In the ηπminus data the a2(1320) with its two-hump D-wave angular distribution is promi-nent see also Fig 1 (a) The D-wave pattern extends to 2 GeVc2 where interference with the a4(2040)can be discerned For higher masses increasingly narrow forwardbackward peaks are observed Thisfeature corresponds to the emergence of a rapidity gap In terms of partial waves it indicates coherentcontributions from larger angular momenta Forwardbackward asymmetries (only weakly affected byacceptance) occur for all masses in both channels which indicates interference of odd and even partialwaves In the ηprimeπminus data the a2(1320) is close to the threshold energy of this channel (11 GeV) andthe signal is not dominant see also Fig 1 (b) A forwardbackward asymmetric interference patternindicating coherent D- and P -wave contributions with mass-dependent relative phase governs the ηprimeπminus

mass range up to 2 GeVc2 In the a4(2040) region well-localised interference is recognised As forηπminus narrow forwardbackward peaking occurs at higher mass but in this case the forwardbackwardasymmetry is visibly larger over the whole mass range of ηprimeπminus

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(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

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(b) D-wave L = 2

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40M

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50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

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40M

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(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

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08 12 16 2 24 28

-50

0

50

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(a) L = 1ΦM

=2minus

Φ2

[deg]

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-50

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(b) L = 2M = 2

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[deg]

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Φ4minus

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Φ2

[deg]

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Φ6minus

Φ2

[deg]

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08 12 16 2 24 28

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-200

-150

-100

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0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

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15 2 25 3 35 4 45 50

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300

400

500

600

121416

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[]

(b) m(ηπminus)

Fig 1 Invariant mass spectra (not acceptance corrected) for (a) ηπminus and (b) ηprimeπminus Acceptances (con-tinuous lines) refer to the kinematic ranges of the present analysis

cosϑG

J

m(ηπminus) [GeVc2]

1 15 2 25 3 35 4 45-1

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002040608

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m(ηprimeπminus) [GeVc2]

15 2 25 3 35 4 45 5-1

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002040608

1

(b) m(ηprimeπminus) vs cosϑGJ

Fig 2 Data (not acceptance corrected) as a function of the invariant ηπminus (a) and ηprimeπminus (b) mass and ofthe cosine of the decay angle in the respective Gottfried-Jackson frames where cosϑGJ = 1 correspondsη(prime) emission in the beam direction Two-dimensional acceptances can be found in Ref [20]

The data were subjected to a partial-wave analysis (PWA) using a program developed at Illinois andVES [21ndash23] Independent fits were carried out in 40 MeVc2 wide bins of the four-body mass fromthreshold up to 3 GeVc2 (so-called mass-independent PWA) Momentum transfers were limited to therange given above

An η(prime)πminus partial-wave is characterised by the angular momentum L the absolute value of the magneticquantum number M = |m| and the reflectivity ε = plusmn1 which is the eigenvalue of reflection aboutthe production plane Positive (negative) ε is chosen to correspond to natural (unnatural) spin-parityof the exchanged Reggeon with JPtr = 1minus or 2+ or 3minus (0minus or 1+ or 2minus ) transfer to the beamparticle [18 24] These two classes are incoherent

In each mass bin the differential cross section as a function of four-body kinematic variables τ is takento be proportional to a model intensity I(τ) which is expressed in terms of partial-wave amplitudesψεLM (τ)

I(τ) =sumε

∣∣∣∣∣∣sumLM

AεLMψεLM (τ)

∣∣∣∣∣∣2

+ non-η(prime) background (1)

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

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m(ηπminus) [GeVc2]

08 12 16 2 24 280

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times103

(b) D-wave L = 2

Events

40M

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m(ηπminus) [GeVc2]

08 12 16 2 24 280

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100

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250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

3000

4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

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300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

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m(ηprimeπminus) [GeVc2]

12 16 2 24 280

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2000

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4000

(b) D-wave L = 2

Events

40M

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m(ηprimeπminus) [GeVc2]

