Measurement of Exclusive π0 Electroproduction Structure Functions and theirRelationship to Transversity GPDs

I. Bedlinskiy,22 V. Kubarovsky,35, 30 S. Niccolai,21 P. Stoler,30 K.P. Adhikari,29 M. Aghasyan,18

M.J. Amaryan,29 M. Anghinolfi,19 H. Avakian,35 H. Baghdasaryan,39, 41 J. Ball,7 N.A. Baltzell,1

M. Battaglieri,19 R. P. Bennett,29 A.S. Biselli,11, 30 C. Bookwalter,13 S. Boiarinov,35 W.J. Briscoe,15

W.K. Brooks,37, 35 V.D. Burkert,35 D.S. Carman,35 A. Celentano,19 S. Chandavar,28 G. Charles,7

M. Contalbrigo,17 V. Crede,13 A. D’Angelo,20, 32 A. Daniel,28 N. Dashyan,41 R. De Vita,19 E. De Sanctis,18

A. Deur,35 C. Djalali,34 D. Doughty,8, 35 R. Dupre,7 H. Egiyan,35, 40 A. El Alaoui,1 L. El Fassi,1

L. Elouadrhiri,35 P. Eugenio,13 G. Fedotov,34 S. Fegan,38 J.A. Fleming,10 T.A. Forest,16 M. Garcon,7

N. Gevorgyan,41 K.L. Giovanetti,23 F.X. Girod,35 W. Gohn,9 R.W. Gothe,34 L. Graham,34

K.A. Griffioen,40 B. Guegan,21 M. Guidal,21 L. Guo,12, 35 K. Hafidi,1 H. Hakobyan,37, 41 C. Hanretty,39

D. Heddle,8, 35 K. Hicks,28 M. Holtrop,26 Y. Ilieva,34, 15 D.G. Ireland,38 B.S. Ishkhanov,33 E.L. Isupov,33

H.S. Jo,21 K. Joo,9 D. Keller,39 M. Khandaker,27 P. Khetarpal,12 A. Kim,24 W. Kim,24 F.J. Klein,6

S. Koirala,29 A. Kubarovsky,30, 33 S.E. Kuhn,29 S.V. Kuleshov,37, 22 N.D. Kvaltine,39 K. Livingston,38

H.Y. Lu,5 I .J .D. MacGregor,38 Y. Mao,34 N. Markov,9 D. Martinez,16 M. Mayer,29 B. McKinnon,38

C.A. Meyer,5 T. Mineeva,9 M. Mirazita,18 V. Mokeev,35, 33 H. Moutarde,7 E. Munevar,35 C.

Munoz Camacho,21 P. Nadel-Turonski,35 G. Niculescu,23, 28 I. Niculescu,23, 35 M. Osipenko,19

A.I. Ostrovidov,13 L.L. Pappalardo,17 R. Paremuzyan,41, ∗ K. Park,35, 24 S. Park,13 E. Pasyuk,35, 2 S.

Anefalos Pereira,18 E. Phelps,34 S. Pisano,18 O. Pogorelko,22 S. Pozdniakov,22 J.W. Price,3 S. Procureur,7

Y. Prok,8, 39 D. Protopopescu,38, 26 A.J.R. Puckett,35 B.A. Raue,12, 35 G. Ricco,14, † D. Rimal,12

M. Ripani,19 G. Rosner,38 P. Rossi,18 F. Sabatie,7 M.S. Saini,13 C. Salgado,27 N. Saylor,30

D. Schott,12 R.A. Schumacher,5 E. Seder,9 H. Seraydaryan,29 Y.G. Sharabian,35 G.D. Smith,38

D.I. Sober,6 D. Sokhan,21 S.S. Stepanyan,24 S. Stepanyan,35 S. Strauch,34, 15 M. Taiuti,14, †

