Differential cross section measurements for n p above the...

PHYSICAL REVIEW C 96 035204 (2017)

Differential cross section measurements for γ n rarr πminus p above the first nucleon resonance region

P T Mattione1 D S Carman1 I I Strakovsky20 R L Workman20 A E Kudryavtsev30 A Svarc29 V E Tarasov30

K P Adhikari33 S Adhikari16 D Adikaram137 Z Akbar17 S Anefalos Pereira24 J Ball8 N A Baltzell141

M Bashkanov13 M Battaglieri25 V Batourine132 I Bedlinskiy30 A S Biselli15 S Boiarinov1 W J Briscoe20

V D Burkert1 T Cao2141 A Celentano25 G Charles37 T Chetry36 G Ciullo1423 L Clark19 P L Cole22 M Contalbrigo23

O Cortes22 V Crede17 A DrsquoAngelo2639 N Dashyan47 R De Vita25 E De Sanctis24 M Defurne8 A Deur1 C Djalali41

M Dugger3 R Dupre28 H Egiyan1 A El Alaoui43 L El Fassi33 P Eugenio17 G Fedotov4041 R Fersch9 A Filippi27

J A Fleming13 A Fradi1128 Y Ghandilyan47 G P Gilfoyle38 K L Giovanetti31 F X Girod1 C Gleason41 E Golovatch40

R W Gothe41 K A Griffioen46 M Guidal28 K Hafidi2 H Hakobyan4347 C Hanretty1 N Harrison1 M Hattawy2

D Heddle91 K Hicks36 G Hollis41 M Holtrop34 S M Hughes13 Y Ilieva2041 D G Ireland19 B S Ishkhanov40

E L Isupov40 D Jenkins44 H Jiang41 H S Jo28 K Joo10 S Joosten42 D Keller45 G Khachatryan47 M Khachatryan37

M Khandaker2235 A Kim10 W Kim32 A Klein37 F J Klein7 V Kubarovsky1 S V Kuleshov3043 L Lanza26 P Lenisa23

K Livingston19 I J D MacGregor19 N Markov10 B McKinnon19 C A Meyer6 Z E Meziani42 T Mineeva43

V Mokeev140 R A Montgomery19 A Movsisyan23 C Munoz Camacho28 G Murdoch19 P Nadel-Turonski120 L A Net41

S Niccolai28 G Niculescu31 I Niculescu31 M Osipenko25 A I Ostrovidov17 M Paolone42 R Paremuzyan34 K Park1

E Pasyuk1 W Phelps16 S Pisano24 O Pogorelko30 J W Price4 S Procureur8 Y Prok3745 D Protopopescu19

B A Raue116 M Ripani18 B G Ritchie3 A Rizzo2639 G Rosner19 F Sabatieacute8 C Salgado35 R A Schumacher6

Y G Sharabian1 A Simonyan47 Iu Skorodumina4041 G D Smith13 D Sokhan19 N Sparveris42 I Stankovic13

S Stepanyan1 S Strauch41 M Taiuti1825 M Ungaro110 H Voskanyan47 E Voutier28 N K Walford7 D Watts13 X Wei1

M H Wood541 N Zachariou13 J Zhang1 and Z W Zhao1237

(CLAS Collaboration)1Thomas Jefferson National Accelerator Facility Newport News Virginia 23606 USA

2Argonne National Laboratory Argonne Illinois 60439 USA3Arizona State University Tempe Arizona 85287 USA

4California State University Dominguez Hills Carson California 90747 USA5Canisius College Buffalo New York 14208 USA

6Carnegie Mellon University Pittsburgh Pennsylvania 15213 USA7The Catholic University of America Washington DC 20064 USA

8CEA Centre de Saclay IrfuService de Physique Nucleacuteaire 91191 Gif-sur-Yvette France9Christopher Newport University Newport News Virginia 23606 USA

10University of Connecticut Storrs Connecticut 06269 USA11University of Dammam Industrial Jubail 31961 Saudi Arabia12Duke University Durham North Carolina 27708-0305 USA13Edinburgh University Edinburgh EH9 3JZ United Kingdom

14Universitarsquo di Ferrara 44121 Ferrara Italy15Fairfield University Fairfield Connecticut 06824 USA

16Florida International University Miami Florida 33199 USA17Florida State University Tallahassee Florida 32306 USA

18Universitagrave di Genova 16146 Genova Italy19University of Glasgow Glasgow G12 8QQ United Kingdom

20The George Washington University Washington DC 20052 USA21Hampton University Hampton Virginia 23668 USA22Idaho State University Pocatello Idaho 83209 USA

23INFN Sezione di Ferrara 44100 Ferrara Italy24INFN Laboratori Nazionali di Frascati 00044 Frascati Italy

25INFN Sezione di Genova 16146 Genova Italy26INFN Sezione di Roma Tor Vergata 00133 Rome Italy

27INFN Sezione di Torino 10125 Torino Italy28Institut de Physique Nucleacuteaire ORSAY Orsay France

29Rudjer Boškovic Institute Bijenicka Cesta 10002 Zagreb Croatia30National Research Center Kurchatov Institute Institute of Theoretical and Experimental Physics Moscow 117218 Russia

31James Madison University Harrisonburg Virginia 22807 USA32Kyungpook National University Daegu 702-701 Republic of Korea

33Mississippi State University Mississippi State Mississippi 39762-5167 USA34University of New Hampshire Durham New Hampshire 03824 USA

35Norfolk State University Norfolk Virginia 23504 USA36Ohio University Athens Ohio 45701 USA

2469-9985201796(3)035204(20) 035204-1 copy2017 American Physical Society

P T MATTIONE et al PHYSICAL REVIEW C 96 035204 (2017)

37Old Dominion University Norfolk Virginia 23529 USA38University of Richmond Richmond Virginia 23173 USA

39Universitarsquo di Roma Tor Vergata 00133 Rome Italy40Skobeltsyn Nuclear Physics Institute 119899 Moscow Russia

41University of South Carolina Columbia South Carolina 29208 USA42Temple University Philadelphia Pennsylvania 19122 USA

43Universidad Teacutecnica Federico Santa Mariacutea Casilla 110-V Valparaiacuteso Chile44Virginia Tech Blacksburg Virginia 24061-0435 USA

45University of Virginia Charlottesville Virginia 22901 USA46College of William and Mary Williamsburg Virginia 23187 USA

47Yerevan Physics Institute 375036 Yerevan Armenia(Received 8 June 2017 revised manuscript received 3 August 2017 published 18 September 2017)

The quasifree γ d rarr πminusp(p) differential cross section has been measured with CLAS at photon beam energiesEγ from 0445 to 2510 GeV (corresponding to W from 1311 to 2366 GeV) for pion center-of-mass anglescos θcm

π from minus072 to 092 A correction for final state interactions has been applied to these data to extract theγ n rarr πminusp differential cross sections These cross sections are quoted in 8428 (Eγ cos θcm

π ) bins a factor ofnearly 3 increase in the world statistics for this channel in this kinematic range These new data help to constraincoupled-channel analysis fits used to disentangle the spectrum of Nlowast resonances and extract their propertiesSelected photon decay amplitudes Nlowast rarr γ n at the resonance poles are determined for the first time and arereported here

DOI 101103PhysRevC96035204

I INTRODUCTION

The determination of the resonance properties for allaccessible baryon states is a central objective in nuclearphysics The extracted resonance parameters provide a crucialbody of information for understanding the nucleon excitationspectrum and for testing models of the nucleon inspired byquantum chromodynamics (QCD) and more recently latticeQCD calculations The spectrum of Nlowast and lowast baryon reso-nances has been extensively studied through meson-nucleonscattering and meson photoproduction experiments Propertiesof the known resonances continue to become better determinedas experiments involving polarized beams targets and recoilmeasurements are expanded and refined [1] Extracted quan-tities include resonance masses widths branching fractionspole positions and associated residues as well as photodecayamplitudes [2] New states have also been found mainlythrough multichannel analyses that are sensitive to states hav-ing a relatively weak coupling to the πN decay channel [3ndash5]

Knowledge of the Nlowast and lowast resonance photodecayamplitudes has largely been restricted to the charged statesApart from lower-energy inverse reaction πminusp rarr γ n mea-surements the extraction of the two-body γ n rarr πminusp andγ n rarr π0n observables requires the use of a model-dependentnuclear correction which mainly comes from final stateinteraction (FSI) effects within the target deuteron Most γ ndata are unpolarized and cover fairly narrow energy rangesOf these only about 400 π0n measurement data points existspanning the full nucleon resonance region [6]

The importance of improving the γ n database relativeto the γp database is directly related to the fact that theelectromagnetic interaction does not conserve isospin sym-metry The amplitude for the reactions γN rarr πX factors intodistinct I = 12 and I = 32 isospin components Aγπplusmn =radic

2(AI=12pn ∓ AI=32) This expression indicates that the ex-

citation of the I = 32 lowast states can be entirely determinedfrom proton target data However measurements from datasetswith both neutron and proton targets are required to determinethe isospin I = 12 amplitudes and to separate the γpNlowast andγ nNlowast photocouplings

This work focuses on negative pion photoproduction off theneutron using a deuteron target A large body of new precisionγ n rarr πminusp differential cross sections for Eγ = 0445 to2510 GeV in laboratory photon energy corresponding toan invariant energy range from W = 1311 to 2366 GeVare reported Pion center-of-mass (cm) production anglesranging from θcm

π = 26 to 135 have been measured duringthe CLAS Collaboration g13 run period [7] These new crosssection data have nearly tripled the world γ n rarr πminusp databasebelow Eγ = 2700 GeV [6]

The γ n rarr πminusp differential cross section was previouslymeasured by the CLAS g10 [8] experiment Those measure-ments contained 855 data points in 50- and 100-MeV-wide binsof beam energy Eγ from 1050 to 3500 GeV corresponding toa W range from 1690 to 2731 GeV However the 8428 datapoints from g13 are a precision measurement of this cross sec-tion with a factor of sim10 increase in data points These data arereported in 10- and 20-MeV-wide bins of beam energy Eγ withoverall normalization uncertainties of sim34 compared to thesim6 to sim10 overall normalization uncertainties achieved byg10 Also unlike the g10 measurements the g13 data cover theW range of the low-mass Nlowast resonances and can be used toinvestigate their helicity amplitudes and resonance parameters