12 16 2 24 280

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200

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700

(c) F -wave L = 3

Events

40M

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m(ηprimeπminus) [GeVc2]

12 16 2 24 280

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(d) G-wave L = 4

Events

40M

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12 16 2 24 280

100

200

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600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

The magnitudes and phases of the complex numbers AεLM constitute the free parameters of the fit Theexpected number of events in a bin is

N propintI(τ)a(τ)dτ (2)

where dτ is the four-body phase space element and a(τ) designates the efficiency of detector and selec-tion Following the extended likelihood approach [24 25] fits are carried out maximizing

lnL sim minusN +

nsumk=1

ln I(τk) (3)

where the sum runs over all observed events in the mass bin In this way the acceptance-corrected modelintensity is fit to the data

The partial-wave amplitudes are composed of two parts a factor fη (fηprime) that describes both the Dalitzplot distribution of the successive η (ηprime) decay [26] and the experimental peak shape and a two-bodypartial-wave factor that depends on the primary η(prime)πminus decay angles In this way the four-body analy-sis is reduced to quasi-two-body The partial-wave factor for the two spinless mesons is expressed byspherical harmonics Thus the full η(πminusπ+π0)πminus partial-wave amplitudes read

ψεLM (τ) =fη(pπminus pπ+ pπ0)times YML (ϑGJ 0)

times

sinMϕGJ for ε = +1

cosMϕGJ for ε = minus1

(4)

and analoguously for ηprime(πminusπ+η)πminus There are no M = 0 and therefore no L = 0 waves for ε = +1The fits require a weak L = M = 0 ε = minus1 amplitude which contributes 05 (11) to the total ηπminus

(ηprimeπminus) intensity This isotropic wave is attributed to incoherent background containing η(prime) whereas thenon-η(prime) background amplitude in Eq 1 is isotropic in four-body phase space

An independent two-body PWA was carried out not taking into account the decays of the η(prime) but usingtight window cuts (plusmn10 MeVc2) on the η(prime) peak in the respective three-body spectra The results werefound to be consistent with the present analysis [18]

The above-mentioned azimuthal sin2 ϕGJ dependence is in agreement with a strong M = 1 dominanceas was experienced earlier [6ndash9] No M gt 1 contributions are needed to fit the data in the present trange with the exception of the ηπminus D-wave where statistics allows the extraction of a small M = 2contribution The final fit model is restricted to the coherent L = 1 minus 6 M = 1 plus L = 2 M = 2partial waves from natural parity transfer (ε = +1) and the incoherent backgrounds introduced above

Incoherence of partial waves of the same naturality leading to additional terms in Eq (1) could arisefrom contributions with and without proton helicity flip or from different t-dependences of the ampli-tudes over the broad t range However for two pseudoscalars incoherence or partial incoherence ofany two partial waves with M = 1 can be accommodated by full coherence with appropriate choice ofphase [7] Comparing PWA results for t above and below 03 (GeVc)2 no significant variation of therelative M = 1 amplitudes with t is observed [18] The L = 2M = 2 contribution shows a differentt-dependence but does not introduce significant incoherence

In general a two-pseudoscalar PWA suffers from discrete ambiguities [24 27 28] The observed in-significance of unnatural-parity transfer crucially reduces the ambiguities In the case of ηπminus the re-maining ambiguities are resolved when the M = 2 D-wave amplitude is introduced For ηprimeπminus ambi-guities occur when the PWA is extended beyond the dominant L = 1 2 and 4 waves We resolve thisby requiring continuous behaviour of the dominant partial waves and of the Barrelet zeros [24] The

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

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40

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120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

350

400

(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

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4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

200

250

300

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(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

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2000

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4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

200

400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

acceptable solutions agree within the statistical uncertainties with the solution selected here which is theone with the smallest L = 3 contribution