W. Tang,28 C.E. Taylor,16 Ye Tian,34 S. Tkachenko,39 M. Ungaro,35, 30 M.F. Vineyard,36, 31

A. Vlassov,22 H. Voskanyan,41 E. Voutier,25 N.K. Walford,6 D.P. Watts,10 L.B. Weinstein,29

D.P. Weygand,35 M.H. Wood,4, 34 N. Zachariou,34 J. Zhang,35 Z.W. Zhao,39 and I. Zonta20, ‡

(The CLAS Collaboration)1Argonne National Laboratory, Argonne, Illinois 604392Arizona State University, Tempe, Arizona 85287-1504

3California State University, Dominguez Hills, Carson, CA 907474Canisius College, Buffalo, NY

5Carnegie Mellon University, Pittsburgh, Pennsylvania 152136Catholic University of America, Washington, D.C. 20064

7CEA, Centre de Saclay, Irfu/Service de Physique Nucleaire, 91191 Gif-sur-Yvette, France8Christopher Newport University, Newport News, Virginia 23606

9University of Connecticut, Storrs, Connecticut 0626910Edinburgh University, Edinburgh EH9 3JZ, United Kingdom

11Fairfield University, Fairfield CT 0682412Florida International University, Miami, Florida 33199

13Florida State University, Tallahassee, Florida 3230614Universita di Genova, 16146 Genova, Italy

15The George Washington University, Washington, DC 2005216Idaho State University, Pocatello, Idaho 8320917INFN, Sezione di Ferrara, 44100 Ferrara, Italy

18INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy19INFN, Sezione di Genova, 16146 Genova, Italy

20INFN, Sezione di Roma Tor Vergata, 00133 Rome, Italy21Institut de Physique Nucleaire ORSAY, Orsay, France

22Institute of Theoretical and Experimental Physics, Moscow, 117259, Russia23James Madison University, Harrisonburg, Virginia 22807

24Kyungpook National University, Daegu 702-701, Republic of Korea25LPSC, Universite Joseph Fourier, CNRS/IN2P3, INPG, Grenoble, France

26University of New Hampshire, Durham, New Hampshire 03824-356827Norfolk State University, Norfolk, Virginia 23504

28Ohio University, Athens, Ohio 4570129Old Dominion University, Norfolk, Virginia 23529

30Rensselaer Polytechnic Institute, Troy, New York 12180-359031University of Richmond, Richmond, Virginia 23173

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32Universita’ di Roma Tor Vergata, 00133 Rome Italy33Skobeltsyn Nuclear Physics Institute, 119899 Moscow, Russia

34University of South Carolina, Columbia, South Carolina 2920835Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606

36Union College, Schenectady, NY 1230837Universidad Tecnica Federico Santa Marıa, Casilla 110-V Valparaıso, Chile

38University of Glasgow, Glasgow G12 8QQ, United Kingdom39University of Virginia, Charlottesville, Virginia 22901

40College of William and Mary, Williamsburg, Virginia 23187-879541Yerevan Physics Institute, 375036 Yerevan, Armenia

(Dated: September 25, 2012)

Exclusive π0 electroproduction at a beam energy of 5.75 GeV has been measured with the JeffersonLab CLAS spectrometer. Differential cross sections were measured at more than 1800 kinematicvalues in Q2, xB , t, and φπ, in the Q2 range from 1.0 to 4.6 GeV2, −t up to 2 GeV2, and xBfrom 0.1 to 0.58. Structure functions σT + εσL, σTT and σLT were extracted as functions of tfor each of 17 combinations of Q2 and xB . The data were compared directly with two handbag-based calculations including both longitudinal and transversity GPDs. Inclusion of only longitudinalGPDs very strongly underestimates σT +εσL and fails to account for σTT and σLT , while inclusion oftransversity GPDs brings the calculations into substantially better agreement with the data. Thereis very strong sensitivity to the relative contributions of nucleon helicity flip and helicity non-flipprocesses. The results confirm that exclusive π0 electroproduction offers direct experimental accessto the transversity GPDs.