The present dataset together with completed polarizedmeasurements for both πminusp and π0n from Jefferson Lab [9]and MAMI [10] are expected to lead to the determinationof well-constrained γ n decay amplitudes in the near futureHowever these new CLAS γ n rarr πminusp data allow for the firstdetermination of selected photon decay amplitudes Nlowast rarr γ nat their pole on the complex plane

035204-2

DIFFERENTIAL CROSS SECTION MEASUREMENTS FOR PHYSICAL REVIEW C 96 035204 (2017)

The organization for this paper is as follows In Sec IIdetails of the g13 experiment and the CLAS detector areprovided Section III outlines the event selection and Sec IVprovides the tracking and triggering efficiency correctionsSection V describes the extraction of the event yields andthe acceptance corrections and Sec VI describes how thebeam-target luminosity was determined Section VII presentsand discusses the measured differential cross sections for thereaction γ n rarr πminusp while Sec VIII reviews the approachfor determining the final state interaction corrections SectionsIX and X describe the Legendre fits and multipole fit resultsrespectively Finally Sec XI provides a summary of this workand the conclusions

II EXPERIMENT

The CLAS g13 experiment [7] ran from October 2006to June 2007 in Hall B at the Continuous Electron BeamAccelerator Facility (CEBAF) at Jefferson Lab in NewportNews Virginia Circularly and linearly polarized taggedbremsstrahlung photon beams were incident on a liquid-deuterium (LD2) target located near the center of the CLASdetector [11] The circularly polarized photon beam portion ofthis experiment called g13a was used for this analysis

For g13a the CEBAF electron beam was supplied at twodifferent energies 1990 and 2655 GeV These electrons weredelivered at currents between 33 and 45 nA in beam bunchesseparated by about 2 ns The electron beam was incident ona 10minus4 radiation-length-thick gold foil radiator to produce thebremsstrahlung photon beam

The dipole magnet of the Hall B photon tagger deflectedthe electron beam and postbremsstrahlung electrons in orderto tag photons produced with energies between sim20 andsim95 of the incident electron beam energy [12] The taggingsystem provided a photon beam energy resolution of sim01of the electron beam energy with a 150-ps timing resolution A64-mm-diameter nickel collimator downstream of the radiatorprovided sim90 beam transmission to the 40-cm-long LD2

target which was centered 20 cm upstream from the center ofthe CLAS detector This resulted in a tagged photon flux onthe order of 107 Hz on the target

The CLAS detector shown in Fig 1 was designed aroundsix superconducting coils arranged in a hexagonal config-uration that produced an approximately toroidal magneticfield surrounding the beamline The magnetic field bentcharged particles through the three regions of multilayer driftchambers for momentum measurements The drift chamberswere positioned between the superconducting coils within sixsectors in azimuthal φ each spanning roughly 60 Chargedparticles produced at a momentum of 1 GeVc were measuredwith a momentum resolution of σ (p)p 05 and withaverage angular resolutions in the fiducial volume of σ (θ )σ (φ) sim 2 mrad [13] For the g13 experiment the torus magnetoperated at sim40 of its maximum current with reversed fieldpolarity (such that negatively charged particles were bent awayfrom the beamline) producing an integrated magnetic field of0972 T m along the track path length at forward angles and0233 T m at 90

FIG 1 Cutaway view of the CLAS detector [11] illustrating thetorus magnet three regions of drift chambers (R1ndashR3) Cherenkovcounters (CC) time-of-flight scintillators (TOF) and electromagneticcalorimeters (EC) The CLAS detector is roughly 10 m in diameter

The start counter (ST) surrounding the target had a timingresolution of 260 ps and was used to determine whichof the 2-ns electron beam bunches was associated withthe recorded physics event [14] The time-of-flight (TOF)scintillator paddles had a timing resolution between 150 and250 ps depending on the length of the paddle and were usedfor particle identification [15] At forward angles Cherenkovcounters (not used for this experiment) could be used toidentify electrons [16] and the electromagnetic calorimeterscould be used to detect electrons and neutral particles [17]

A coincidence between the start counter and TOF scintilla-tors in at least two of the six CLAS sectors was required fortriggering of the data acquisition With slightly more than twomonths of running 20 billion physics events were recorded inthe g13a dataset

III EVENT SELECTION

The γ d rarr πminusp(p) differential cross section was measuredseparately for the 1990- and 2655-GeV beam data and thesecross section results were combined as discussed in Sec VIIThe yields of the γ d rarr πminusp(p) reaction were determinedby reconstructing the πminus and scattered (higher momentum)proton with the lower momentum proton missing The protonin the deuteron typically has a momentum from Fermi motionof less than 200 MeVc [18] (and peaks at sim50 MeVc) andwas often stopped before it could escape the LD2 target

The reconstructed beam energy and track momenta wereslightly distorted by effects not taken into account during theevent reconstruction These effects included uncertainties inthe incident electron beam energy unaccounted for energylosses as the tracks traversed the detector and drift chambermisalignments and inaccuracies in the magnetic field map that

035204-3


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610

Proton Candidates(a)

p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610

Candidatesminusπ(b)

FIG 2 β vs momentum for proton (a) and πminus (b) candidatesβ is centered at zero for the protons and πminusrsquos and the neighboringbands are from other particle types such as π+rsquos or from choosingthe wrong beam bunch

affected the reconstructed track momenta Each of these effectswas studied and resulted in beam energy and track momentumcorrections on the order of a few percent [19]

A Particle identification

Initially all reconstructed positively and negatively chargedtracks were treated as candidates for the proton and πminusrespectively Then for each combination of proton and πminuscandidates their start counter hits were used to select thebeam bunch corresponding to the event The arrival time ofthe beam bunches was known to a resolution of 50 ps and wasused as a reference time for the particle identification Figure 2shows the β vs momentum distributions of the proton andπminus candidates where β is the difference between β = pEusing the candidate mass and β determined from the trackpath length (from the event vertex to the TOF system) and thetrack hit time from the TOF paddle β is centered at zerofor the protons and πminusrsquos and the neighboring bands are from

Vertex-Z (cm)60minus 50minus 40minus 30minus 20minus 10minus 0 10 20

Cou

nts

0

2

4

6

8

10

12

14

16

18

610times Reconstructed Tracks

FIG 3 The vertex z of the reconstructed tracks in γ d rarrπminusp(p) Tracks with z gt 5 cm were cut removing backgroundsfrom the aluminum end cap of the target assembly at z = 7 cm

other particle types such as π+rsquos or from choosing the wrongbeam bunch

For proton identification a momentum-dependent plusmn5σ cutwas applied on β No particle identification cut was usedto identify πminusrsquos since the background from electron muonand kaon events was negligible as seen in Fig 2(b) Poorlyperforming or miscalibrated TOF counters were excluded fromthe analysis

B Vertex cuts and missing momentum

The vertex-z distribution of the reconstructed tracksdefined as their distance-of-closest-approach to the nominalbeamline (defined as the z axis) is shown in Fig 3 A cutwas applied requiring that the reconstructed vertex z of boththe proton and the πminus be less than 5 cm The target extendedfrom minus40 to 0 cm in vertex z so this cut was used to removebackgrounds from beam photons striking the aluminum endcap of the target assembly

To illustrate the missing momentum distribution of γ d rarrπminusp(p) events a plusmn3σ cut was applied around the missingmass peak of the proton Figure 4(a) shows the missingmomentum distribution after this cut The missing momentumis primarily peaked at low momenta due to Fermi motionand the high-momentum tail is primarily from rescatteringevents Figure 4(b) shows that the slow-proton momentum isuniformly distributed in cos θ where θ is the angle betweenthe missing momentum and the beam in the laboratory frameA cut was applied at 200 MeVc to reject the majority of therescattering events Since there are still rescattering effectspresent after this cut the γ d rarr πminusp(p) cross section isquoted as ldquoquasifreerdquo

IV CLAS EFFICIENCY STUDIES

A Tracking efficiency

To determine the charged particle tracking efficiency theCLAS drift chamber wire hit efficiencies were studied by

035204-4


Missing Momentum (GeVc)0 02 04 06 08 1

Cou

nts

0

5

10

15

20

25610times (p)minusπprarrdγ

(a)

)θMissing Momentum cos(1minus 05minus 0 05 1

Mis

sing

Mom

entu

m (

GeV

c)

0

01

02

03

04

05

06

07

08

09

1

0

50

100

150

200

250

300

310times(p)minusπprarrdγ

(b)

FIG 4 (a) The γ d rarr πminusp(p) missing momentum and (b)the same missing momentum vs cos θ of the missing momentumin the laboratory frame The low-momentum quasifree protonsfollowed the Fermi motion distribution and were relatively uniformlydistributed in cos θ The high-momentum tail of rescattered protonswas removed by the 200-MeVc cut on the missing momentum[indicated by the red vertical line in (a)]

determining how often a given sense wire recorded a hit when areconstructed track passed nearby To make sure that the studywas unbiased the efficiencies were only evaluated when therewere significantly more hits on the track than the minimumneeded for reconstruction

These studies allowed issues associated with missing wiresdue to bad high-voltage connections and amplifier low-voltageshorts to be taken into account Furthermore these studieswere able to determine tracking inefficiencies due to readoutelectronics problems cable disconnects and cable swapsGroups of wires that were correlated with a common problemwere grouped together in the simulation so that they wereeither kept or rejected as a whole The efficiency calculatedand applied for the regions with cable swaps or disconnects

does not properly model the experimental data so these regionswere eliminated from the analysis In this manner a very goodmatch of the tracking efficiency in the simulation code to theCLAS hardware was possible A comparison of the trackingefficiencies for each CLAS drift chamber sector is available inRef [19]

The track reconstruction efficiencies for protons and πminusrsquoswere studied by analyzing the γ d rarr πminusp(p) and γ d rarrpp(πminus) topologies respectively and determining how oftenthe missing particle was reconstructed when it was in thefiducial region of the detector These studies were performedwith both experimental and phase-space Monte Carlo (MC)simulated data as a function of track momentum and directionFor the g13 experiment these reconstruction efficiencies were95 or higher in the nominal fiducial regions of the detectorFigure 5 shows the ratio of these reconstruction efficiencies εfor the proton which was computed as

εRatio = εSimulation minus εExperiment

εExperiment (1)