The results of the PWA are presented as intensities of all included partial waves in Figs 3 4 and as rela-tive phases with respect to the L = 2 M = 1 wave in Fig 5 The plotted intensities are the acceptance-corrected numbers of events in each mass bin as derived from the |AεLM |2 of Eq 1 Feedthrough ofthe order of 3 from the dominant a2(1320) signal is observed in the L = 4 ηπminus distribution asshown in light colour in Fig 3 Relative intensities integrated over mass up to 3 GeVc2 taking intoaccount the respective η(prime) decay branchings are given in Table 1 The ratio of the summed intensitiesis I(ηπminus)I(ηprimeπminus) = 40 plusmn 03 This ratio is not affected by luminosity its error is estimated fromthe uncertainty of the acceptance The ηπminus yield is larger for all even-L waves Conversely the odd-Lyields are larger in the ηprimeπminus data

The ηπminus P -wave intensity shows a compact peak of 400 MeVc2 width centred at a mass of 14 GeVc2Beyond 18 GeVc2 it disappears The D-wave intensity is a factor of twenty larger than the P -waveintensity These observations resemble those at lower beam energy [7 9] A similar P -wave peak wasobserved in pn annihilation at rest where it appears with an intensity comparable to that of the D-wave [29] The present D-wave is characterised by a dominant a2(1320) peak and a broad shoulder thatextends to higher masses and possibly contains the a2(1700) An M = 2 D-wave intensity is foundat the 5 level The G-wave shows a peak consistent with the a4(2040) and a broad bump centred atabout 27 GeVc2 The F H and I-waves (L = 3 5 6) adopt each less than 1 of the intensity in thepresent mass range but are significant in the likelihood fit as can be judged from the uncertainties givenin Table 1

The ηprimeπminus P andD-wave have comparable intensities The former peaks at 165 GeVc2 drops to almostzero at 2 GeVc2 and displays a broad second maximum around 24 GeVc2 The D-wave shows a two-part structure similar to ηπminus but with relatively larger intensity of the shoulder The G-wave distributionshows an a4(2040) plus bump shape as observed for ηπminus In contrast to the G and I-waves the oddF and H-waves have an order of magnitude more relative intensity than in the ηπminus data The F -wavedistribution features a broad peak around 26 GeVc2

Phase motions in both systems can best be studied with respect to the D-wave which is present withsufficient intensity in the full mass range The rapid phase rotations caused by the a2(1320) and a4(2040)resonances are discernible The P versus D-wave phases in both systems are almost the same from theηprimeπminus threshold up to 14 GeVc2 where a branching takes place Given the similarity of the D-waveintensities after applying a kinematical factor (see below) it is suggestive to ascribe the different relativephase motions in the 14 GeVc2-20 GeVc2 range to the P -wave It is noted that the P -wave intensitiesdrop dramatically within this region almost vanishing at 18 GeVc2 in ηπminus and at 2 GeVc2 in ηprimeπminusIn contrast the G- versus D-phase motions are almost identical All phase differences tend to constantvalues at high masses which is a wave-mechanical condition for narrow angular focussing

Fits of resonance and background amplitudes to these PWA results (so-called mass-dependent fits) lead tostrongly model-dependent resonance parameters If these fits are restricted to masses below 19 GeVc2comparable to previous analyses a simple model incorporating only P and D-wave Breit-Wigner am-plitudes and a coherent D-wave background yields π1(1400) ηπminus resonance parameters and π1(1600)ηprimeπminus resonance parameters consistent with those of Refs [7ndash9] However the inclusion of higher massesdemands additional model amplitudes in particular additional D-wave resonances and coherent P -wavebackgrounds The presence of a coherent background in the P -wave is suggested by the PWA results inFigs 3 4 5 (a) The vanishing of the intensities around 20 GeVc2 is ascribed to destructive interferencewithin this partial wave and the relatively slow phase motion across the ηprimeπminus P -wave peak demands theadditional amplitude in order to dampen the π1(1600) phase rotation Fitted P -wave resonance masses inboth channels are found to be shifted upwards by typically 200 MeVc2 when introducing constant-phase

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

500

1000

1500

2000

2500

3000

(a) P -wave L = 1

Events

40M

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m(ηπminus) [GeVc2]

