Probing Generalized Parton Distributions (GPDs) in Exclusive Processes Volker D. Burkert Charles Hyde-Wright Xiangdong Ji Fundamental questions in electron scattering GPD-sensitive results at low energies The dedicated 6 GeV program at Jlab What will we learn about the proton at 12 GeV? Summary V. Burkert, Presentation to PAC23 on Physics at 12 GeV

Fundamental questions in electron scattering? 1950: Does the proton have finite size and structure? Elastic electron-proton scattering the proton is not a point-like particle but has finite size charge and current distribution in the proton, GE/GM Nobel prize 1961- R. Hofstadter Deeply inelastic scattering discover quarks in ‘scaling’ of structure functions quark longitudinal momentum distribution quark helicity distribution 1960-1990: What is the internal structure of the proton? Nobel prize 1990 - J. Friedman, H. Kendall, R. Taylor We can soon celebrate a half century of electron scattering. So, we can ask what are the most fundamental questions that have been addressed in electron scattering. Today: How are these representations of the proton, form factors and quark distributions, connected?

Form factors, parton distributions, and GPDs X. Ji, D. Muller, A. Radyushkin .. Proton form factors, transverse charge & current distributions A. Belitsky and D. Muller, Nucl.Phys.A711(2002)118 .. (Infinite momentum frame) Quark longitudinal momentum & helicity distributions GPDs connect form factors and parton distribution This question has been addressed theoretically by introducing the GPDs, independently by several theorists, most notably by Ji, Muller and Anatoly, and many more joint them during the past 5 years.

GPDs & Deeply Virtual Exclusive Processes Deeply Virtual Compton Scattering (DVCS) t g x = xB 2 - xB (in the Bjorken regime) hard processes H(x,x,t), E(x,x,t),.. x+x x-x These objects can be accessed experimentally in Deeply Virtual Exclusive Processes, most notably in Deeply Virtual Compton Scattering, or DVCS. GPDs are Q2 independent (only QCD evolution) x + x, x-x = longitudinal momentum fraction -t = Fourier conjugate to transverse impact parameter

[ ] ò Link to DIS and Elastic Form Factors [ [ ] ] ò å ò å ò ò ) , ( ~ x E H q Link to DIS at =t=0 ), - D = Link to form factors (sum rules) 1 [ ] ò å dx H q ( x , x , t ) = F1 ( t ) Dirac FF q 1 [ ] ò å [ ] ò - x + - JG = = 1 ) , ( 2 E H xdx J q Access to quark angular momentum (Ji’s sum rule) X. Ji, Phy.Rev.Lett.78,610(1997) dx E q ( x , x , t ) = F2 ( t ) Pauli FF q 1 1 ~ ~ ò dx H q ( x , x , t ) = G ( t ) , ò dx E q ( x , x , t ) = G ( t ) GPD H is reduced to the quark momentum distribution at xi=0, t-0, and H~ to the helicity distribution in this limit. Note that E and E~ have no correspondence in the parton picture. The x-moments of GPD H and E are given by the Dirac, and Pauli form factors, and H~ and E~ by the axial ff and the induced pseudoscalar ff. An important conncetion is made with the total quark angular momentum contribution to the proton spin in Ji's sum rule. A , q P , q - 1 - 1

Modeling Generalized Parton Distributions Quark distribution q(x) -q(-x) DIS only measures at x=0 Accessed by cross sections Accessed by beam/target spin asymmetry t=0 How do GPDs look like? This shows a model representation of GPD H at t=0. H is plotted as a function of x and xi. DIS can access only the slice at xi=0 with the usual quark distirbutions here and the negative antiquark distributions. As we go away from xi=0 we dial into two-parton correlations. With increasing xi the quark's momenta are increasingly different in size and the two quaks look more and more like a quar-anti-quark pair or meson. This is why the shape of this surface changes dramatically.

Scaling cross sections for photon and meson production M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017 1/Q6 g 1/Q6 1/Q4 The experimental tools to access the GPD surfaces are photon production and meson production. The scaling cross sections are shown here. The scaling cross section for photons dominates at high Q2 over meson production.

Access GPDs through DVCS - BH interference Eo = 11 GeV Eo = 6 GeV Eo = 4 GeV BH DVCS (M. Vanderhaeghen, private communication) DVCS/BH comparable, allows asymmetry, cross section measurements d4 dQ2dxBdtd ~ |TDVCS + TBH|2 BH DVCS TBH : determined by Dirac & Pauli form factors TDVCS: determined by GPDs Ds ~ sinfIm{(F1H(x,x,t)+ k1(F1+F2)H(x,x,t)+k2F2E(x,x,t)}df ~ Twist-2: Helicity difference:

Measurement of exclusive DVCS with CLAS GPD analysis of HERA/CLAS/HERMES data in LO/NLO , a = 0.20 for CLAS in LO A. Feund, M. McDermott, M. Strikman, hep-ph/0208160 Beam Spin Asymmetry 1999 data, E=4.2GeV A. Belitsky et al. Phys. Rev. Lett. 87 (2001) a = 0.202 ± 0.028stat ± 0.013sys (twist-2) b = -0.024 ± 0.021stat ± 0.009sys (twist-3) A = asinf + bsin2f Beam spin asymmetry <-t> = 0.19GeV2 <xB>= 0.19 2001/2002 data E=5.75GeV, very preliminary (15% sample) sinf AUL xB = 0.2-0.4 - t = 0.2-0.5 GeV2 <Q2>= 2.2GeV2 <xB> = 0.35 A t (1+t/0.71)2

