Munoz Camacho, C.

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The Generalized Parton Distributions program in HallA at Jefferson LabC. Munoz CamachoTo cite this version:C. Munoz Camacho. The Generalized Parton Distributions program in Hall A at Jefferson Lab.Sixth International Conference on Perspectives in Hadronic Physics, May 2008, Trieste, Italy.8 p., 2008. <in2p3-00342846>HAL Id: in2p3-00342846http://hal.in2p3.fr/in2p3-00342846Submitted on 28 Nov 2008HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.The Generalized Parton Distribution program inHall A at Jefferson LabC. Muñoz CamachoLPC Clermont-Ferrand CNRS/IN2P3, F-63177 Aubière, FranceAbstract. Recent results on the Generalized Parton Distribution (GPD) program at Jefferson Lab(JLab) will be presented. The emphasis will be in the Hall A program aiming at measuringQ2−dependences of different terms of the Deeply Virtual Compton Scattering (DVCS) cross sec-tion. This is a fundamental step before one can extract GPD information from JLab DVCS data.Neutral pion production will also be discussed and results from the CLAS collaboration will beshown. Finally, the upcoming program in Hall A, using both a 6 GeV beam (≈ 2010) and a 11 GeVbeam (≈ 2015) will be described.Keywords: Generalized Parton Distributions (GPDs), Exclusive reactions.PACS: 13.60.Fz, 13.40.Gp, 14.20.Dh, 13.60.HbINTRODUCTIONMeasurements of electro-weak form factors determine nucleon spatial structure, anddeep inelastic scattering (DIS) of leptons off the nucleon measures parton distributionfunctions, which determine longitudinal momentum distributions. The demonstration byJi [1], Radyushkin [2], and Müller et al. [3], of a formalism to relate the spatial and mo-mentum distributions of the partons allows the exciting possibility of determining spatialdistributions of quarks and gluons in the nucleon as a function of the parton wavelength.These new structure functions, now called generalized parton distributions (GPD), be-came of experimental interest when it was shown [1] that they are accessible throughdeep virtual Compton scattering (DVCS) and its interference with the Bethe-Heitler(BH) process (Fig. 1). The factorization proofs [4, 5] confirmed the connection betweenDVCS and DIS. Diehl et al. [6] showed that the twist-2 and twist-3 contributions in theDVCS-BH interference terms (the first two leading orders in a 1/√Q2 expansion) couldbe extracted independently from the azimuthal-dependence of the helicity-dependentcross section. Burkardt [7] showed that the t-dependence of the GPDs is the Fourierconjugate to the transverse spatial distribution of quarks in the infinite momentum frameas a function of momentum fraction. Ralston and Pire [8], Diehl [9] and Belitsky etal. [10] extended this interpretation to the general case of skewness ξ 6= 0.CURRENT EXPERIMENTAL SITUATIONThese concepts stimulated an intense experimental effort in DVCS. The H1 [11, 12] andZEUS [13] collaborations measured the cross section for xB ≈ 10−3. The HERMES col-laboration measured relative beam-helicity [14] and beam-charge asymmetries [15, 16].Relative beam-helicity [17] and longitudinal target [18] asymmetries were measured atthe Thomas Jefferson National Accelerator Facility (JLab) by the CLAS collaboration.The first dedicated DVCS experiment ran in Hall A at JLab [19]. Helicity-correlatedcross section of electroproduction of photons were measured with high statistical accu-racy as a function of Q2 (Fig. 2).The combination of Compton form factors (CFF) extracted from these data (Fig. 3)was found to be independent of Q2, within uncertainties. This exciting result stronglysupports the twist-2 dominance of the imaginary part of the DVCS amplitude. GPDs canthen be accessed experimentally at the kinematics