DOI: 11.1103/PhysRevLett.109.112001 PACS numbers: 13.60Le, 14.20.Dh, 14.40.Be, 24.85.+p

A major goal of hadronic physics is to describe thethree dimensional structure of the nucleon in termsof its quark and gluon fields. Deep inelastic scatter-ing experiments have provided a large body of infor-mation about quark longitudinal momentum distri-butions. Exclusive electron scattering experiments,in which all final state particles are measured, havebeen rather successfully analyzed and interpreted byRegge models which are based on hadronic degreesof freedom (see, for example, Refs. [1, 2]).

However, during the past decade the handbagmechanism has become the leading theoretical ap-proach for extracting nucleon quark and gluon struc-ture from exclusive reactions such as deeply virtualCompton scattering (DVCS) and deeply virtual me-son electroproduction (DVMP). In this approach thequark distributions are parameterized in terms ofgeneralized parton distributions (GPDs). The GPDscontain information about the distributions of boththe longitudinal momentum and the transverse po-sition of partons in the nucleon. In the handbagmechanism the reaction amplitude factorizes intotwo parts. One part describes the basic hard elec-troproduction process with a parton within the nu-cleon, and the other - the GPD- contains the distri-bution of partons within the nucleon which are theresult of soft processes. While the former is reac-tion dependent, the latter is a universal property ofnucleon structure common to the various exclusivereactions. This is schematically illustrated in Fig. 1.While the handbag mechanism should be most appli-cable at asymptotically large photon virtuality Q2,DVCS experiments at Q2 as low as 1.5 GeV2 appearto be described rather well at leading twist by the

handbag mechanism, while the range of validity ofleading order applicability of DVMP is not as clearlydetermined.

There are eight GPDs. Four correspond to partonhelicity conserving (chiral-even) processes, denotedby Hq, Hq, Eq and Eq. Four correspond to partonhelicity-flip (chiral-odd) processes [3, 4], Hq

T , HqT ,

EqT and EqT . The GPDs depend on three kinematicvariables: x, ξ and t, where x is the average par-ton longitudinal momentum fraction and ξ (skew-ness) is half of the longitudinal momentum fractiontransferred to the struck parton. The skewness canbe expressed in terms of the Bjorken variable xBas ξ ' xB/(2 − xB), in which xB = Q2/(2p · q),q is the four-momentum of the virtual photon andQ2 = −q2. The momentum transfer to the nucleonis t = (p − p′)2, where p and p′ are the initial andfinal four momenta of the nucleon.

In the forward limit where t → 0, Hq and Hq

reduce to the parton density distributions q(x) andparton helicity distributions ∆q(x) respectively. Thefirst moments in x of the chiral-even GPDs are re-lated to the elastic form factors of the nucleon: theDirac form factor F q1 (t), the Pauli form factor F q2 (t),the axial-vector form factor gqA(t) and the pseu-doscalar form factor hqA(t) [5].

Most of the reactions studied, such as DVCS orvector meson production, are at leading order pri-marily sensitive to the chiral-even GPDs. Very lit-tle is known about the chiral-odd GPDs. Hq

T be-comes the transversity function hq1(x) in the forwardlimit. The chiral-odd GPDs are difficult to accesssince subprocesses with a quark helicity-flip are sup-pressed. However, a complete description of nucleon

3

structure requires the knowledge of the transversityGPDs as well as chiral even GPDs.

Pseudoscalar meson electroproduction, and inparticular π0 production in the reaction ep→ e′p′π0,was identified [6, 7] as especially sensitive to thehelicity-flip subprocesses. Evidence of their possiblecontribution to π+ electroproduction in target spinasymmetry data [8] was noted in Ref. [7]. A disad-vantage of π+ production is that the interpretationis complicated by the dominance of the longitudi-nal π+-pole term, which is absent in π0 production.In addition, for π0 production the structure of theamplitudes further suppresses the quark helicity con-serving amplitudes relative to the helicity-flip ampli-tudes [7]. On the other hand, π0 cross sections overa large kinematic range are much more difficult toobtain than for π+ for two reasons: First, the crosssections are much smaller than for π+, and second,the clean detection of π0s requires the measurementof their two decay photons.