08 12 16 2 24 280

20

40

60

80

100

120

times103

(b) D-wave L = 2

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50

100

150

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250

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(c) F -wave L = 3

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

1000

2000

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4000

5000

6000

7000

(d) G-wave L = 4

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

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100

150

200

250

300

350

400

(e) H-wave L = 5

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

100

200

300

400

500

600

700

(f) I-wave L = 6

Events

40M

eVc2

m(ηπminus) [GeVc2]

08 12 16 2 24 280

50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

1000

2000

3000

4000

5000

(a) P -wave L = 1

Events

40M

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12 16 2 24 280

1000

2000

3000

4000

(b) D-wave L = 2

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

100

200

300

400

500

600

700

(c) F -wave L = 3

Events

40M

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12 16 2 24 280

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400

600

800

1000

(d) G-wave L = 4

Events

40M

eVc2

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12 16 2 24 280

100

200

300

400

500

600

(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

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0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

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50010001500200025003000350040004500

(g) D-wave L = 2M = 2

Fig 3 Intensities of the L = 1 minus 6 M = 1 and L = 2 M = 2 partial waves from the partial-waveanalysis of the ηπminus data in mass bins of 40 MeVc2 width The light-colored part of the L = 4 intensitybelow 15 GeVc2 is due to feedthrough from the L = 2 wave The error bars correspond to a change ofthe log-likelihood by half a unit and do not include MC fluctuations which are on the order of 5

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40M

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100

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(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

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(b) L = 2M = 2

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[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

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(b) D-wave L = 2

Events

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m(ηprimeπminus) [GeVc2]

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(c) F -wave L = 3

Events

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(d) G-wave L = 4

Events

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(e) H-wave L = 5

Events

40M

eVc2

m(ηprimeπminus) [GeVc2]

12 16 2 24 280

50

100

150

200

250

300

350

(f) I-wave L = 6

Fig 4 Intensities of the L = 1minus6 M = 1 partial waves from the partial-wave analysis of the ηprimeπminus datain mass bins of 40 MeVc2 width (circles) Shown for comparison (triangles) are the ηπminus results scaledby the relative kinematical factor given in Eq (7)

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

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(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

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Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

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Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

Φ1minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-50

0

50

100

150

200

250

(a) L = 1ΦM

=2minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28-100

-50

0

50

100

150

200

250

(b) L = 2M = 2

Φ3minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-200

-150

-100

-50

0

50

100

(c) L = 3

Φ4minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(d) L = 4

Φ5minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(e) L = 5

Φ6minus

Φ2

[deg]

m(η(prime)πminus) [GeVc2]

08 12 16 2 24 28

-250

-200

-150

-100

-50

0

50

(f) L = 6

Fig 5 Phases ΦL of the M = 1 partial waves with angular momentum L relative to the L = 2M = 1wave of ηπminus (triangles) and ηprimeπminus (circles) systems For ηπminus the phase between the P and D-waves isill-defined in the region of vanishing P -wave intensity between 18 and 205 GeVc2 (shaded) Panel (b)shows the relative M = 2 versus M = 1 phase of the ηπminus D-wave

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

model backgrounds as in Ref [23] In the present Letter we refrain from proposing resonance parame-ters for the exotic P -wave or even the exotic F and H-waves observed here The present observations atmasses beyond the a2(1320) and the π1 structures might stimulate extensions of resonance-productionmodels as eg multi-Regge models [13]

For the distinct a2(1320) and a4(2040) resonances mass-dependent fits using a standard relativisticBreit-Wigner parameterisation which for the a2 includes also the ρπ decay in the parameterisation ofthe total width [6] give the following results

m(a2) = 1315plusmn 12 MeVc2 Γ(a2) = 119plusmn 14 MeVc2

m(a4) = 1900+80minus20 MeVc2 Γ(a4) = 300+80

minus100 MeVc2

B2 equivN(a2 rarr ηprimeπminus)

N(a2 rarr ηπ)= (5plusmn 2)

B4 equivN(a4 rarr ηprimeπminus)

