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Physics Letters B 564 (2003) 21–26

www.elsevier.com/locate/np

Measurement of the transverse–longitudinal cross sectionsthe p(e,e′p)π0 reaction in the region

MIT-Bates OOPS Collaboration

C. Kunza, N.I. Kaloskamisb, M.O. Distlera,1, Z.-L. Zhoua, R. Alarconc, D. Barkhuffa,A.M. Bernsteina,∗, W. Bertozzia, J. Calarcoi, F. Casagrandea, J. Chena, J. Comfortc,

G. Dodsona,2, A. Dooleye, K. Dow a, M. Farkhondeha, S. Georgakopoulosb, S. Gilada,R. Hicksd, A. Hottad, X. Jiangd,3, A. Karabarbounisb, S. Kowalskia, D.J. Margaziotisf,

C. Mertzc,b, R. Miskimend, I. Nakagawaa, C.N. Papanicolasb, M.M. Pavana,4,G. Petersond, A. Ramirezc, D. Rowntreea, A.J. Sartye,5, J. Shawd, E. Sixc,

N. Sparverisb, S.-B. Soonga, S. Stiliarisb, T. Tamaeg, D. Tiegera, C. Tschalaera,G. Tsentalovicha, W. Turchinetza, C.E. Vellidisb, G.A. Warrena,6, S. Williamsonh,

A. Youngc, J. Zhaoa, T. Zwarta

a Physics Department and Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USAb Institute of Accelerating Systems and Applications and Department of Physics, University of Athens, Athens, Greece

c Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287, USAd Department of Physics, University of Massachusetts at Amherst, Amherst, MA 01003, USA

e Department of Physics, Florida State University, Tallahassee, FL 32306, USAf Department of Physics and Astronomy, California State University at Los Angeles, Los Angeles, CA 90032, USA

g Laboratory of Nuclear Science, Tohoku University, Sendai 982-0826, Japanh Nuclear Physics Laboratory, University of Illinois, Urbana, IL 61820, USA

i Department of Physics, University of New Hampshire, Durham, NH 03824, USA

Received 19 March 2003; received in revised form 29 April 2003; accepted 6 May 2003

Editor: J.P. Schiffer

Abstract

Accurate measurements of the p(e,e′p)π0 reaction were performed atQ2 = 0.127 (GeV/c)2 in the resonance energregion. The experiments at the MIT-Bates Linear Accelerator used an 820 MeV polarized electron beam withof-plane magnetic spectrometer system (OOPS). In this Letter we report the first simultaneous determination ofTL and TL′ (“fifth” or polarized) cross sections at lowQ2 where the pion cloud contribution is predicted to dominthe quadrupole amplitudes (E2 and C2). These are the real and imaginary parts of the transverse–longitudinal inamplitudes and provide a sensitive determination of the Coulomb quadrupole amplitude and a test of reaction calcComparisons with model calculations are presented. The empirical MAID calculation gives the best overall agreementaccurate data. The parameters of this model for the values of the resonant multipoles are|M1+(I = 3/2)| = (40.9 ± 0.3) ×10−3/mπ , CMR = C2/M1 = −6.5 ± 0.3%, EMR= E2/M1 = −2.2 ± 0.9%, where the errors are due to the experimeuncertainties.

0370-2693 2003 Elsevier Science B.V.doi:10.1016/S0370-2693(03)00675-0

Open access under CC BY license.

22 MIT-Bates OOPS Collaboration / Physics Letters B 564 (2003) 21–26

2003 Elsevier Science B.V.

Keywords: EMR; CMR; Electro-pion production; Out-of-plane

Open access under CC BY license.

eda-in-

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-[16]