This letter presents the results of a measurementof π0 electroproduction cross sections. The primaryfocus here is in its interpretation within the frame-work of the handbag model and on its sensitivity,within this framework, of accessing the quark helic-ity flip GPDs.

FIG. 1: Schematic diagram of the π0 electroproductionamplitude in the framework of the handbag mechanism.The helicities of the initial and final nucleons are denotedby ν and ν′, the incident photon and produced meson byµ and µ′ and the active initial and final quark by λ andλ′. The arrows in the figure represent the correspondinghelicities.

The handbag mechanism is schematically illus-trated in Fig. 1. The reaction can be written asa linear sum of amplitudes, each of which factorizesinto two processes. In the framework of Ref. [4]:

1. A process in which the incident virtual pho-ton of helicity µ = 0,±1 interacts with a singlequark within the nucleon having a momentum frac-tion x+ξ/2 and helicity λ = ±1/2, to produce a me-son with helicity µ′ = 0 and a returning quark withmomentum fraction x− ξ/2 and helicity λ′ = ±1/2,

which is absorbed to form the final nucleon. Inthe present study for transversely polarized photonsλ′ = −λ, µ = ±1 and ν′ = ±ν.

2. Process 1 is convoluted with a GPD, whichencodes the distribution of quark and gluon longi-tudinal momentum fractions and transverse spatialdistributions within the nucleon.

The primary contributing GPDs in meson produc-tion for transverse photons are HT , which charac-terizes the quark distributions involved in nucleonhelicity-flip, and ET (= 2HT +ET ) which character-izes the quark distributions involved in nucleon non-helicity-flip processes [9],[10]. This GPD describesthe density of transversely polarized quarks in anunpolarized nucleon [9],[10].

The relative contributions of the nucleon helicity-flip and nucleon helicity non-flip processes determinethe t dependence of the differential cross sections.

Exclusive π0 electroproduction was measured atJefferson Lab with the CLAS large acceptance spec-trometer [11] . Cross sections were extracted over awide range in Q2, t , xB and φπ (the azimuthal angleof the pion production plane relative to the electronscattering plane.) The incident electron beam en-ergy was 5.75 GeV. The target was liquid hydrogenof length 2.5 cm. The integrated luminosity was 20fb−1. The CLAS detector consists of six identicalsectors within a toroidal magnetic field. Each sectoris equipped with three layers of drift chambers todetermine the trajectory of charged particles, a gasCherenkov counter for electron identification, a scin-tillation hodoscope for time-of-flight measurement,and an electromagnetic calorimeter (EC) for elec-tron identification and photon detection for anglesgreater than 21◦. A forward angle calorimeter wasadded to the standard CLAS configuration down-stream of the target for the detection of pion decayphotons in the forward direction (4.5◦ to 15◦). A su-perconducting solenoid around the target was usedto trap Moller electrons along the beam axis, whilepermitting detection of photons starting at 4.5◦, pro-tons in the range 21◦ to 60◦, and electrons from 21◦

to 45◦. All four final-state particles of the reactionep→ e′p′π0, π0 → γγ were detected.

The kinematic requirements for the accepted datawere: Q2 ≥ 1 GeV2, center-of-mass energy W ≥ 2GeV, and scattered electron energy E′ ≥ 0.8 GeV.The corresponding range of xB was from 0.1 to 0.58.The electrons were identified by requiring both aCherenkov signal and an appropriate energy depo-sition in the EC calorimeter. Protons were iden-tified by TOF measurement. Geometric cuts wereapplied to include only regions of the detector withwell understood acceptance and efficiency, as well aselectron and proton target vertex position cuts, toensure well-identified events.

The photons from π0 → γγ decays were detected

4

in the electromagnetic calorimeters. Once all fi-nal particles were identified, the exclusive reactionep → e′p′π0 was selected as follows: The angle be-tween the direction of the reconstructed π0s andthe missing momentum for ep → e′p′X had to beless than 2◦. 3σ cuts were made on the miss-ing mass M2

X(ep → e′p′X) = m2π0 , the missing

mass MX(ep → e′γγX) = Mp, the missing en-ergy EX(ep → e′p′π0) = 0, and the invariant massMγγ = mπ0 . The background under the π0 invariantmass peak, typically 3 to 5%, was subtracted usingthe data in the sidebands.