Thus regions with an efficiency ratio significantly greater(less) than zero are regions where the reconstruction efficiencywas much lower (higher) in the experiment than in the MCsimulation The discrepancies seen in the figure at the edges ofthe acceptance are due to a mismatch between the simulatedand experimental geometry These regions were cut from theanalysis so that only regions that were accurately modeled inthe simulation were included in the cross section measurementThe efficiency ratio distributions for the πminusrsquos which were bentdifferently in the CLAS magnetic field are similar but requiredseparate cuts The absolute minimum accepted proton and πminusmomenta were 360 and 100 MeVc respectively

B Triggering efficiency

As discussed in Sec II the g13a trigger was designed torecord events with a ST and TOF coincidence in at least twosectors of CLAS To determine the triggering efficiency theγ d rarr πminuspp topology was studied with the requirement thatthe three final state particles be in different sectors For everypair of particles that registered as contributing to the triggerthe triggering rate of the third particle was studied

Figure 6 shows the proton and πminus triggering efficienciesin a representative sector as a function of the track angleand momentum Because these efficiencies were studied asa function of all kinematics they include both TOF andST efficiency effects The proton triggering was efficient ingeneral but was low in a few of the TOF paddles due to oneor both of the photomultiplier tubes (PMTs) at the end of thescintillators having low gain

However the πminus efficiencies were significantly worse thanthose of the proton This was because πminusrsquos deposited much lessenergy than protons of the same momentum in the scintillatorsdue to their higher velocity A number of inefficient channelswere present due to low gain TOF PMTs (even though theywere set at their maximum voltage) These PMTs were stillefficient for hit readout as the 100-mV triggering thresholdwas much higher than the 20-mV detection threshold The ef-ficiencies for the other sectors are available in Ref [19] These

035204-5


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3

05minus04minus03minus02minus01minus

0

01

02

03

04

05Proton Efficiency Ratio(b)

(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04

06Proton Efficiency Ratio(a)

FIG 5 The proton reconstruction efficiency ratio defined byEq (1) as a function of laboratory polar angle In (a) sector φ isthe azimuthal angle relative to the center of the CLAS sector Bothplots are summed over all CLAS sectors The magenta lines indicatethe cuts used to reject data that were not accurately modeled by thesimulation

triggering efficiencies were applied to the MC simulation tomodel these event losses

V YIELDS AND ACCEPTANCE

The γ d rarr πminusp(p) data were separated into 10- and20-MeV-wide Eγ bins and 002- to 004-wide bins in cos θcm

π where θcm

π is the angle between the πminus and the beam in theπminusp cm frame These data spanned the range from 0440 to

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1

Proton Triggering Efficiency Sector 2

(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1

Triggering Efficiency Sector 2minusπ

(b)

FIG 6 The proton (a) and πminus (b) triggering efficiencies in CLASsector 2 in terms of momentum p vs laboratory polar angle θ Theproton triggering was efficient in general but the πminus efficiency wasaffected over portions of the acceptance due to low-gain TOF PMTs

2520 GeV in beam energy and minus072 to 092 in cos θcmπ for a

total of 8428 bins In each bin the missing-proton peaks werefit to double-Gaussian functions over a linear backgroundan example of which is shown in Fig 7 A double-Gaussianfunction is defined as the sum of two Gaussians with identicalmeans but different heights and widths The larger primaryGaussian was used to model the Gaussian-scattering portionof the signal distribution and the smaller secondary Gaussianwas used to fit the tails of the signal distribution

The backgrounds are primarily due to misidentified protonsand πminusrsquos or selection of the wrong beam photon Theγ d rarr πminusp(p) yield was defined as the number of eventsabove the background within the plusmn45σ fit range about themissing-proton peak There were over 400 million γ d rarrπminusp(p) events in the g13a experimental data sample usedfor this analysis

035204-6


)2 Missing Mass (GeVcminusπprarrdγ08 085 09 095 1 105 11 115 12

Cou

nts

0

50

100

150

200

250

300

350

400

450

) lt 003θ cos(le (GeV) lt 126 0 γ Ele125

FIG 7 Sample fit of the missing-proton peak in the missing massoff of γ d rarr πminusp The signals were fit to a double-Gaussian functionover a linear background The blue line shape represents the double-Gaussian fit function the magenta line shape represents the linear fitfunction and the black line shape represents the total fit function

A total of 18 billion MC γ d rarr πminuspp events were simu-lated for each electron beam energy to calculate the acceptancecorrections These data were evaluated separately in orderto individually compute the cross sections for the differentrun ranges The George Washington University (GWU) SAIDGB12 cross section predictions [8] based on the world dataof the γ n rarr πminusp reaction were used to generate the eventdistributions After a preliminary quasifree γ d rarr πminusp(p)cross section measurement was obtained from the g13 datathis measurement was used to generate the final simulateddata A comparison of the reconstructed γ d rarr πminusp(p) yieldbetween the experimental data and the MC is shown inFig 8 This shows that the inefficient regions of the detectorare well modeled by the simulation Thus any variationsof the detector acceptance across the widths of the narrowyield-extraction bins did not cause an incorrect modeling ofthe CLAS acceptance

The same analysis procedure and cuts used to select theγ d rarr πminusp(p) final state in the experimental data were usedfor the simulated data However a sim5 yield correction factorYCF was applied to the experimental yields to correct for eventlosses from choosing the incorrect beam bunch which wasnot modeled in the simulation This correction factor wasdetermined by studying the γ d rarr πminusp(p) yield from all otherbeam bunches recorded in the event The uncertainties on thiscorrection factor were sim0003 from statistics and sim088from systematics determined by studying the variation in thecorrection factor with beam energy

Since the CLAS acceptance rapidly falls off near the edgesof the detector cross section measurements in these regionshad systematic uncertainties that were difficult to quantifyIn addition small mismatches between the generated MCdistribution and the experimental data could cause large uncer-tainties in regions of low acceptance To remove these regionsbins with an acceptance less than 20 of the maximum

)cmπθcos(

1minus 05minus 0 05 1

Yie

ld

020406080

100120140160180200

310times = 0655 GeVγE

)cmπθcos(


Yie

ld

05

10152025303540


FIG 8 A comparison of the reconstructed γ d rarr πminusp(p) yieldsbetween the experimental data (black) and the simulation (red) as afunction of the pion cm angle cos θcm

π in two selected beam energybins for the 2655-GeV data The simulated yields have been scaledsuch that their integral matches that of the experimental data

acceptance within each Eγ bin were rejected from the analysisThe CLAS acceptance of the γ d rarr πminusp(p) reaction for theCLAS g13 experiment after this cut is shown in Fig 9 forselected beam energy bins Overall the acceptance variedbetween 5 and 50 and the large dips were primarily dueto triggering inefficiencies and drift chamber problem areas

The systematic uncertainty due to event selection was typi-cally less than 2 although it increased to 10 near the edgesof the detector The uncertainty due to the yield extractionwas less than 5 These uncertainties were determined byvarying the widths of the cuts used and the range and startingparameters of the missing mass fits

The systematic uncertainties due to the acceptance cor-rections were typically less than 5 but increased to 10in problematic regions with low triggering or drift chamberacceptance These uncertainties were determined by studyinghow the acceptance-corrected yields changed when individualCLAS sectors and target vertex-z bins were removed from theanalysis A small number of bins had large (5) systematicuncertainties for half of the CLAS sectors and were removedfrom the results Overall the angular-dependent systematicuncertainties varied between 1 and 15

VI LUMINOSITY DETERMINATION

The number of tagged photons incident on the target whilethe data acquisition (DAQ) system was ready to record events

035204-7

P T MATTIONE et al PHYSICAL REVIEW C 96 035204 (2017)A

ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE

FIG 9 The CLAS acceptance in selected energy bins as afunction of the pion cm angle cos θcm

π The dips in the acceptanceare primarily due to triggering inefficiencies and problematic areasof the drift chambers

Nγ was calculated separately for each tagger counter as [20]

Nγ = εNe (2)

where ε is the tagging ratio of the given tagger counter andNe is the number of detected electron hits in that counterwhile the DAQ was ready Ne was calculated from the rateof ldquoout-of-timerdquo electron hits and the livetime of the DAQldquoOut-of-timerdquo hits are from electrons that did not coincide intime with the trigger and were used so that the rate calculationwas not biased by the trigger

The tagging ratios ε were determined by taking severalnormalization runs throughout the g13 experiment Duringthese runs a total absorption counter (TAC) was inserted intothe beamline to determine the number of photons incident onthe target The TAC was positioned about 25 m downstreamof CLAS and consisted of a single lead-glass block A PMTattached to the block was used to count the number of photonsincident on the TAC which was 100 efficient [11] A lowbeam current of 01 nA was necessary to prevent radiationdamage to the TAC during these normalization runs

For each normalization run the tagging ratios were calcu-lated for each tagger counter as [20]

ε = NTAC

N (1 minus α) (3)

where N is the total number of electron hits in a given taggercounter NTAC is the total number of these hits that representcoincident matched photon hits in the TAC for that taggercounter and α is the photon attenuation factor This factortakes into account the fraction of the photons incident on thetarget that did not reach the TAC This photon attenuationfactor was sim4 and was energy independent [21] These

losses were primarily due to electron-positron pair productionand Compton scattering as the photons interacted with thetarget and the beamline components The tagging ratios weretypically 60ndash72 for the 1990-GeV data and between 73and 82 for the 2655-GeV data Because the beam wascollimated through a 64-mm opening the tagging ratios werelower for the 1990-GeV data due to the larger beam dispersionof the lower-energy beam

In total approximately 468 trillion tagged photons wereincident on the CLAS target in this analysis The statis-tical uncertainty on the flux measurement ranged between00024 and 014 and are reported as energy-dependentnormalization uncertainties The systematic uncertainty ofthe photon flux was determined by examining the stabilityof the flux-normalized yields of γ d rarr πminusp(p) throughoutthe experimental run These systematic uncertainties were04 and 07 for the 1990- and 2655-GeV data respec-tively and are reported as energy-independent normalizationuncertainties

In addition the systematic uncertainties on the targetlength and density determinations were each 04 and weredominated by thermal contraction and temperature variationrespectively These uncertainties are reported as energy-independent normalization uncertainties

VII DIFFERENTIAL CROSS SECTIONS

The data from the 1990- and 2655-GeV electron beamenergies were merged together to produce the final set of mea-sured γ d rarr πminusp(p) differential cross sections This mergingwas performed by calculating an uncertainty-weighted averageof the two cross section measurements in bins where both wereavailable In bins where data were only available from onebeam energy only that result was used

The differential cross section of the γ d rarr πminusp(p) reactionwas calculated for each bin of photon beam energy Eγ andcos θcm