of JLab.A dedicated DVCS experiment on the neutron (E03-106) followed E00-110. Usinga deuterium target, E03-106 provided the first measurements of DVCS on the neutron,particularly sensitive to the least known GPD E, and DVCS on the deuteron [20]. A firstconstraint on the orbital angular momentum of quarks inside the nucleon (Fig. 4) wasobtained relying on the VGG model of GPDs [21].Deep neutral meson productionThe pi0 electroproduction longitudinal cross section provides an extremely interestingaccess to GPDs. Indeed, if factorization applies, it provides a promising way to perform aflavor separation of GPDs. Moreover, pi0 production probes only the “polarized” GPDsin the nucleon (H˜ and E˜), which contain information about the spatial distribution ofthe quark spin. This complements DVCS measurements, where all GPDs participate.E00-110 measured the pi0 electroproduction cross section at Q2 = 2.3 GeV2 and Eb =5.75 GeV. From the azimuthal dependence of the cross section, 3 interference crosssections (σLT , σT T and σLT ′) and the combination σT + εσL were extracted. E00-110 could not perform an L/T separation of the cross section in order to access thelongitudinal part that is (potentially) related to GPDs. However, in a future approvedexperiment (E07-007 [22]), the σL contribution will be isolated for three different binsin Q2, and therefore we will measure all 5 independent cross sections as a function ofQ2. This will provide, for the first time, a test of factorization for the longitudinal pi0cross section and thus demonstrate (or not) the feasibility of extracting GPD data fromthis interesting channel.The CLAS collaboration has recently published beam spin asymmetries (BSA) for pi0FIGURE 1. DVCS and BH processes: the two interfering contributions to the electroproduction ofphotons.)4DVCS cross section (nb/GeV 2  = 1.9 GeV 2 Q 2  = 1.5 GeV 2 Q (deg)φ-0.0200.0290 180 270 (deg)φ-0.0200.0290 180 270 (deg)φ-0.0200.0290 180 270 (deg)φ-0.0200.0290 180 270-0.04-0.0200.020.04 E00-110Total fitTwist - 2-0.04-0.0200.020.04-0.04-0.0200.020.04-0.04-0.0200.020.04-0.0200.02-0.0300.03 2< t > = - 0.33 GeV  2< t > = - 0.28 GeV  2< t > = - 0.23 GeV  2< t > = - 0.17 GeV)4DVCS cross section (nb/GeVbeam helicity-independentbeam helicity-dependent (deg)φ90 180 270E00-110 2|BH+DVCS| 2|BH| 2 - |BH| 2|BH+DVCS| (deg)φ90 180 270 (deg)φ90 180 270 (deg)φ90 180 270E00-110Total fitTwist - 200.050.1-0.0200.02 2< t > = - 0.33 GeV  2< t > = - 0.28 GeV  2< t > = - 0.23 GeV  2< t > = - 0.17 GeVFIGURE 2. Data and fit to the helicity-dependent d4Σ/dQ2dxBdtdφ , and the helicity-independentd4σ/[dQ2dxBdtdφ ] cross sections, as a function of the azimuthal angle φ between the leptonic andhadronic planes. All bins are at 〈xB〉 = 0.36. Error bars show statistical uncertainties. Solid lines showtotal fits with one-σ statistical error bands. The green line is the |BH|2 contribution to d4σ . The first threerows show the helicity-dependent cross section for values of Q2 = 1.5,1.9 and 2.3 GeV2, respectively.The last row shows the helicity-independent cross section for Q2 = 2.3 GeV2.)2-t (GeV0.15 0.2 0.25 0.3 0.35, E)H~ (H, IIm C012345 2 = 1.5 GeV2Q2 = 1.9 GeV2Q2 = 2.3 GeV2QVGG modelFIGURE 3. Extracted imaginary part of the twist-2 angular harmonic as function of t. Superposedpoints are offset for visual clarity. Their error bars show statistical uncertainties.uJ-1 -0.8 -0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8 1dJ-1-0.8-0.6-0.4-0.2-00.20.40.60.81HERMES Preliminaryp-DVCSJLab Hall An-DVCSGPDs from :Goeke et al., Prog. Part. Nucl. Phys. 47 (2001), 401.Code VGG (Vanderhaeghen, Guichon and Guidal) 0.14± = 0.18 5.0uJ + dJAHLT GPDs [36]Lattice QCDSF (quenched) [40]Lattice QCDSF (unquenched) [41]LHPC Lattice (connected terms) [42]FIGURE 4. Experimental