Corrections for the inefficiencies in track recon-struction and detector inefficiencies were applied.The acceptance was calculated using the standardGEANT3-based CLAS Monte-Carlo simulation soft-ware. The Monte-Carlo generator for exclusive π0

electroproduction was parameterized to be consis-tent with the data. The ratio of the number of re-constructed Monte-Carlo events to the data eventswas typically a factor of about 12. Thus the statis-tical error introduced by the acceptance calculationwas much smaller than for the data.

The data were binned in Q2, xB , t and φπ, and dif-ferential cross sections d4σ/dQ2dxBdtdφπ were ob-tained for more than 1800 bins.

Radiative corrections were calculated using thesoftware package EXCLURAD [12], which had beenpreviously developed and used for analyzing earlierCLAS π0 experiments. Radiative corrections de-pend on Q2, t, xB and φπ. They vary from 5 to 10%,depending on the kinematics.

An overall normalization factor of 1.12 was ob-tained from comparing elastic cross sections requir-ing e-p coincidence, with published data. A system-atic uncertainty of ±6% was applied to the resultingcross sections due to this correction.

Other systematic uncertainty studies includedthe electron, proton and photon particle identifica-tion, the variation of the cuts on missing massesMX(ep → e′γγX) and MX(ep → e′p′X), missingenergy, fiducial volumes, invariant mass Mγγ andradiative corrections. The overall systematic uncer-tainties were estimated at about 10%.

The structure functions are related to the differ-ential cross sections by [7]

d4σ

dQ2dxBdtdφπ= Γ(Q2, xB , E)

1

2π(σT + εσL

+ε cos 2φπσTT +√

2ε(1 + ε) cosφπσLT ). (1)

The Hand convention [13] was adopted for the def-inition of the virtual photon flux factor Γ. The un-separated cross section σU = σT+εσL, and the inter-ference terms σLT and σTT were extracted from thecosφπ and cos 2φπ dependences of the cross sections.The extracted structure functions as functions of −tare presented in Fig. 2 for 6 of the 17 bins in Q2 and

xB bins, for which have the largest kinematic cover-age and for which there are theoretical calculations.A recent experiment, Ref. [14], measured π0 crosssections in a limited kinematic range. When theirresults are projected to the present Q2 the unsepa-rated cross sections agree within a few percent.

The results of two GPD-based models [15, 16] aresuperimposed in Fig. 2. The contributions fromtransversely polarized photons are primarily fromHT and ET . Reference [15] obtains the followingrelations:

σT =4παe2κ

µ2π

Q4[(1− ξ2)|〈HT 〉|2 −

t′

8m2|〈ET 〉|2] (2)

and

σTT =4παe2κ

µ2π

Q4

t′

8m2|〈ET 〉|2. (3)

Here κ(Q2, xB) is a phase space factor, t′ = t− tmin,and the brackets 〈HT 〉 and 〈ET 〉 denote the convo-lution of the elementary process with the GPDs HT

and ET .The contribution σL accounts for only a small

fraction in both calculations (typically less than afew percent) of the unseparated σT +εσL in the kine-matic regime under investigation. This is becauseH and E, the GPDs which are responsible for theleading-twist structure function σL, are very small.This is not the case for ET and HT which contributeto σT and σTT . In addition, the transverse cross sec-tions are strongly enhanced by the chiral condensatethrough the parameter µπ = m2

π/(mu +md), wheremu and md are current quark masses [7].