π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF

(Eγ )A(Eγ cos θcm

π

) (4)

where cos θcmπ is the bin width in cos θcm

π Ar is theeffective atomic weight of the neutrons in the deuterium targetρ is the target density L is the target length NA is Avogadrorsquosnumber is the photon flux in the given photon energy binY is the experimental yield in the given bin A is the simulatedacceptance in the given bin and YCF is the yield correctionfactor discussed in Sec V The factor of 2π is due to theintegration over the azimuthal angle φ in the binning usedfor the cross section calculation The statistical uncertainty ofthe cross section was calculated for each bin by combining thestatistical uncertainties of the experimental yield and simulatedacceptance in quadrature and ranged between 03 and 5These uncertainties were dominated by the yield uncertaintiesAll data from this measurement are included in the CLASphysics database [22]

035204-8


To study the stability of the overall normalization of theγ d rarr πminusp(p) cross section measurements it was calculatedseparately for several different run ranges throughout bothbeam energy settings of the experiment Overall the totalspread between the measurements was 24 and is reportedas an energy-independent normalization uncertainty Thisuncertainty takes into account any systematic differencesbetween the 1990- and 2655-GeV data that were mergedtogether The total normalization uncertainties were about34 and were primarily due to this run range-dependentvariation in the cross section measurements and the FSIcorrections which are discussed in Sec VIII The totaluncertainty on the γ d rarr πminusp(p) cross sections is typicallybetween 42 and 15

To extract the γ n rarr πminusp differential cross sectionsmodel-dependent final state interaction corrections were ap-plied to the γ d rarr πminusp(p) data as discussed in Sec VIIIThese data were split up into 157 photon energy bins from0440 to 2520 GeV 10 MeV wide below 15 GeV and20 MeV wide above The γ n rarr πminusp differential cross sectionmeasurements are shown for 40 of these Eγ bins in Figs 10 and11 compared against previous measurements and availablepartial wave analysis solutions They are also shown inFig 12 vs W in four bins of cos θcm

π These figures includeγ n rarr πminusp measurements from CLAS g10 [8] SLAC [23]DESY [24] MAMI-B [25] and Frascati [26] and πminusp rarr γ nmeasurements from BNL [27] LBL [28] and LAMPF [29]Only the angle-dependent uncertainties are shown for allmeasurements All non-CLAS g13 data shown in Figs 10 and11 are within plusmn10 MeV of the selected g13 energy bin andall non-CLAS g13 data shown in Fig 12 are within cos θcm

π

of plusmn005 of the g13 angle binThe differential cross section peaks at low energy due to

(1232) and Nlowast resonance production and at forward anglesdue to t-channel pion exchange Below Eγ = 1 GeV the newCLAS g13 data dominate the previous world measurementswith cos θcm

π bins 002 wide and total uncertainties typicallyless than 10 in this range The CLAS g13 data aresystematically lower than the DESY [24] BNL [27] andSLAC [23] measurements in several energy bins and eachof these measurements quote normalization uncertainties ofabout 5 There is also a discrepancy in the trend of thedata at forward angles between the CLAS g13 and SLACmeasurements below Eγ = 0800 GeV with the g13 datarising more sharply at forward angles

Above Eγ = 1 GeV the g13 data are reported in bins thatare 003 wide in cos θcm

π up to 15 GeV and 004 wide incos θcm

π above 15 GeV Here the CLAS g10 data [8] werethe previous highest-statistics measurement reported in 50-and 100-MeV-wide beam energy bins The g13 data are inexcellent agreement with these measurements as the g10 datahave normalization uncertainties of sim6 to sim10 that are notshown in the figures

The SAID PR15 [30] Bonn-Gatchina BG2014-02 [4] andMAID2007 [31] curves shown in these figures did not includethe new CLAS g13 data in their fits and the MAID2007 fitdoes not include the CLAS g10 measurements either The datain these previous fits and in the new SAID MA27 fit thatincludes the g13 data are discussed in Sec X

VIII FINAL STATE INTERACTIONS

The γ n rarr πminusp cross sections were extracted on a freeneutron from the deuteron data in the quasifree kinematicregion of the γ d rarr πminuspp reaction which has a fast knocked-out proton p1 and a slow proton spectator p2 assumednot to be involved in the pion production process In thisquasifree region the reaction mechanism corresponds to theldquodominantrdquo impulse approximation (IA) diagram in Fig 13(a)with the slow proton p2 emerging from the deuteron vertexHere the differential cross section on the deuteron can berelated to that on the neutron target in a well understoodway [see eg Eq (22) of Ref [32] and references therein]Figure 13(a) illustrates this dominant IA diagram as well asthe ldquosuppressedrdquo IA diagram with the protons interchangedThis approximation with the additional assumption that theneutron is at rest in the deuteron allows for the identificationof the quasifree cross section dσ

don the deuteron with that on

the neutron where d is the solid angle of the outgoing pionin the γ n rest frame The γ n cross section can be calculated as

dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd

(γ d) is the quasifree CLAS g13 measurement onthe deuteron and R(Eγ θcm

π ) is the FSI correction factor thattakes into account the FSI effects discussed below as well asthe identity of the two protons in the γ d reaction This factoris defined as the ratio between the full contribution of thethree diagrams in Fig 13 and that of the dominant IA diagramin Fig 13(a) There are two critical factors to consider whenusing this approach (1) the neutron is bound in the deuteronand not at rest and (2) there are NN - and πN -FSI effects

Factor (1) means that the effective mass of the neutron

meff =radic

(pd minus ps)2 asymp mn minus εd minus p 2s mN (6)

is not equal to the mass of the free neutron mn Here pd ps ps εd and mN are the deuteron four-momentum four- andthree-momenta of the spectator proton the deuteron bindingenergy and the nucleon mass respectively Also the invariantmass

radicsπN of the final πN system

radicsπN = radic

sγN =radic

[(Eγ + md minus Es)2 minus ( pγ minus ps)2] (7)

depends on the proton-spectator momentum ps (sγN is theinvariant mass squared of the initial γN state) Here Eγ

(Es) md and pγ are the total energy of the initial photon(proton-spectator) the deuteron mass and the photon three-momentum respectively and Eγ = | pγ |

Sinceradic

sπN depends on ps the γN rarr πN cross sectionextracted from the deuteron data with an undetected nucleonspectator is averaged over an energy range that depends onthe kinematic cuts employed for ps Thus the effective photonlaboratory energy Eγn (defined through the relation sγN =m2

n + 2mnEγn for the γ n rarr πminusp reaction) and the pion cmangle θcm

π are smeared due to the deuteron wave function(DWF) This smearing has been estimated from a simplifiedcalculation where the γ d rarr πminuspp amplitude is proportionalto the DWF and depends only on the laboratory momentumof one of the final protons say p2 Here Eγn is determined

035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE

FIG 10 Selected cross section data for γ n rarr πminusp vs cos θcmπ below Eγ = 105 GeV CLAS g13 (black open circles) SLAC [23] (blue

open triangles) DESY [24] (violet open squares) MAMI-B [25] (cyan open down triangles) and Frascati [26] (pink open stars) πminusp rarr γ n

data BNL [27] (green open diamonds) LBL [28] (orange closed diamonds) and LAMPF [29] (gray closed circles) fits SAID MA27 (bluesolid lines) SAID PR15 [30] (red dot-dashed lines) BG2014-02 [4] (green dashed lines) and MAID2007 [31] (violet dotted lines) The y

axes are log scale Only angle-dependent uncertainties are shown for all data The total normalization uncertainties for the CLAS g13 data areabout 34

035204-10

DIFFERENTIAL CROSS SECTION MEASUREMENTS FOR PHYSICAL REVIEW C 96 035204 (2017)b

sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE

FIG 11 Selected cross section data for γ n rarr πminusp vs cos θcmπ above Eγ = 105 GeV CLAS g13 (black open circles) CLAS g10 [8]

(red open pluses) SLAC [23] (blue open triangles) and DESY [24] (violet open squares) fits SAID MA27 (blue solid lines) SAID PR15[30] (red dot-dashed lines) BG2014-02 [4] (green dashed lines) and MAID2007 [31] (violet dashed lines) The y axes are log scale Onlyangle-dependent uncertainties are shown for all data The total normalization uncertainties for the CLAS g13 data are about 34

035204-11

P T MATTIONE et al PHYSICAL REVIEW C 96 035204 (2017)b

sr)

μ (

Ωdσd

1minus10

1

10) = -035cm

πθcos( ) = 0cmπθcos(

W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(

FIG 12 Selected cross section data for γ n rarr πminusp vs W CLASg13 (black open circles) CLAS g10 [8] (red open pluses) SLAC [23](blue open triangles) DESY [24] (violet open squares) MAMI-B[25] (cyan open down-triangles) and Frascati [26] (pink open stars)πminusp rarr γ n data BNL [27] (green open diamonds) LBL [28] (orangeclosed diamonds) and LAMPF [29] (gray closed circles) fits SAIDMA27 (blue solid lines) SAID PR15 [30] (red dot-dashed lines)BG2014-02 [4] (green dashed lines) and MAID2007 [31] (whichterminates at W = 2 GeV or Eγ = 165 GeV) (violet dotted lines)The y axes are log scale Only angle-dependent uncertainties areshown for all data The total normalization uncertainties for the CLASg13 data are about 34

through the above-mentioned relation with the effective massof the pion-proton pair with the other proton p1 The distortionof the extracted γ n rarr πminusp cross sections due to the smearingeffect is negligible as was shown in Ref [25]

Factor (2) corresponds to the inclusion of the FSI cor-rections Their leading terms correspond to the Feynmandiagrams shown in Figs 13(b) and 13(c) The GWU SAIDdatabase contains phenomenological amplitudes for the re-actions πN rarr πN [33] NN rarr NN [34] and γN rarr πN[35] which were used as inputs to calculate the dominant

γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)

FIG 13 Feynman diagrams for the leading terms of the γ d rarrπminuspp amplitude (a) IA (b) pp-FSI and (c) πN-FSI The filledblack circles represent the FSI vertices The wavy dashed solidand double lines correspond to the photons pions nucleons anddeuterons respectively

diagrams of the GWU-ITEP FSI approach The full Bonnpotential [36] was used for the deuteron description

Calculations of the γ d rarr πminuspp differential cross sectionswith the FSI taken into account (including all diagrams inFig 13) were done for the present g13 data as they were donepreviously for the CLAS g10 data (Eγ = 1050 to 2700 GeVand θcm