Experimental confirmation of the deviation of thnucleon shape from spherical symmetry is of funmental significance and has been the subject oftense investigation [1] since this possibility was orinally raised by Glashow [2]. For theJ = 1/2 nucleon,this has focused on the determination of the elecand Coulomb quadrupole amplitudes (E2, C2) inpredominantly M1 (magnetic dipole-quark spin fliγ ∗N → transition. Thus, measurements of theand C2 amplitudes represent deviations from sphcal symmetry of the N, system and not the nucleoalone. The experimental difficulty is that the E2/M1and C2/M1 ratios are small (typically −2 to −8%at low four momentum transfered,Q2). In this case thenon-resonant (background) and resonant quadruamplitudes are the same order of magnitude. Thfore, experiments have to be designed to attain thequired precision to separate the signal and backgrocontributions. This has been accomplished for phopion reactions using polarized photon beams [3,4]

Observation of the deviation from spherical symetry in pion electroproduction is more pronouncthan in photoproduction. This is due to the interfence between the longitudinal C2 and the dominM1 amplitudes in theσTL cross section [5]. On thother hand, the presence of the additional longitunal multipoles means that there are more multipoledetermine and, therefore, more extensive data mutaken. The experiments for an extensive databasewould allow a model independent analysis havebegun [1,6–8]. At the present time one must relyreaction models to extract the resonant M1, E2,C2 amplitudes of interest from the data. As has bpointed out in previous publications, the model er

* Corresponding author.E-mail address: bernstein@lns.mit.edu (A.M. Bernstein).

1 Now at Universität, Mainz, Germany.2 Now at ORNL, Oak Ridge, TN 37831, USA.3 Now at Rutgers University, Piscataway, NJ 08855, USA.4 Now at TRIUMF, Vancouver, Canada.5 Now at St. Mary’s Univ., Halifax, Canada, B3H 3C3.6 Now at Universitat Basel, Switzerland.

t

can be much larger than the experimental error [5,6Therefore, it is important to test model calculationsa range of center of mass (CM) energiesW in theregion of 1232 MeV, the resonant energy, whicprovides a range of background and resonant amtudes. It is also important to determine specific crsections (e.g.,σTL, σTL′ ) which are primarily sensitiveto the C2 and background amplitudes, respectivelythis Letter we present the first measurement thatvides such information at and below the resonaenergy at lowQ2. This requires a polarized electrobeam and out of plane hadron detection.

In the constituent quark model the d statemixtures in the nucleon and wave functions arecaused by the hyperfine tensor interaction betwquarks [11]. However this effect contributes onlysmall portion of the observed quadrupole signalThe pion cloud contribution to the nucleon andstructure is primarily in the p wave. This is duethe spontaneously broken chiral symmetry of QCin which the pion, an almost Goldstone boson, intacts with hadrons via gradient coupling [12]. Thefore, it is not surprising [7] that model calculatio[13–15] have shown that at lowQ2 the pion cloud con-tributes significantly to the M1 amplitude and dominates the E2 and C2 contributions to theγ ∗N →

transition. The present experiment was performeQ2 = 0.127(GeV/c)2 which is close to the predictemaximum of the pion cloud contribution [13–15Thus, this experiment is ideally suited to test theseculations.

The coincident p(e,e′π) cross section in the onephoton-exchange-approximationcan be written as

(1)dσ

dωdΩedΩcmπ

= Γvσh(θ,φ),

where

σh(θ,φ)= σT + εσL + √2ε(1+ ε) σTL cosφ

+ εσTT cos 2φ

+ hpe√

2ε(1− ε) σTL′ sinφ,

MIT-Bates OOPS Collaboration / Physics Letters B 564 (2003) 21–26 23

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al

e,e in-

samep-

re

tal

firstionstwoionhe

beisns

ole

gni-ouldundthe

ole

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Γv is the virtual photon flux,h= ±1 is the electron helicity, pe is the magnitude of the longitudinal electropolarization,ε is the virtual photon polarization parameter,θ andφ are the pion CM polar and azimuthangles relative to the momentum transferq, andσL ,σT, σTL, and σTT are the longitudinal, transverstransverse–longitudinal, and transverse–transversterference cross sections, respectively [16].