N(a4 rarr ηπ)= (23plusmn 7)

(5)

Here N stands for the integrated Breit-Wigner intensities of the given decay branches The errors givenabove are dominated by the systematic uncertainty which is estimated by comparing fits with and withoutcoherent backgrounds a2(1700) or π1(1400) The masses and B2 agree with the PDG values [26] Thedecay branching ratio B4 is extracted here for the first time

Table 1 Intensities (yields) integrated over the mass range up to 3 GeVc2 for the partial waves withM = 1 (and M = 2 for L = 2) relative to L = 2M = 1 in ηπminus (set to 100) These yields take intoaccount the decay branching ratios of η(prime) into πminusπ+γγ Errors are derived from the log-likelihood fitand do not include the common uncertainty (8) of the acceptance ratio of the two channels The lastcolumn lists ηπminus over ηprimeπminus yield ratios derived from the scaled intensities (see text Eq (8)) The first(second) value of RL corresponds to range parameter r = 0 fm (r = 04 fm)

L yield (ηπminus) yield (ηprimeπminus) RL

1 54plusmn 03 128plusmn 04 008minus 012

2 100 (fixed) 130plusmn 03 084minus 118

2 M = 2 54plusmn 02

3 039plusmn 007 114plusmn 013 014minus 019

4 100plusmn 03 257plusmn 018 080minus 097

5 012plusmn 004 028plusmn 010 013minus 015

6 087plusmn 008 036plusmn 005 066minus 074

For a detailed comparison of the results from the mass-independent PWA of both channels their differentphase spaces and angular-momentum barriers are taken into account For the decay of pointlike particlestransition rates are expected to be proportional to

g(mL) = q(m)times q(m)2L (6)

with break-up momentum q(m) [30ndash32] Overlaid on the PWA results for ηprimeπminus in Fig 4 are those forηπminus multiplied in each bin by the relative kinematical factor

c(mL) = btimes gprime(mL)

g(mL) (7)

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

where g(prime) refers to η(prime)πminus with break-up momentum q(prime) and the factor b = 0746 accounts for thedecay branchings of η and ηprime into πminusπ+γγ [26]

By integrating the invariant mass spectra of each partial wave scaled by [g(prime)(mL)]minus1 from the ηprimeπminus

threshold up to 3 GeVc2 we obtain scaled yields I(prime)L and derive the ratios

RL = btimes ILI primeL (8)

As an alternative to the angular-momentum barrier factors q(m)2L of Eq (6) we have also used Blatt-Weisskopf barrier factors [33] For the range parameter involved there an upper limit of r = 04 fmwas deduced from systematic studies of tensor meson decays including the present channels [30 31]whereas for r = 0 fm Eq (6) is recovered To demonstrate the sensitivity of RL on the barrier modelthe range of values corresponding to these upper and lower limits is given in Table 1

The comparison in Fig 4 reveals a conspicuous resemblance of the even-L partial waves of both channelsThis feature remains if r = 04 fm but the values of RL increase with increasing r (Table 1) Thissimilarity is corroborated by the relative phases as observed in Figs 5 (d) and (f) The observed behaviouris expected from a quark-line picture where only the non-strange components nn (n = u d) of theincoming πminus and the outgoing system are involved The similar values of RL for L = 2 4 6 suggestthat the respective intermediate states couple to the same flavour content of the outgoing system

The quark-line estimate (see Eq (3) in [31]) for the a2(1320) decay branching using r = 04 fm and theisoscalar mixing angle in the quark flavour basis φ = 393 [32] is B2 = 39 for our mass value Thisis in reasonable agreement with the present measurement An analogous calculation for the a4(2040)yields B4 = 118 which is below the experimental value A larger range parameter r would improvethe agreement