π = 32 to 157) [8] and MAMI-B data (Eγ = 0301to 0455 GeV and θcm

π = 58 to 141) [25]The GWU-ITEP FSI calculations [32] are available over

a broad energy range (threshold to Eγ = 2700 GeV) andfor the full cm angular range (θcm

π = 0 to 180) Figure14 shows the FSI correction factor R = R(Eγ θcm

π ) for theγ n rarr πminusp differential cross section as a function of θcm

π fordifferent energies over the range of the CLAS g13 experimentOverall the FSI correction factor R lt 1 while the value ofR varied from 70 to 90 depending on the kinematicsThe behavior of R is very smooth vs pion production angleNote that R(Eγ θcm

π ) is the FSI correction factor for theCLAS quasifree γ d rarr πminuspp cross section averaged over thelaboratory photon energy Eγ bin width

The contribution of FSI calculations [32] to the overallsystematic normalization uncertainty is estimated to be about22 (the sensitivity to the DWF is 1 and to the numberof steps in the integration of the fivefold integrals is 2)No sensitivity was found to the kinematic cuts used for thedetected protons in CLAS

IX LEGENDRE ANALYSIS

Legendre expansions provide a model-independent ap-proach suitable for presentation of modern detailed (high-precision high-statistics and narrow energy and angularbinning) data for pion photoproduction reactions [37] Thisapproach is applicable both to cross sections and to po-larization observables it is much more compact and vi-sual than traditional methods (see for instance Figs 10ndash12) at least at energies within the nucleon resonanceregion The Legendre coefficients reveal specific correla-tions and interferences between resonant states of definiteparities

The small statistical uncertainties of the g13 data obtainedhere allow a correspondingly robust determination of theLegendre polynomial coefficients AJ (W ) These coefficientswere very difficult to determine unambiguously with previ-ously published πminus photoproduction data of lower statisticalaccuracy Because of the limited angular range of the g13data several sets of quasidata were generated using the MA27SAID solution (see Sec X for details) in bins with width cos θcm

π = 005 for the forward and backward directions tocover the full angular range

It is important to note that the MA27 solution wasconstrained at the forward and backward angular rangesbeyond the extent of the g13 data by the existing worlddata shown in Figs 10ndash12 However as the available datado not span the full cos θcm

π range for the W range of the g13data the MA27 quasidata were conservatively assigned 10uncertainties which matches the largest of the experimentaluncertainties reported within the g13 data excepting a fewregions with a problematic acceptance determination Conser-

035204-12


FIG 14 The FSI correction factor R(Eγ θcmπ ) for selected beam energies vs cos θcm

π where θcmπ is the polar angle of the outgoing πminus

in the rest frame of the πminus and the fast proton The fast knocked-out protons p1 with momentum gt200 MeVc were selected while the slowproton spectators p2 have momentum lt200 MeVc The 2 normalization uncertainties are not shown

vative assignment of uncertainties in these regions is importantas these regions are quite sensitive to the highest partial waves

As expected for such a fit using orthogonal polynomialsthe Legendre coefficients AJ (W ) decrease markedly for largeJ With the energy range and precision of the g13 data amaximum value of J = 10 was found to be sufficient todescribe the data (similar to the analysis of the CLAS π0

and π+ beam asymmetry measurements [38]) Thus theinfinite series is truncated as

dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)

where the total cross section σ tot = 4πA0(W )In Fig 15 the Legendre coefficients A0(W ) to A10(W )

are shown as a function of W from the fit of the CLAS g13dσd data and the dσd data generated from the MA27predictions The individual Legendre coefficients have beenscaled by n times AJ + m to allow plotting on a common abscissaThe n and m scaling values are given in the subplots of Fig 15

The results of our fits yield unprecedented detail on theenergy dependence of the Legendre coefficients AJ (W ) andshould prove useful for performing a phase shift analysis ofpion photoproduction data for the present energy range Asexpected from the form of Eq (28) of Ref [37] resonancecontributions from the second third and fourth resonanceregions combine to produce clear peaks in the coefficient

A0(W ) It is interesting that all AJ (W ) coefficients showstructure for the W = 13 to 18 GeV range which was alsoseen in the MAMI A2 π0 data [30] However wide structuresare also visible in the range W = 18 to 20 GeV mostlikely attributable to contributions from one or more nucleonresonances known in this energy range with spin up to 72 aswas seen in the recent CLAS g8 π0 and π+ beam asymmetrymeasurement Legendre analysis [38]

The Legendre fit results shown in Fig 15 do not includeany assignment of model uncertainties associated with theextrapolations of the MA27 model beyond the range of theavailable data Such assignments could be expected to benon-negligible for the higher Legendre moments shown hereHowever our purpose in displaying the Legendre fit results isnot to perform a quantitative amplitude analysis but to show-case how the precision g13 cross section measurements canprovide significant constraints on the resonance contributionsover a broad range in W

X MULTIPOLE ANALYSIS

The SAID parametrization of the transition amplitude Tαβ

used in the hadronic fits to the πN scattering data is given as

Tαβ =sum

σ

[1 minus KC]minus1ασ Kσβ (9)

035204-13


FIG 15 Coefficients of the Legendre polynomials AJ (W ) (blue filled circles) from the fits of the CLAS g13 γ n rarr πminusp cross section dataThe error bars represent the AJ (W ) uncertainties from the fits in which only the statistical uncertainties were used The AJ (W ) coefficientshave been scaled (dashed horizontal lines) by n times AJ + m to enable easy visualization The red vertical arrows in the top row of plots indicatethe masses of the PDG four-star resonances (Breit-Wigner masses) in this energy range [2] The upper row of arrows corresponds to Nlowast stateswith isospin I = 12 and the lower row corresponds to lowast states with I = 32

where α β and σ are channel indices for the πN πρN and ηN channels Here Kαβ are the Chew-MandelstamK matrices which are parametrized as polynomials in thescattering energy Cα is the Chew-Mandelstam function anelement of a diagonal matrix C in channel space which isexpressed as a dispersion integral with an imaginary part equalto the two-body phase space [39]

In Ref [40] it was shown that this form could be extendedto Tαγ to include the electromagnetic channel as

Tαγ =sum

σ

[1 minus KC]minus1ασ Kσγ (10)

Here the Chew-Mandelstam K-matrix elements associatedwith the hadronic channels are kept fixed from the previousSAID solution SP06 [33] and only the electromagneticelements are varied The resonance pole and cut structures arealso fixed from hadronic scattering This provides a minimaldescription of the photoproduction process where only the Nlowastand lowast states present in the SAID πN scattering amplitudesare included in this multipole analysis

For each angular distribution a normalization constant(X) and its uncertainty (εX) were assigned The quantity εX

is generally associated with the normalization uncertainty(if known) The modified χ2 function to be minimized

is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)

where the subscript i labels the data points within the distribu-tion θ exp

i is an individual measurement θi is the correspondingcalculated value and εi represents the total angle-dependentuncertainty The total χ2 is then found by summing over allmeasurements This renormalization freedom is essential forobtaining the best SAID fit results For other data analyzedin the fit such as the total cross sections and excitation datathe statistical and systematic uncertainties were combined inquadrature and no renormalization was allowed

In the previous fits to the γ n rarr πminusp differential crosssections of Ref [8] the unrestricted best fit gave renormaliza-tion constants X significantly different from unity As can beseen from Eq (11) if an angular distribution contains manymeasurements with small statistical uncertainties a change inthe renormalization may improve the fit with only a modestχ2 penalty Here however the weight of the second term inEq (11) has been adjusted by the fit for each dataset to keep therenormalization constants approximately within εX of unityThis was possible without degrading the overall fit χ2 as canbe seen in Fig 16

035204-14


FIG 16 Comparison of the previous SAID solution PR15 [30]applied to the present g13 data with (blue filled triangles) and withoutFSI corrections (black open circles) and the new SAID MA27 (redfull circles) solution obtained after adding the present g13 data withFSI corrections into the fit (the solid lines connecting the points areincluded only to guide the eye) Shown are the fit χ2 per data pointvalues averaged within each energy bin Eγ where the horizontaldashed lines (blue (black) for PR15 and red for MA27) show theoverall χ 2 per data point values from Table II

With the new high-precision γ n rarr πminusp cross sectionsfrom the CLAS g13 dataset a new SAID multipole analysis hasbeen completed This new global energy-dependent solutionhas been labeled as MA27 The overall fit quality of the presentMA27 and previous SAID PR15 solutions are compared inTables I and II The inclusion of the g13 dataset showssignificant improvement in the comparisons between theπminusp fits and data (χ2dp for PR15 = 208 and χ2dpfor MA27 = 110) as shown in Fig 16 and Table I Thisdemonstrates the power of these cross section measurementswith their small uncertainties The overall comparison of thePR15 and MA27 solutions in Table II shows that the fitχ2dp values are essentially unchanged for the π0p andπ+n channels but are notably worse for the π0n channelwhich has very low statistics The overall χ2 per data pointincluding all available data and the new g13 data for PR15 isχ2dp = 219 (103 74747 353) and for MA27 is χ2dp =199 (94 24847 353)

TABLE I Comparison of χ 2 per data point (dp) belowEγ = 27 GeV (W = 25 GeV) for the γ n rarr πminusp channel usingpredictions for the recent SAID PR15 [30] and the current MA27solution The first row of solutions compares the fit quality to theavailable data not including the CLAS g13 data The second rowcompares the solutions to the available data including the g13 dataThe last row compares the solutions only to the g13 data

Data Solution χ 2(πminusp dp)

Existing data PR15 65413162 = 207without g13 MA27 71123162 = 225Existing data PR15 2405211590 = 208with g13 MA27 1644211590 = 142Only PR15 175118452 = 207g13 MA27 93308452 = 110

In Figs 17ndash19 I = 12 multipole amplitudes from thepresent and previous SAID fits are compared to predictionsfrom the MAID and Bonn-Gatchina groups The Bonn-Gatchina analysis has been regularly updated whereas theMAID fit was published in 2007 and therefore does notinclude any results from the past decade including the recentCLAS g10 cross section measurements of Ref [8] The crosssection requires I = 32 multipoles as well but these arehighly constrained by proton-target measurements and havenot changed significantly with the addition of neutron-targetmeasurements (and therefore are not shown here) In themultipole plots the subscript n denotes a neutron target andplusmn gives the value of j = plusmn 12 while the superscript givesthe isospin index