The TL and the TL′ (transverse–longitudinal) crossections are the real and imaginary parts of the scombination of interference multipole amplitudes. Aproximate expressions for these are:

σTL(θ)= −sinθ Re[ATL +BTL cosθ ],σTL′(θ)= sinθ Im[ATL +BTL cosθ ],ATL ≈ −q

kL∗

0+M1+,

(2)BTL ≈ −6q

kL∗

1+M1+,

where the pion production multipole amplitudes adenoted byMl±, El±, andLl±, indicating their char-acter (magnetic, electric, or longitudinal), their toangular momentum(J = l± 1/2), andq andk are thepion and photon center of mass momenta. In thetwo lines of Eq. (2) it has been assumed that the pare produced in s and p waves only. In the nextlines an additional truncated multipole approximatis made, namely, only terms which interfere with tdominant magnetic dipole amplitudeM1+ are kept.The exact formulas without this approximation canfound in [16]. In model calculations [13,14,17,18] thapproximation is not made and significant deviatiofrom the truncated multipole approximation occur.

As has been previously demonstrated,σTL is sen-sitive to the magnitude of the longitudinal quadrupamplitude C2 [5]. Adding a measurement ofσTL′ tothis provides a stringent test of the background matudes and phases of the reaction calculations. It shbe pointed out that a determination of the backgroamplitudes is an important part of the physics ofγπN system.

To precisely determine the resonant quadrupamplitude in theγ ∗N → transition at lowQ2 and toaddress the issue of background contributions, agram has been developed at the MIT-Bates Linearcelerator. For this purpose we have developed a spout-of-plane magnetic spectrometer system (OOPSwhich the spectrometers are deployed symmetric

l

about the momentum transferq [10]. We observed theTL′ cross section using a polarized electron beam0.85% duty factor at an energy of 820 MeV. A typcal polarization and an average current were 37%6 µA, respectively. A liquid H2 target was used incylindrical cell of 1.6 cm diameter with a 4.3 µm thicHavar wall. The scattered electrons were detectethe One Hundred Inch Proton Spectrometer (OHIand the coincident protons in two out-of-plane sptrometers deployed at a fixed laboratory angle relato q and with out-of-plane anglesφ = 225, 315. Thefocal plane instrumentation of each spectrometer csisted of three horizontal drift chambers for trackconstruction and scintillators for triggering. Detailoptics studies were done for each spectrometer,the detection efficiencies were measured as functof all independent reaction coordinates. The totalficiency of the system was calibrated by using eltic electron scattering data from the liquid H2 target.Boiling effects in the target were studied by varyithe beam current and they were negligible. The phspace normalization of the cross section and varcorrections applied to the data, including radiative crections, were calculated with a Monte Carlo simution. The cross sections were obtained from the pathe phase space of the two spectrometers which wmatched in four dimensions(W,Q2, θ,φ) [19], whereW is a central invariant mass.

The experiment was performed atQ2 = 0.127(GeV/c)2, W = 1232 and 1170 MeV. The results ankinematic settings are presented in Table 1 andFigs. 1–3. The helicity asymmetryATL′(θ,φ) is

ATL′(θ,φ)= σh=1(θ,φ)− σh=−1(θ,φ)

σh=1(θ,φ)+ σh=−1(θ,φ),

(3)=√

2ε(1− ε) σTL′(θ)sin(φ)

σunpol(θ,φ),

where the quantities were defined in Eq. (1) andσunpolis the electron helicity independent part (the first foterms) ofσh. To first approximation this quantity ca

Table 1Results of the present p(e,e′p)π0 experiment atQ2 = 0.127(GeV/c)2

W (MeV) θ σ0 = σT + εσL (µb/sr) σTL (µb/sr) σTL′ (µb/sr)

1170 119 17.31± 0.90 0.91± 0.18 1.65± 0.551232 129 26.39± 0.47 2.83± 0.20 3.11± 0.55

24 MIT-Bates OOPS Collaboration / Physics Letters B 564 (2003) 21–26

d

ntee oherecesnti-set

19]

theivelesree

lcu-bi-ch

ithme-alsoions

e-

oft

ionion

ofs,

edrsofin

the

a–sund

n

Fig. 1. The helicity asymmetryATL′ for the p(e,e′p)π0 reactionatQ2 = 0.127 (GeV/c)2 plotted versusθ , the CM angle betweenthe outgoing pion and the momentum transferq . The curves areMAID [17] (solid), Sato–Lee [13] (dashed), DMT [14] (dotted), andispersion theory [18] (dot-dashed).