On the other hand the odd-L ηprimeπminus intensities are enhanced by a factor 5minus 10 as compared to ηπminus seeFig 4 Table 1 The P -wave fits well into the trend observed for the F and H-waves which also carryexotic quantum numbers It is suggestive to ascribe these observations to the dominant 8otimes 8 and 1otimes 8character of the ηπminus and ηprimeπminus SU(3)flavour configurations respectively When the former couples toan octet intermediate state Bose symmetry demands even L whereas the latter may couple to the non-symmetric odd-L configurations The importance of this relation was already pointed out in previousdiscussions of the exotic π1 where in particular the hybrid (gqq) or the lowest molecular state (qqqq)have 1otimes 8 character [3ndash5]

A P -wave peak consistent with quoted resonance parameters [26] appears in each channel In the ηprimeπminus

channel its relatively large contribution is directly visible in Fig 2(b) The forwardbackward asymme-try ascribed to L = 1 3 5 amplitudes interfering with the even-L ones extends to higher masses wherea transition to rapidity-gap phenomena (central production) is expected In the ηπminus data the asymmetryis much less pronounced

In conclusion two striking features characterise the systematic behaviour of partial waves presentedhere

(i) The even partial waves with L = 2 4 6 show a close similarity between the two channels both inthe intensities as function of mass ndash after scaling by the phase-space and barrier factors ndash as wellas in their phase behaviour

(ii) The odd partial waves with L = 1 3 5 carrying non-qq quantum numbers are suppressed in ηπminus

with respect to ηprimeπminus underlining the importance of flavour symmetry

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

Acknowledgements

We gratefully acknowledge the support of the CERN management and staff as well as the skills andefforts of the technicians of the collaborating institutions This work was made possible by the financialsupport of our funding agencies

References

References

[1] E Klempt A Zaitsev Glueballs Hybrids Multiquarks Experimental facts versus QCD inspiredconcepts Phys Rept 454 (2007) 1ndash202 arXivhep-ph07084016 doi101016jphysrep200707006

[2] N Brambilla et al QCD and strongly coupled gauge theories challenges and perspectives to besubmitted to EPJCarXiv14043723

[3] F Close H Lipkin New Experimental Evidence for Four Quark Exotics the Serpukhov φπ Res-onance and the GAMS ηπ Enhancement Phys Lett B196 (1987) 245ndash250 doi1010160370-2693(87)90613-7

[4] F Iddir et al qqg hybrid and qqqq diquonium interpretation of the GAMS 1minus+ resonancePhysLett B205 (1988) 564ndash568 doi1010160370-2693(88)90999-9

[5] S U Chung E Klempt J G Koumlrner SU(3) classification of p-wave ηπ and ηprimeπ systemsEur Phys J A15 (2002) 539ndash542 arXivhep-ph0211100 doi101140epjai2002-10058-0

[6] G Beladidze et al Study of πminusN rarr ηπminusN and πminusN rarr ηprimeπminusN reactions at 37 GeVc PhysLett B313 (1993) 276ndash282 doi1010160370-2693(93)91224-B

[7] S Chung et al Evidence for exotic JPC = 1minus+ meson production in the reaction πminusp rarr ηπminuspat 18 GeVc Phys Rev D60 (1999) 092001 arXivhep-ex9902003 doi101103PhysRevD60092001

[8] E I Ivanov et al Observation of exotic meson production in the reaction πminusp rarr ηprimeπminuspat 18 GeVc Phys Rev Lett 86 (2001) 3977ndash3980 arXivhep-ex0101058 doi101103PhysRevLett863977

[9] V Dorofeev et al The JPC = 1minus+ hunting season at VES AIP Conf Proc 619 (2002) 143ndash154arXivhep-ex0110075 doi10106311482444

[10] A Donnachie P Page Interpretation of experimental JPC exotic signals Phys Rev D58 (1998)114012 arXivhep-ph9808225 doi101103PhysRevD58114012

[11] A Szczepaniak M Swat A Dzierba S Teige ηπ and ηprimeπ Spectra and Interpretation of PossibleExotic JPC = 1minus+ Mesons Phys Rev Lett 91 (2003) 092002 arXivhep-ph0304095doi101103PhysRevLett91092002