Changes in the multipole amplitudes can be seen in acomparison of the SAID curves in Figs 17ndash19 Consistencyamong the analyses is visible in multipoles containing adominant resonance such as the nE

122minus and nM

122+ multipoles

However the nE121+ and nM

121+ multipoles differ even at the

qualitative level This discrepancy is evident in the proton-target multipoles as well

The full world database of γ n rarr πminusp experiments aboveEγ = 12 GeV contains mainly differential cross sectionsapart from some beam asymmetry measurements fromYerevan [41] GRAAL [42] and CEA [43] Ultimately moremeasurements of the polarization observables are needed inthe πminusp and π0n channels in order to fully constrain theunderlying reaction amplitudes New γ n measurements fromthe CLAS g14 dataset [44] will significantly add to theavailable polarization observable measurements

Looking for significant changes in the imaginary parts ofthe multipoles (Figs 17ndash19) in the energy region below theolder set of CLAS g10 cross sections [8] several Nlowast rarr γ nphotodecay amplitudes have been extracted at their polepositions on the complex plane This is the first determinationof these amplitudes for the N (1440)12+ N (1535)12minusN (1650)12minus and N (1720)32+ states A new approach hasbeen applied to determine the pole positions and residuesfrom the pion photoproduction multipoles [45] The method isbased on a Laurent expansion of the multipoles M(W ) witha Pietarinen series representing the regular (nonpole) part ofthe energy dependence as

M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)

Here W a(i)minus1 and Wi are complex numbers representing

the cm energy residues and pole positions for the ith polerespectively and BL(W ) is a regular function in the wholecomplex plane A general unknown analytic function B(W )can be expanded into a power series of Pietarinen functions as

BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0

en Z(W )n + middot middot middot

035204-15


TABLE II Comparison of χ 2 per data point (dp) below Eγ = 27 GeV (W = 25 GeV) for all γN rarr πN channels using predictionsfor the recent SAID PR15 [30] and the current MA27 solution The fit quality for the π 0p π+n πminusp and π 0n channels is compared to theavailable data including the g13 data

Data Solution χ 2(π 0p dp) χ 2(π+n dp) χ 2(πminusp dp) χ 2(π 0n dp)

Existing data PR15 54 98525 540 = 215 23 5589859 = 239 24 05211 590 = 208 1152364 = 316with g13 MA27 55 53025 540 = 217 20 7369859 = 210 16 44211 590 = 142 1540364 = 423

X(W ) = α minus radicxP minus W

α + radicxP minus W

Y (W ) = β minus radicxQ minus W

β + radicxQ minus W

Z(W ) = γ minus radicxR minus W

γ + radicxR minus W

(13)

where cndnen and αβγ are real numbers that representtuning parameters and coefficients of the Pietarinen functionsX(W ) Y (W ) and Z(W ) respectively A variable number ofseries was used depending on the structure of the nonpole partof each amplitude and xP xQ and xR represent the branchpoints for each Pietarinen function Once the pole position andresidue were determined the photodecay amplitude at the polecould be constructed as described in Ref [46] The residue ofthe corresponding πN elastic scattering amplitude required inthis construction was taken from the SAID analysis of elasticscattering data [33]

The A12(n) and A32(n) neutron helicity ampli-tudes for N (1440)12+ N (1535)12minus N (1650)12minus andN (1720)32+ for the new SAID MA27 solution are comparedin Table III to the recent SAID GB12 [8] and BG2013[47] solutions that were based on fits to all available dataat the time including the CLAS g10 dataset [8] From thistable the photodecay amplitudes determined from the MA27solution can be directly compared against the Breit-Wignerdeterminations In addition Table III includes a comparisonto the older MAID2007 [31] solution to the relativized quarkmodel predictions of Ref [48] and to the current PDG values[2] The uncertainties on the modulus and phase quoted in Ta-ble III for the new MA27 solution were derived by comparingthe global energy-dependent and energy-independent single-energy amplitudes (see Ref [49] for a discussion on the twoapproaches) The comparison gave residues with uncertaintiesExtracting the photodecay amplitudes and considering thespread of possible values gave the MA27 uncertainties Thesecomparisons showed that the parameters from the MA27solution are reasonably well under control

The pole-valued and Breit-Wigner amplitudes from thefits are generally consistent in terms of the moduli Thecomparisons are reasonable for the N (1440)12+ and theN (1535)12minus For the N (1650)12minus the change from GB12[8] is significant and the result is in reasonable agreement withBG2013 [47] which used the FSI corrected g10 γ n rarr πminuspcross sections that were used for GB12 The N (1650)12minusstate has been difficult to describe as it is so close to theN (1535)12minus and the ηN cusp however this pole-valueddetermination is believed to be more model independent than

the Breit-Wigner amplitude [45] which is reflected in thequoted uncertainties shown in Table III For the N (1720)32+the differences with respect to the BG2013 solution [47] aresignificant and indicate that the CLAS g13 data provide tighterconstraints in the coupled-channel model fits

Comparing the new SAID MA27 solution with the rel-ativized quark model predictions of Ref [48] there aresignificant differences in the helicity amplitudes for theN (1440)12+ and N (1650)12minus while the helicity amplitudesfor the N (1535)12minus and N (1720)32+ are in good agree-ment With respect to the current PDG values [2] Table IIIshows good correspondence with the MA27 solution forN (1440)12+ and N (1535)12minus but sizable disagreementsfor the higher-lying states

A direct comparison of the quoted uncertainties on the neu-tron helicity amplitudes from the different solutions presentedin Table III must be made with some caution For the MA27GB12 and BG2013 listings the uncertainties do not take intoaccount the significant model dependence in fitting the sparsedatabase In fact the variance of the extracted results fromdifferent solutions fitting the same database would providea reasonable estimate for this model dependence Howeverthis direct comparison is not possible given the different datasets employed for the different solutions shown in Table IIIConsidering this issue it is still meaningful that the overallquoted uncertainties for the helicity amplitudes from the MA27solution are noticeably reduced relative to the BG2013 solutionand to the GB12 solution [in particular for the N (1650)12minus]due to a combination of two factors The first is the increasedsize of the database for MA27 that includes the new g13 γ ncross sections and the second is the reduced model dependenceof the pole fit approach employed for MA27

XI SUMMARY AND CONCLUSIONS

A comprehensive set of γ n rarr πminusp differential crosssections at 157 photon energies has been determined withCLAS using a tagged-photon beam at incident photon energiesfrom 0445 to 2510 GeV These data provide a factor ofnearly 3 increase to the worldrsquos data for this channel at theseenergies To extract the γ n cross section from the γ d data FSIcorrections were included using a diagrammatic techniquethat takes into account a kinematic cut with momenta below(above) 200 MeVc to select slow (fast) outgoing protonsIn this analysis the FSI correction factor depended on thephoton energy and meson production angle and was averagedover the rest of the variables in the region of the quasifreeprocess on the neutron

The data collected in this CLAS g13 dataset spans abroad energy range from just above the isobar throughthe second third and fourth resonance regions These data

035204-16


FIG 17 Neutron multipole I = 12 amplitudes [in attometer (am) units] from threshold to W = 243 GeV (Eγ = 27 GeV) For theamplitudes the subscript n denotes a neutron target the subscript plusmn gives the value of j = plusmn 12 and the superscript gives the isospinindex The red solid (blue dash-dotted) lines correspond to the new SAID MA27 (old PR15 [30]) solution The magenta dotted (black dashed)lines give the BG2014-02 [4] (MAID2007 [31] which terminates at W = 2 GeV) solution The vertical arrows indicate the Breit-Wigner mass(WR) and the upper and lower horizontal bars show the partial (πN ) and the full () widths respectively of the resonances extracted by theBreit-Wigner fit of the πN data associated with the SAID solution SP06 [33] The red vertical arrows for (a) and (b) indicate the η productionthreshold

extend far into the poorly studied high-mass region aboveW sim 18 GeV where many resonances are expected to existbut have not been firmly established The precision of thedata can be seen not only in the presented differential cross

sections but also through the uncertainties on the extractedLegendre coefficients This approach of fitting the excitationfunctions with a Legendre series presents the data in a morecompact and visual manner These results will be useful for

035204-17


FIG 18 Neutron multipole I = 12 amplitudes [in attometer (am) units] from threshold to W = 243 GeV (Eγ = 27 GeV) The notationof the multipoles is the same as in Fig 17

performing detailed phase shift analyses to better understandthe resonant amplitudes

On the experimental side further improvements in thepartial wave analyses await more precision data specificallyin the region above Eγ = 05 GeV involving polarizedphotons andor polarized targets The data that are presentlyavailable are provided in Ref [6] Due to the closing of

hadron facilities new πminusp rarr γ n experiments are notplanned and only γ n rarr πminusp measurements are possibleat electromagnetic facilities using deuterium targets Theagreement of these new γ n rarr πminusp cross section data withexisting inverse πminus photoproduction measurements indicatesthat these g13 measurements are reliable despite the use ofdeuterium as an effective neutron target

035204-18



As part of this new dataset for γ n rarr πminusp a new SAIDmultipole analysis called MA27 has been completed Thisenergy-dependent solution which includes the CLAS g13data provides an improved understanding of the Nlowast resonanceparameters for several states compared to the previous GB12SAID solution that does not include the g13 CLAS data Inthe MA27 solution several photodecay amplitudes Nlowast rarr γ nhave been extracted at their pole positions on the complex planewith very small uncertainties This is the first-ever determina-tion of the excited neutron multipoles for the N (1440)12+N (1535)12minus N (1650)12minus and N (1720)32+ resonancescontributing a crucial complement to the excited protonspectra In addition these new precision γ n rarr πminusp datawill provide important and necessary constraints to advancecoupled-channel analysis fits that are sorely lacking γ n dataover nearly the full nucleon resonance region

ACKNOWLEDGMENTS

The authors acknowledge the outstanding efforts of thestaff of the Accelerator and the Physics Divisions at JeffersonLab that made this experiment possible This work wassupported by the US Department of Energy the NationalScience Foundation the Scottish Universities Physics Alliance(SUPA) the United Kingdomrsquos Science and TechnologyFacilities Council the National Research Foundation ofKorea the Italian Instituto Nazionale di Fisica Nuclearethe French Centre National de la Recherche Scientifiquethe French Commissariat agrave lrsquoEnergie Atomique and theDeutsche Forschungsgemeinschaft (SFB 1044) This materialis based upon work supported by the US Department ofEnergy Office of Science Office of Nuclear Physics underContract No DE-AC05-06OR23177 The authors AEK andVET also acknowledge the support of Grant No RFBR16-02-00767