With the inclusion of the quark helicity non-conserving chiral-odd GPDs, which contribute pri-marily to σT and σTT and, to a lesser extent σLT ,the model agrees moderately well with the data. De-viations in shape become greater at smaller t′ forthe unseparated cross section σU . The behavior ofthe cross section near the threshold t′ is determinedby the interplay between HT and ET . If ET dom-inates, the cross section becomes small as t′ → 0.For the GPDs of Ref. [15] the parameterization wasguided by the lattice calculation results of Ref. [10],while Ref. [16] used a GPD Reggeized diquark-quarkmodel to obtain the GPDs. The results in Fig. 2 forthe model of Ref. [15] (solid curves), in which ET isdominant, agree rather well with the data. In par-ticular, the structure function σU begins to decreaseas −t becomes small, showing the effect of ET . Inthe model of Ref. [16](dashed curves) HT is domi-nant, which leads to a large rise in cross section as−t′ becomes small. Thus, in their parameterization,the relative contribution of ET to HT appears to beunderestimated. One can make a similar conclusionfrom the comparison between data and model pre-dictions for σTT . This shows the sensitivity of the

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dσ/dt[nb/G

eV2 ]

dσ/dt[nb/G

eV2 ]

FIG. 2: The extracted structure functions vs. t for the bins with the best kinematic coverage and for which thereare theoretical calculations. The data and curves are as follows: black-σU (= σT + εσL), blue-σTT , and red-σLT . Theshaded bands reflect the experimental systematic uncertainties.The curves are theoretical predictions produced withthe models of Refs. [15] (solid) and [16] (dashed).

measured π0 structure functions for constraining thetransversity GPDs.

From Eq. (2) for σT and Eq. (3) for σTT one canconclude that |σTT | < σT < σU . One sees fromFig. 2 that −σTT is a sizable fraction of the unsep-arated cross section while σLT is very small, whichimplies that contributions from transversely polar-ized photons play a dominant role in the π0 electro-production process.

In conclusion, differential cross sections of exclu-sive pion electroproduction have been obtained inthe few GeV region over a wide range of Q2, xb andt. While the general features of π0 electroproductionhave been described by recent Regge models [1, 2],the focus of this letter is on the handbag mecha-nism in terms of quark and gluon degrees of free-dom. Within the handbag interpretation, the dataappear to confirm the expectation that pseudoscalar,and in particular π0, electroproduction is a uniquelysensitive process to access the transversity GPDs ETand HT . The measured unseparated cross section ismuch larger than expected from leading-twist hand-

bag calculations. This means that the contributionof the longitudinal cross section σL is small in com-parison with σT . The same conclusion can be madein an almost model independent way from compari-son of the cross section σU , σTT and σLT [17].

Detailed interpretations are model dependent andquite dynamic in that they are strongly influencedby new data as they become available. In particular,calculations are in progress to compare the theoreti-cal models with the single beam spin asymmetriesobtained earlier with CLAS [18] and longitudinaltarget spin asymmetries which are currently underanalysis.

In the near future new data on η production andratios of η to π0 cross sections are expected to furtherconstrain GPD models. Extracting σL and σT withimproved statistical accuracy and performing newmeasurements with transversely and longitudinallypolarized targets would also be very useful.

We thank the staff of the Accelerator and PhysicsDivisions at Jefferson Lab for making the exper-iment possible. We also thank G. Goldstein, S.

6

Goloskokov, P. Kroll, J. M. Laget and S. Liuti formany informative discussions and clarifications oftheir work, and making available the results of theircalculations. This work was supported in part bythe U.S. Department of Energy and National Sci-ence Foundation, the French Centre National de laRecherche Scientifique and Commissariat a l’EnergieAtomique, the French-American Cultural Exchange(FACE), the Italian Istituto Nazionale di Fisica Nu-cleare, the Chilean Comision Nacional de Investi-gacion Cientıfica y Tecnologica (CONICYT), theNational Research Foundation of Korea, and the UKScience and Technology Facilities Council (STFC).The Jefferson Science Associates (JSA) operates theThomas Jefferson National Accelerator Facility forthe United States Department of Energy under con-tract DE-AC05-06OR23177.

∗ Current address:Institut de Physique Nucleaire OR-SAY, Orsay, France

† Current address:INFN, Sezione di Genova, 16146Genova, Italy

‡ Current address:Universita’ di Roma Tor Vergata,00133 Rome Italy

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