be extracted from the data without detailed MoCarlo calculations of the phase-space acceptancthe apparatus, and therefore has a smaller error. Tare only small corrections due to the finite acceptanof the spectrometers. In the quoted results, the quaties have been referred to the central spectrometertings [19]. The absolute values of the TL′ cross sec-tions,σTL′ , have also been extracted from the data [and are presented here.

We note that the sign ofATL′ is negative. In theπ0 channel the recoil protons were detected withprotons being emitted in the forward direction relatto q, the momentum transfer with out-of-plane angφpq = 45, 135. In Eq. (1) the angles of the pion ainvolved, andφ = 225, 315. Therefore, a negativsign forATL′ means that the sign ofσTL′ is positive.

The experimental results are compared to calations [13,14,17,18] in Figs. 1–3. The most amtious calculation is the Sato–Lee model [13] whicalculates all of the multipoles andπ–N scatteringfrom dynamical equations. It is in agreement wthe photoproduction data (some of the model paraters were fit to these data). The Sato–Lee modelagrees with our data for the unpolarized cross sect

f

-

Fig. 2. Cross sections for the p(e,e′p)π0 reaction forW = 1170 MeV,Q2 = 0.127 (GeV/c)2 plotted versusθ . Panel(a) is for σ0 = σT + εσL . Panel (b) is forσTL and panel (c) is forσTL′ . See Fig. 1 captions for an explanation of the curves.

σ0 = σT +εσL , but unfortunately, is in strong disagrement with our measurements ofσTL andσTL′ . The dis-persion relations calculation [18] agrees with someour data but disagrees with ourσTL measurements aW = 1170 MeV. On the other hand dispersion relatcalculations provide good agreement with photo-pproduction data [20].

The Mainz Unitary Model (MAID) is a flexibleway to fit observed cross sections as a functionQ2 [17]. It incorporates Breit–Wigner resonant termBorn terms, higher N∗ resonances, and is unitarizusing empiricalπ–N phase shifts. The parameteof the model have been previously fit to a rangedata, including our previous results [5], and arereasonable agreement with our data [17] withexception ofσTL (θ = 119, W = 1170 MeV) whichis in disagreement with all calculations. The DubnMainz–Taipei (DMT) model [14] includes dynamicfor the resonant channels and uses the backgroamplitudes of the MAID model. This model is i

MIT-Bates OOPS Collaboration / Physics Letters B 564 (2003) 21–26 25

4]u-

ponn-entedab

bu-al-

].

a

d

onsryhenstonsetion

n-nsled

23,ich. Atpiner-odeltherthece

sum

stntednedfor

ingessasby

the

Fig. 3. Cross sections for the p(e,e′p)π0 reaction forW = 1232 MeV,Q2 = 0.127 (GeV/c)2 plotted versusθ . Panel(a) is for σ0 = σT + εσL . Panel (b) is forσTL and panel (c) is forσTL′ . See Fig. 1 captions for an explanation of the curves.

reasonable agreement with our data at resonance (W =1232 MeV) but not withσ0 andσTL below resonance(W = 1170 MeV).

The Sato–Lee and DMT dynamical models [13,1predict that the pion cloud is the dominant contribtion to the quadrupole amplitudes at low values ofQ2.This behavior is an expected consequence of the staneous breaking of chiral symmetry in QCD [7]. Ufortunately these models are not in overall agreemwith our data. In contrast, the Sato–Lee model showmuch better predictions of the recently reported JLHall B result for the p(e,e′p)π0 reaction in the re-gion forQ2 from 0.4 to 1.8 (GeV/c)2 [21]. This seemsto indicate that the dominant meson cloud contrition, which is predicted to be a maximum near our vues ofQ2, is not quantitatively correct.