TABLE III Moduli [in (GeV)minus12] and phases (in degrees) of the neutron helicity amplitudes A12(n) and A32(n) from the SAID MA27solutions (third column) The Breit-Wigner neutron photodecay amplitudes are compared from SAID GB12 [8] (fourth column) from BG2013[47] (fifth column) and from MAID2007 [31] (sixth column) The relativized quark model predictions from Ref [48] (seventh column) areincluded along with the PDG values (eighth column) [2]

Resonance Coupling MA27 GB12 BG2013 MAID2007 Capstick PDG 2016modulus phase

N (1440)12+ A12(n) 0065 plusmn 0005 5 plusmn 3 0048 plusmn 0004 0043 plusmn 0012 0054 minus0006 0040 plusmn 0010N (1535)12minus A12(n) minus0055 plusmn 0005 5 plusmn 2 minus0058 plusmn 0006 minus0093 plusmn 0011 minus0051 minus0063 minus0075 plusmn 0020N (1650)12minus A12(n) 0014 plusmn 0002 minus30 plusmn 10 minus0040 plusmn 0010 0025 plusmn 0020 0009 minus0035 minus0050 plusmn 0020N (1720)32+ A12(n) minus0016 plusmn 0006 10 plusmn 5 minus0080 plusmn 0050 minus0003 0004 minus0080 plusmn 0050N (1720)32+ A32(n) 0017 plusmn 0005 90 plusmn 10 minus0140 plusmn 0065 minus0031 0011 minus0140 plusmn 0065

035204-19


[1] A V Anisovich et al Eur Phys J A 52 284 (2016)[2] C Patrignani et al (Particle Data Group) Chin Phys C 40

100001 (2016)[3] D Roumlchen M Doumlring H Haberzettl J Haidenbauer U-G

Meiszligner and K Nakayama Eur Phys J A 51 70 (2015)[4] The Bonn-Gatchina analyses are available through the Bonn

website httppwahiskpuni-bonnde see also E Gutz et alEur Phys J A 50 74 (2014)

[5] H Kamano S X Nakamura T S H Lee and T Sato PhysRev C 88 035209 (2013)

[6] W J Briscoe I I Strakovsky and R L Workman GWU CNSDAC SAID database located at httpgwdacphysgwueduanalysispr_analysishtml

[7] P Nadel-Turonski B L Berman Y Ilieva D G Ireland andA Tkabladze Few-Body Syst 43 227 (2008)

[8] W Chen H Gao W J Briscoe D Dutta A E Kudryavtsev MMirazita M W Paris P Rossi S Stepanyan I I StrakovskyV E Tarasov and R L Workman Phys Rev C 86 015206(2012) W Chen et al (CLAS Collaboration) Phys Rev Lett103 012301 (2009)

[9] Nlowast Resonances in Pseudoscalar-Meson Photoproduction fromPolarized Neutrons in H middot D and a Complete Determinationof the γ n rarr K0 Amplitude spokespersons F Klein andA Sandorfi (CLAS Collaboration) JLab Proposal E06ndash101Newport News VA USA 2006 Pion Photoproduction from aPolarized Target Spokespersons N Benmouna W J BriscoeI I Strakovsky S Strauch and G V OrsquoRielly (CLASCollaboration) JLab Proposal E03ndash105 Newport News VAUSA 2003

[10] Meson Production off the Deuteron II spokespersons W JBriscoe V V Kulikov K Livingston and I I Strakovsky(MAMI A2 Collaboration) MAMI Proposal MAMI-A2-0213Mainz Germany 2013 Meson Production off the DeuteronI spokespersons W J Briscoe and I I Strakovsky (A2Collaboration at MAMI) MAMI Proposal MAMI-A2-0212Mainz Germany 2012

[11] B A Mecking et al Nucl Instrum Methods Phys Res SectA 503 513 (2003)

[12] D I Sober et al Nucl Instrum Methods Phys Res Sect A440 263 (2000)

[13] M D Mestayer et al Nucl Instrum Methods Phys Res SectA 449 81 (2000)

[14] Y G Sharabian et al Nucl Instrum Methods Phys Res SectA 556 246 (2006)

[15] E S Smith et al Nucl Instrum Methods Phys Res Sect A432 265 (1999)

[16] G S Adams et al Nucl Instrum Methods Phys Res Sect A465 414 (2001)

[17] M Amarian et al Nucl Instrum Methods Phys Res Sect A460 239 (2001)

[18] M Lacombe B Loiseau R Vinh Mau J Cocircteacute and P PireacutesPhys Lett B 101 139 (1981)

[19] P T Mattione and D S Carman CLASndashNote 2017ndash001 (2017)httpsmisportaljlaborgulPhysicsHall-BclasviewFilecfm2017-001pdfdocumentId=754

[20] J Ball and E Pasyuk Jefferson Lab CLAS-Note2005-002 (2005) httpsmisportaljlaborgulPhysicsHall-BclasviewFilecfm2005-002pdfdocumentId=24

[21] R Schumacher CLASndashNote 2001ndash010 (2001) httpswwwjlaborgHall-Bnotesclas_notes0101-010pdf

[22] CLAS physics database httpclaswebjlaborgphysicsdb[23] P E Scheffler and P L Walden Nucl Phys B 75 125 (1974)[24] P Benz et al Nucl Phys B 65 158 (1973)[25] W J Briscoe A E Kudryavtsev P Pedroni I I Strakovsky

V E Tarasov and R L Workman Phys Rev C 86 065207(2012)

[26] M Beneventano S DrsquoAngelo F de Notaristefani P MonacelliL Paoluzi A Proia F Sebastiani and M Severi NuovoCimento A 19 529 (1974)

[27] A Shafi et al (Crystal Ball Collaboration) Phys Rev C 70035204 (2004)

[28] A J Weiss D J Blasberg J C Comiso R P Haddock BM K Nefkens L J Verhey M B Zeller K M Crowe AFainberg and P Truoel Nucl Phys B 101 1 (1975)

[29] G J Kim J Arends W J Briscoe J Engelage B M KNefkens M E Sadler and H J Ziock Phys Rev D 40 244(1989)

[30] P Adlarson et al (A2 Collaboration) Phys Rev C 92 024617(2015)

[31] The MAID analyses are available through the Mainz websitehttpwwwkphkphuni-mainzdeMAID see also D DrechselS S Kamalov and L Tiator Eur Phys J A 34 69 (2007)

[32] V E Tarasov W J Briscoe H Gao A E Kudryavt-sev and I I Strakovsky Phys Rev C 84 035203(2011)

[33] R A Arndt W J Briscoe I I Strakovsky and R L WorkmanPhys Rev C 74 045205 (2006)


[35] M Dugger et al (CLAS Collaboration) Phys Rev C 76 025211(2007)

[36] R Machleidt K Holinde and C Elster Phys Rep 149 1(1987)

[37] Ya I Azimov I I Strakovsky W J Briscoe and R LWorkman Phys Rev C 95 025205 (2017)


[39] R A Arndt J M Ford and L D Roper Phys Rev D 32 1085(1985)

[40] R L Workman M W Paris W J Briscoe and I I StrakovskyPhys Rev C 86 015202 (2012)

[41] F Adamyan et al J Phys G Nucl Phys 14 835 (1988) LAbrahamian et al Sov J Nucl Phys 32 69 (1980)

[42] G Mandaglio et al (GRAAL Collaboration) Phys Rev C 82045209 (2010) G Giardina (private communication)

[43] J Alspector D Fox D Luckey C Nelson L S Osbourne GTarnopolsky Z Bar-Yam J de Pagter J Dowd W Kern andS M Matin Phys Rev Lett 28 1403 (1972)

[44] D Ho et al (CLAS Collaboration) Phys Rev Lett 118 242002(2017)

[45] A Svarc M Hadzimehmedovic H Osmanovic J Stahov LTiator and R L Workman Phys Rev C 89 065208 (2014)

[46] R L Workman L Tiator and A Sarantsev Phys Rev C 87068201 (2013)

[47] A V Anisovich V Burkert E Klempt V A NikonovA V Sarantsev and U Thoma Eur Phys J A 49 67(2013)

[48] S Capstick Phys Rev D 46 2864 (1992)[49] R A Arndt W J Briscoe I I Strakovsky and R L Workman

Phys Rev C 66 055213 (2002)

035204-20


37Old Dominion University Norfolk Virginia 23529 USA38University of Richmond Richmond Virginia 23173 USA

39Universitarsquo di Roma Tor Vergata 00133 Rome Italy40Skobeltsyn Nuclear Physics Institute 119899 Moscow Russia

41University of South Carolina Columbia South Carolina 29208 USA42Temple University Philadelphia Pennsylvania 19122 USA

43Universidad Teacutecnica Federico Santa Mariacutea Casilla 110-V Valparaiacuteso Chile44Virginia Tech Blacksburg Virginia 24061-0435 USA

45University of Virginia Charlottesville Virginia 22901 USA46College of William and Mary Williamsburg Virginia 23187 USA

47Yerevan Physics Institute 375036 Yerevan Armenia(Received 8 June 2017 revised manuscript received 3 August 2017 published 18 September 2017)

The quasifree γ d rarr πminusp(p) differential cross section has been measured with CLAS at photon beam energiesEγ from 0445 to 2510 GeV (corresponding to W from 1311 to 2366 GeV) for pion center-of-mass anglescos θcm

π from minus072 to 092 A correction for final state interactions has been applied to these data to extract theγ n rarr πminusp differential cross sections These cross sections are quoted in 8428 (Eγ cos θcm

π ) bins a factor ofnearly 3 increase in the world statistics for this channel in this kinematic range These new data help to constraincoupled-channel analysis fits used to disentangle the spectrum of Nlowast resonances and extract their propertiesSelected photon decay amplitudes Nlowast rarr γ n at the resonance poles are determined for the first time and arereported here

DOI 101103PhysRevC96035204

I INTRODUCTION

The determination of the resonance properties for allaccessible baryon states is a central objective in nuclearphysics The extracted resonance parameters provide a crucialbody of information for understanding the nucleon excitationspectrum and for testing models of the nucleon inspired byquantum chromodynamics (QCD) and more recently latticeQCD calculations The spectrum of Nlowast and lowast baryon reso-nances has been extensively studied through meson-nucleonscattering and meson photoproduction experiments Propertiesof the known resonances continue to become better determinedas experiments involving polarized beams targets and recoilmeasurements are expanded and refined [1] Extracted quan-tities include resonance masses widths branching fractionspole positions and associated residues as well as photodecayamplitudes [2] New states have also been found mainlythrough multichannel analyses that are sensitive to states hav-ing a relatively weak coupling to the πN decay channel [3ndash5]