[12] S Donnachie H G Dosch O Nachtmann P Landshoff Pomeron Physics and QCD CambMonogr Part Phys Nucl Phys Cosmol Cambridge University Press 2002

[13] T Shimada A Martin A Irving Double regge exchange phenomenology Nucl Phys B142(1978) 344 doi1010160550-3213(78)90209-2

[14] P Abbon et al The COMPASS Experiment at CERN Nucl Inst Meth A577 (2007) 455ndash518arXivhep-ex0703049 doi101016jnima200703026

[15] M Alekseev et al The COMPASS 2008 Spectrometer to be submitted to Nucl Instr and MethA (2014)

[16] T Schluumlter et al Large-Area Sandwich Veto Detector with WLS Fibre Readout for HadronSpectroscopy at COMPASS Nucl Inst and Meth A654 (2011) 219 arXiv11084587doi101016jnima201105069

[17] T Schluumlter The exotic ηprimeπminus Wave in 190 GeV πminusprarr πminusηprimep at COMPASS in B Grube S PaulN Brambilla (Eds) Proceedings of the XIV International Conference on Hadron SpectroscopyeConf C110613 2011 arXiv11086191URL httpwwwslacstanfordedueconfC110613

[18] T Schluumlter The πminusη and πminusηprime systems in exclusive 190 GeV πminusp reactions at COMPASS(CERN) PhD thesis Ludwig-Maximilians-Universitaumlt Muumlnchen (2012)URL httpwwwcompasscernchcompasspublicationstheses20125Fphd5Fschlueterpdf

[19] CERN GEANT ndash Detector Description and Simulation Tool (October 1994)

[20] T Schluumlter Odd and Even Partial Waves of ηπminus and ηprimeπminus in 191 GeV πminusp PoS(Hadron 2013)085 arXiv14014067

[21] G Ascoli et al Partial Wave Analysis of the 3π Decay of the A2 Phys Rev Lett 25 (1970) 962doi101103PhysRevLett25962

[22] I Karchaev D Ryabchikov private communication

[23] M Alekseev et al Observation of a JPC = 1minus+ exotic resonance in diffractive dissociationof 190 GeVc πminus into πminusπminusπ+ Phys Rev Lett 104 (2010) 241803 arXiv09105842doi101103PhysRevLett104241803

[24] S U Chung Techniques of amplitude analysis for two pseudoscalar systems Phys Rev D56(1997) 7299ndash7316 doi101103PhysRevD567299

[25] R Barlow Extended maximum likelihood Nucl Inst Meth A297 (3) (1990) 496 ndash 506 doi1010160168-9002(90)91334-8

[26] J Beringer et al Review of Particle Physics PhysRev D86 (2012) 010001 doi101103PhysRevD86010001

[27] A Martin et al A Study of Isospin 1 Meson States Using 10 GeVc KminusK0 Production DataPhys Lett B74 (1978) 417 doi1010160370-2693(78)90693-7

[28] S Sadovsky On the ambiguities in the partial wave analysis of πminusp rarr ηπ0n reaction Tech repIHEP 91-75 IHEP Protvino (1991)

[29] A Abele et al Exotic ηπ state in pd annihilation at rest into πminusπ0ηpspectator Phys Lett B423(1998) 175ndash184 doi101016S0370-2693(98)00123-3

[30] K Peters E Klempt The suppression of ss pair creation from tensor meson decays PhysLettB352 (1995) 467ndash471 doi1010160370-2693(95)00457-V

[31] A Abele et al Study of the π0π0ηprimefinal state in pp annihilation at rest Phys Lett B404 (1997)179ndash186 doi101016S0370-2693(97)00526-1

[32] A Bramon R Escribano M Scadron The η minus ηprime mixing angle revisited Eur Phys J C7 (1999)271ndash278 arXivhep-ph9711229 doi101007s100529801009

[33] F von Hippel C Quigg Centrifugal-barrier effects in resonance partial decay widths shapes andproduction amplitudes Phys Rev D5 (1972) 624ndash638 doi101103PhysRevD5624