Recently, a measurement ofATL′ for the p(e,e′p)π0

reaction in the region was performed at Mainz [22The kinematics include a range ofQ2 values from 0.17to 0.26 (GeV/c)2 and backwardθ angles. These dat

-

disagreed with the MAID [17], Sato–Lee [13], anDMT [14] models.

It is of interest to compare the TL and TL′ resultspresented here with those of the recoil polarizatiwhich are proportional to the real and imaginaparts of interference multipole amplitudes. For tp(e,e′p)π0 channel the outgoing proton polarizatiohave been observed in parallel kinematics (the proemitted alongq or θ = 180) [23,24]. For this case thobservables in the truncated multipole approximaare:

σ0px ∝ Re[AxTL

],

σ0py ∝ Im[ByTL

],

σ0px ∝ Re[CzTL

],

AxTL ByTL ≈ (

4L∗1+ −L∗

0+ +L∗1−

)M1+,

(4)CzTT ≈ |M1+|2 + Re[(

6E∗1+ − 2E∗

0+)M1+

],

where σ0 = σT + εσL , px , py , and pz are definedin [17], and the constants of proportionality cotain only kinematic factors (for the full expressiosee [16]). This shows both the similarity and detaidifference between a measurement of TL and TL′ andthe recoil polarizations. In the published papers [24] the data were compared to the MAID model whis found not to be in good agreement with the datathe present time we do not have sufficient data todown the multipoles that are responsible for this diffence (a discussion of the data requirements for mindependent analyses is presented in [7]). On the ohand, there is a possible experimental problem inexperimental values of the recoil polarizations sinthe data do not agree with a model independentrule [25].

The empirical MAID calculation gives the beoverall agreement with the accurate data presehere but also with the overall set of the data obtaiby our collaboration. The parameters of this modelthe values of the resonant multipoles are|M1+(I =3/2)| = (40.9 ± 0.3) × 103/mπ , CMR = C2/M1 =−6.5 ± 0.3%, EMR= E2/M1 = −2.2 ± 0.9%. Theerrors are experimental and were obtained by varythe magnitudes in MAID of the resonant amplitudby one σ in a χ2 fit to our data. In a previoupaper [5] we showed that the dominant error wdue to model uncertainties, which was estimatedtaking the differences between the multipoles of

26 MIT-Bates OOPS Collaboration / Physics Letters B 564 (2003) 21–26

delthisodeant,

ress

ul-nary

L)

edt is]ob-

ar-

etainu-n atenc-x-

k-tedher-d-scheion,

01,ited

lear

ng

lly,

0-

1;4)

.

.

92)

ate

8)

ub-

.),eticrld

different models. We argue here that only one mois in reasonable agreement with our data, and soapproach can no longer be used. Therefore, the merrors come from uncertainties in the non-resonmultipole amplitudes of the MAID calculation whichat the present time, are not known. We plan to addthis issue in a future publication.

In conclusion, we have performed the first simtaneous measurement of both the real and imagiparts of the transverse–longitudinal interference (Tcross section for the p(e,e′p)π0 reaction in the re-gion at a lowQ2 where the meson cloud is predictto be the leading cause of deformation [13–15]. Ifound that only the more empirical MAID model [17is in reasonable agreement with the accurate datatained forσ0 = σT + εσL andσTL′ and also with ourprevious data [5]. On the other hand, for recoil polization data obtained at the sameQ2 [23,24], and forATL′ taken at slightly higher values ofQ2 [22], thereare possible problems with the MAID model. At thpresent time there are not sufficient data to ascerwhich multipoles might be responsible for this sitation. We are presently analyzing new data takeQ2 = 0.127 (GeV/c)2 which should provide a moraccurate determination of these values [26] in conjution with the new generation, double polarization eperiments [27].

Acknowledgements

We would like to thank the Bates staff for maing this experiment possible. This work is supporin part by the US Department of Energy and tNational Science Foundation Grant-in-Aid for Intenational Scientific Research, by the Ministry of Eucation, Science, and Culture Japan, and DeutForschungsgemeinschaft, the Humboldt Foundatand the EC-IHP Network ESOP.

l

References

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