Knowledge of the Nlowast and lowast resonance photodecayamplitudes has largely been restricted to the charged statesApart from lower-energy inverse reaction πminusp rarr γ n mea-surements the extraction of the two-body γ n rarr πminusp andγ n rarr π0n observables requires the use of a model-dependentnuclear correction which mainly comes from final stateinteraction (FSI) effects within the target deuteron Most γ ndata are unpolarized and cover fairly narrow energy rangesOf these only about 400 π0n measurement data points existspanning the full nucleon resonance region [6]

The importance of improving the γ n database relativeto the γp database is directly related to the fact that theelectromagnetic interaction does not conserve isospin sym-metry The amplitude for the reactions γN rarr πX factors intodistinct I = 12 and I = 32 isospin components Aγπplusmn =radic

2(AI=12pn ∓ AI=32) This expression indicates that the ex-

citation of the I = 32 lowast states can be entirely determinedfrom proton target data However measurements from datasetswith both neutron and proton targets are required to determinethe isospin I = 12 amplitudes and to separate the γpNlowast andγ nNlowast photocouplings

This work focuses on negative pion photoproduction off theneutron using a deuteron target A large body of new precisionγ n rarr πminusp differential cross sections for Eγ = 0445 to2510 GeV in laboratory photon energy corresponding toan invariant energy range from W = 1311 to 2366 GeVare reported Pion center-of-mass (cm) production anglesranging from θcm

π = 26 to 135 have been measured duringthe CLAS Collaboration g13 run period [7] These new crosssection data have nearly tripled the world γ n rarr πminusp databasebelow Eγ = 2700 GeV [6]

The γ n rarr πminusp differential cross section was previouslymeasured by the CLAS g10 [8] experiment Those measure-ments contained 855 data points in 50- and 100-MeV-wide binsof beam energy Eγ from 1050 to 3500 GeV corresponding toa W range from 1690 to 2731 GeV However the 8428 datapoints from g13 are a precision measurement of this cross sec-tion with a factor of sim10 increase in data points These data arereported in 10- and 20-MeV-wide bins of beam energy Eγ withoverall normalization uncertainties of sim34 compared to thesim6 to sim10 overall normalization uncertainties achieved byg10 Also unlike the g10 measurements the g13 data cover theW range of the low-mass Nlowast resonances and can be used toinvestigate their helicity amplitudes and resonance parameters

The present dataset together with completed polarizedmeasurements for both πminusp and π0n from Jefferson Lab [9]and MAMI [10] are expected to lead to the determinationof well-constrained γ n decay amplitudes in the near futureHowever these new CLAS γ n rarr πminusp data allow for the firstdetermination of selected photon decay amplitudes Nlowast rarr γ nat their pole on the complex plane

035204-2



II EXPERIMENT









III EVENT SELECTION



035204-3


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610







Cou

nts

0

2

4

6

8

10

12

14

16

18











035204-4



Cou

nts

0

5

10

15

20


(a)


Mis

sing

Mom

entu

m (

GeV

c)

0

01

02

03

04

05

06

07

08

09

1

0

50

100

150

200

250

300


(b)







εExperiment (1)






035204-5


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3


0

01

02

03

04


(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04






π where θcm


(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(b)





035204-6



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20



II EXPERIMENT









III EVENT SELECTION



035204-3


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610







Cou

nts

0

2

4

6

8

10

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14

16

18











035204-4



Cou

nts

0

5

10

15

20


(a)


Mis

sing

Mom

entu

m (

GeV

c)

0

01

02

03

04

05

06

07

08

09

1

0

50

100

150

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250

300


(b)







εExperiment (1)






035204-5


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3


0

01

02

03

04


(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04






π where θcm


(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(b)





035204-6



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610


p (GeVc)0 05 1 15 2 25 3

βΔ

02minus

015minus

01minus

005minus

0

005

01

015

02

1

10

210

310

410

510

610







Cou

nts

0

2

4

6

8

10

12

14

16

18











035204-4



Cou

nts

0

5

10

15

20


(a)


Mis

sing

Mom

entu

m (

GeV

c)

0

01

02

03

04

05

06

07

08

09

1

0

50

100

150

200

250

300


(b)







εExperiment (1)






035204-5


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3


0

01

02

03

04


(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04






π where θcm


(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(b)





035204-6



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20



Cou

nts

0

5

10

15

20


(a)


Mis

sing

Mom

entu

m (

GeV

c)

0

01

02

03

04

05

06

07

08

09

1

0

50

100

150

200

250

300


(b)







εExperiment (1)






035204-5


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3


0

01

02

03

04


(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04






π where θcm


(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(b)





035204-6



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


(deg)θ0 20 40 60 80 100 120 140

p (G

eVc

)

0

05

1

15

2

25

3


0

01

02

03

04


(deg)θ0 20 40 60 80 100 120 140

(de

g)φ

Sec

tor-

30minus

20minus

10minus

0

10

20

30

06minus

04minus

02minus

0

02

04






π where θcm


(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(a)

(deg)θ0 20 40 60 80 100 120

p (G

eVc

)

0

02

04

06

08

1

12

14

16

18

2

0

02

04

06

08

1


(b)





035204-6



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20



Cou

nts

0

50

100

150

200

250

300

350

400

450






)cmπθcos(


Yie

ld

020406080

100120140160180200


)cmπθcos(


Yie

ld

05

10152025303540









035204-7


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


ccep

tanc

e

01

02

03

04

05 = 0655 GeVγE = 1205 GeVγE

)cmπθcos(

05minus 0 05

Acc

epta

nce

01

02

03

04

05 = 175 GeVγE

)cmπθcos(

05minus 0 05 1

= 231 GeVγE




Nγ = εNe (2)




ε = NTAC

N (1 minus α) (3)








π as

dσ

d

(Eγ cos θcm

π

)

= 1

2π( cos θcm

π

) Ar

ρLNA

Y(Eγ cos θcm

π

)YCF


π

) (4)



035204-8





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20





π












dσ

d(γ n) = R

(Eγ θcm

π

)minus1 dσ

d(γ d) (5)

where dσd




meff =radic




radicsπN = radic

sγN =radic




Sinceradic




035204-9


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


bsr

)μ

(Ω

dσd

10

W = 1311 GeV = 0445 GeVγE

W = 1332 GeV = 0475 GeVγE

W = 1353 GeV = 0505 GeVγE

W = 1374 GeV = 0535 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1394 GeV = 0565 GeVγE

W = 1415 GeV = 0595 GeVγE

W = 1434 GeV = 0625 GeVγE

W = 1454 GeV = 0655 GeVγE

bsr

)μ

(Ω

dσd

10

W = 1473 GeV = 0685 GeVγE

W = 1492 GeV = 0715 GeVγE

W = 1511 GeV = 0745 GeVγE

W = 1529 GeV = 0775 GeVγE

bsr

)μ

(Ω

dσd

1

10W = 1548 GeV

= 0805 GeVγEW = 1566 GeV

= 0835 GeVγEW = 1584 GeV

= 0865 GeVγEW = 1601 GeV

= 0895 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1

10 W = 1619 GeV = 0925 GeVγE

)cmπθcos(


W = 1636 GeV = 0955 GeVγE

)cmπθcos(


W = 1653 GeV = 0985 GeVγE

)cmπθcos(


W = 1670 GeV = 1015 GeVγE





035204-10


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


sr)

μ (

Ωdσd

1minus10

1

W = 1693 GeV = 1055 GeVγE

W = 1720 GeV = 1105 GeVγE

W = 1747 GeV = 1155 GeVγE

W = 1774 GeV = 1205 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1800 GeV = 1255 GeVγE

W = 1826 GeV = 1305 GeVγE

W = 1852 GeV = 1355 GeVγE

W = 1877 GeV = 1405 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1

W = 1902 GeV = 1455 GeVγE

W = 1929 GeV = 1510 GeVγE

W = 1977 GeV = 1610 GeVγE

W = 2024 GeV = 1710 GeVγE

bsr

)μ

(Ω

dσd 1minus10

1 W = 2070 GeV = 1810 GeVγE

W = 2115 GeV = 1910 GeVγE

W = 2159 GeV = 2010 GeVγE

W = 2202 GeV = 2110 GeVγE

)cmπθcos(


bsr

)μ

(Ω

dσd 1minus10

1 W = 2244 GeV = 2210 GeVγE

)cmπθcos(


W = 2286 GeV = 2310 GeVγE

)cmπθcos(


W = 2326 GeV = 2410 GeVγE

)cmπθcos(


W = 2366 GeV = 2510 GeVγE



035204-11


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20


sr)

μ (

Ωdσd

1minus10

1

10) = -035cm


W (GeV)14 16 18 2 22 2

bsr

)μ

(Ω

dσd

1minus10

1

10) = 03cm

πθcos(

W (GeV)14 16 18 2 22 24

) = 06cmπθcos(




γ

d

p12

p21

πminus

(c)d

γ πminus

p12

p21

(a)

γ

d

p1

p2

πminus

(b)


















035204-12








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20








dσ(W cos θcm

π

)d

=10sum

J=0

AJ (W ) PJ

(cos θcm

π

) (8)









Tαβ =sum

σ


035204-13





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20





Tαγ =sum

σ





is given by

χ2 =sum

i

(Xθi minus θ

expi

εi

)2

+(

X minus 1

εX

)2

(11)




035204-14









122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


035204-15











(13)










035204-16





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

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122minus and nM

122+ multipoles






M(W ) =ksum

i=1

a(i)minus1

W minus Wi

+ BL(W ) (12)



BL(W ) =Msum

n=0

cn X(W )n +Nsum

n=0

dn Y (W )n

+Nsum

n=0


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(13)










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ACKNOWLEDGMENTS





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Phys Rev C 66 055213 (2002)

035204-20











(13)










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ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20





035204-17






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20






035204-18




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20




ACKNOWLEDGMENTS





035204-19
















































Phys Rev C 66 055213 (2002)

035204-20
















































Phys Rev C 66 055213 (2002)

035204-20

Differential cross section measurements for n p above the...

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