constraint on Ju and Jd quark angular momenta from the present n-DVCSresults [20]. A similar constraint from the p-DVCS target spin asymmetry measured by HERMES, anddifferent lattice QCD based calculations are also shown.electroproduction [23]. Fig. 5 (left) shows the kinematic coverage of the data and theBSA as a function of φ for a typical kinematic bin. The BSA can be written as:BSA =−→σ −←−σ−→σ +←−σ=α sinφ1+β cosφ + γ cos2φ)2 (GeV2 Q1234Bx0.1 0.2 0.3 0.4 0.5-0.0500.050.10.150.2)2-t (GeV0 0.5 1 1.5α-0.0500.050.10.150.2-0.050.1-0.050.1-0.0500.050.10.150.2-0.0500.050.10.150.2-0.0500.050.10.150.2-0.0500.050.10.15-0.0500.050.10.15-0.0500.050.10.15-0.0500.050.10.15-0.0500.050.10.150.2-0.0500.050.10.150.2-0. 500.050.10.150.2FIGURE 5. Kinematic coverage and typical BSA as a function of φ for pi0 electroproduction, asmeasured by the CLAS collaboration [23] (left). The parameter A from a fit by the function Asinφ isshown on the right for each bin in Q2, xB and t.withα =√2ε(1− ε)σLT ′σT + εσLFig. 5 (right) shows the results of the parameter A of a fit of experimental BSA bythe expression Asinφ , which reproduces well the shape of the data. A non-zero BSAindicates a non-zero value of σLT ′ .FUTURE DVCS PROGRAM WITH CEBAF AT 6 GEVA new experiment E07-007 was recently approved with the highest scientific rating (A)by the JLab Program Advisory Committee (PAC-31) and will run in the next 2–3 years.E07-007 will use the important lessons we learned in E00-110 to further test and explorethe potential of DVCS to measure GPDs.In E00-110 we managed to determine the photon electroproduction helicity-independent (unpolarized) cross section. This additional information was not in theinitial goal of the E00-110 experiment, and we were only able to measure it at onesingle value of Q2 = 2.3 GeV2 (Fig. 2). We found that the total cross section was muchlarger than the BH contribution. The excess in the cross section is then coming from boththe interference term (BH–DVCS) and the DVCS2 contribution. These contributionscontain different kinds of GPD combinations. The interference term is proportionalto a linear combination of GPD integrals, whereas the DVCS2 is related to a bilinearcombination of GPD integrals.The harmonic φ structure of the DVCS cross section does not allow the independentdetermination of the BH-DVCS interference and the DVCS2 contributions. Indeed,the interference I and DVCS2 terms have the following harmonic structure (withQ =√Q2):I =i0/Q2 + i1cosϕ/Q+ i2cos2ϕ/Q2 + i3cos3ϕ/QP1P2DVCS2 = d0/Q2 +d1cosϕ/Q3 +d2cos2ϕ/Q4 . (1)The product of the BH propagators reads:P1P2 = 1+p1Qcosϕ +p2Q2cos2ϕ . (2)Reducing to a common denominator (×P1P2), one obtains:P1P2I +P1P2DVCS2 = (i0 +d0)/Q2 +d1p1/2/Q4 + p2d2/2/Q6+[i1/Q+(p1d0+d1)/Q3+(p1d2 + p2d1)/2/Q5]cosϕ+[i2/Q2 +(p2d0 + p1d1/2+d2)/Q4]cos2ϕ+[i3/Q+(p1d2 + p2d1)/2/Q5]cos3ϕ+[p2d2/4/Q6]cos4ϕ . (3)One sees in Eq. (3) that the interference I and the DVCS2 terms mix at leading orderin 1/Q in the azimuthal expansion.Interference and DVCS2 separationE07-007 was approved to measure the photon electroproduction helicity-independentcross section as a function of Q2 and at different incident beam energies. The differentbeam energy dependence of the DVCS2 and BH·DVCS interference term complementthe azimuthal analysis of the cross section in order to provide a complete separation ofthese two contribution.Scaling of the real part of the DVCS amplitudeThe Q2−dependence of these observables will provide a strong scaling test of the realpart of the DVCS amplitude that will complement the one obtained in E00-110 from thehelicity-correlated cross section. Testing scaling on the real part of the DVCS amplitudeis indeed a very stringent check. The imaginary part of the DVCS amplitude accessGPDs along one kinematical line x = ±ξ . In JLab kinematics x ∈ [ξ ,1] and the twist-2 amplitude of DVCS describes the emission and absorption of a quark with differentmomentum fractions. The real part of the DVCS amplitude is related to GPD integralsover their full domain −1 < x < 1. Over the region x ∈ [−ξ ,ξ ] the twist-2 amplitudecorrespond to the emission of a quark-antiquark pair from the initial proton, and in theregion x ∈ [−1,−ξ ] one has emission and reabsorption of antiquarks. Therefore, testingthe scaling properties of GPD integrals tests the twist-2 dominance of DVCS over a widevariety of partonic configurations.Separation of the longitudinal pi0 electroproduction cross sectionIn addition to these fundamental measurements on DVCS, E07-007 will concurrentlymeasure the pi0 electroproduction cross section for different beam energies. We success-fully measured the pi0 electroproduction cross section in E00-110. However, since weonly ran at one incident beam energy, the longitudinal and transverse separation of thecross section could not be done. E07-007 will allow the first separation of the longitudi-nal cross section, using the Rosenbluth technique. A factorization theorem holds for thelongitudinal pi0 electroproduction cross section that relates it, at sufficiently large Q2, toa different flavor combination of GPDs. This channel is an essential element to make aflavor decomposition of GPDs, which is impossible to obtain from DVCS on the protonalone.E07-007 will test the Q2−dependence of the longitudinal cross section and checkif the factorization is applicable at the Q2 values currently accessible experimentally(around Q2∼ 2 GeV2). If this test turns out positive, very interesting and complementaryinformation on GPDs will be available from this channel.E08-025: Rosenbluth-like separation on the neutronAn equivalent DVCS program at 6 GeV using a deuterium target was approvedearlier this year and will run concurrently with E07-007. It will allow to separate theinterference and DVCS2 terms on neutron observables. This will complement E07-007on the proton.12 GEV PROGRAMThe experimental GPD program is at the heart of the scientific motivation of the majorJefferson Lab upgrade to 12 GeV.E12-06-114 [24] is a wide experimental program of DVCS high precision cross-section measurements in Hall A with CEBAF at 12 GeV, enthusiastically approvedby JLab PAC-30. With polarized 6.6, 8.8, and 11 GeV beams incident on the liquidhydrogen target, we will provide a major survey of proton DVCS in almost the entirekinematic range accessible with CEBAF at 12 GeV (Fig. 6).REFERENCES1. X.-D. Ji, Phys. Rev. Lett. 78, 610–613 (1997), hep-ph/9603249.2. A. V. Radyushkin, Phys. Rev. D56, 5524–5557 (1997), hep-ph/9704207.3. D. Mueller, D. Robaschik, B. Geyer, F. M. Dittes, and J. Horejsi, Fortschr. Phys. 42, 101 (1994),hep-ph/9812448.4. J. C. Collins, and A. Freund, Phys. Rev. D59, 074009 (1999), hep-ph/9801262.5. X.-D. Ji, and J. Osborne, Phys. Rev. D58, 094018 (1998), hep-ph/9801260.6. M. Diehl, T. Gousset, B. Pire, and J. P. Ralston, Phys. Lett. B411, 193–202 (1997), hep-ph/9706344.7. M. Burkardt, Phys. Rev. D62, 071503 (2000), hep-ph/0005108.Bjx0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9)2 (GeV2 Q05102<4 GeV2W 11 GeV≤beamUnphysical with E= 6.6 GeVbeamE= 8.8 GeVbeamE= 11.0 GeVbeamE= 5.75 GeVbeamEDVCS measurements in Hall A/JLabFIGURE 6. Approved DVCS kinematics for H(e,e′γ)p measurements in Hall A with 3, 4, and 5pass beams of CEBAF at 12 GeV. The diamond shapes trace the approximate acceptance of the Hall AHigh Resolution Spectrometer in each setting. 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The Generalized Parton Distributions program in Hall A at Jefferson Lab

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