Measurement of exclusive DVCS with CLAS AUL = sUL-sUL Target single spin asymmetry: e p epg DsUL ~ KImF1H + .. ~ sUL+sUL + - H(x,x,t) Direct access to a - twist-2 b - higher twist Longitudinal target spin asymmetry asinf + bsin2f <xB> = 0.25 <Q2> = 1.6 GeV2 <-t> = 0.25 GeV2 AUL 0.1 -0.1 0.2 0.3 -0.2 0. fg*g(o) 2000 data, E=5.65GeV, 10% sample very preliminary

Exclusive ep epr0 production Compare with GPD formalism and models W=5.4 GeV HERMES (27GeV) xB=0.38 xB=0.31 CLAS (4.3 GeV) Q2 (GeV2) GPD formalism approximately describes data at xB<0.35, Q2 >1.5 GeV2

New equipment, full reconstruction of final state The JLab Program @ 6 GeV New equipment, full reconstruction of final state DVCS CLAS and Hall A Full reconstruction of final state ep epg ALU, Ds for several Q2 bins xB , F, t- dependence Im(TDVCS) Kinematical dependence of DVCS observables and GPDs Leading and higher twist contributions, QCD corrections Modeling of GPDs CLAS DVMP ro, w production at W > 2 GeV, Q2 = 1.0 - 4.5 GeV2 p0/h, p+ production

Kinematics coverage for deeply exclusive experiments no overlap with other existing experiments compete with other experiments ELFE Upgraded CEBAF complementary & unique

The JLab GPD Program @ 12 GeV DVCS: DVCS/BH interference with polarized beam twist-2/3, Q2 evolution linear combination of GPDs Differential cross section moments of GPDs DVCS/BH interference with polarized targets access different combinations of GPDs DVMP: Establish kinematics range where theory is tractable (if not known) Separation of flavor- and spin-dependent GPDs (ro, w, p0,h, K+,0 ) Access Jq contributions at xB >0.15 Quark distributions in transverse coordinates DDVCS: Allows access to x = x kinematics ep epg* e+e- DDVCS: Hard baryon spectroscopy ep egD, (egN*)

DVCS/BH projected for CLAS++ at 11 GeV 972 data points measured simultaneously + high t (not shown) Q2, xB, t ranges measured simultaneously. A(Q2,xB,t) Ds (Q2,xB,t) s (Q2,xB,t)

DVCS with CLAS++ at 11 GeV 2% of all data points that are measured simultaneously. Q2=5.5GeV2 xB = 0.35 -t = 0.25 GeV2 Q2=2.75GeV2 xB = 0.35 -t = 0.25 GeV2

DVCS/BH twist-2 with CLAS++ at 11 GeV Sensitivity to models of GPDs Q2, xB, t ranges measured simultaneously. Measure ALU, Ds and s(DVCS) simultaneously

DVCS/BH Ds interference projected for Hall A E = 11 GeV Q2 = 6 GeV2 xB = 0.37 L=1037cm-2s-1 400 hours MAD spectrometer ECAL @ -12.5o, 300 cm distance SC array @ -7o

DVCS/BH Ds interference projected for Hall A E = 11 GeV Q2 = 7 GeV2 xB = 0.50 L=1037cm-2s-1 400 hours MAD spectrometer ECAL @ -12.5o, 300 cm distance SC array @ -10.5o

Beam spin asymmetry projected data for Hall A Separation of twist-2/twist-3 Ds ~ Asinf + Bsin2f A: twist-2 B: twist-3

CLAS++ Deeply Virtual r0 Production at 11 GeV sL/sT Separation via stot <xB> = 0.35 <-t> = 0.30 sL/sT Separation via ro p+p- decay distribution and SCHC Test the Q2 evolution of sL , sT => factorization Rosenbluth separation => test SCHC assumption other kinematics measured simultaneously

CLAS++ - r0/w production with transverse target 2 D (Im(AB*))/p Asymmetry depends linearly on the GPD E, which enters Ji’s sum rule. At high xB strong sensitivity to u-quark contributions. T AUT = - |A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2 A ~ (euHu - edHd) B ~ (euEu - edEd) K. Goeke, M.V. Polyakov, M. Vanderhaeghen Q2= 5GeV2, DQ2=1 -t = 0.5GeV2 Dt = 0.2 L=1035cm-2s-1 2000hrs sL dominance w has similar sensitivity to proton quark spin

HallC - SHMS & HMS - ep ep+n Expected errors for L/T separation at high Q2: t=tmin

From Observables to GPDs Procedures to extract GPDs from experimental data are currently under intense development. Approximations for certain kinematics (small x, t), allow extraction of dominant GPDs (e.g. H(x,x,t)) directly. Fit parametrizations of GPDs to large sets of data. Constraint by “forward” parton distribution Polynomiality conditions Elastic form factors Meson distribution amplitudes Partial wave expansion techniques. generalized quark distributions given by sum over t-channel exchanges make connection to total quark spin by analysing S- and D-wave exchanges

“Tomographic” Images of the Proton’s Quark Content (Transverse space and IMF) transversely polarized target M. Burkardt NPA711 (2002)127 1 Impact parameter: -t b = T x 0 Extension to x > 0 , M. Diehl, Eur. Phys. J.C25 (2002)223

Summary GPDs uniquely connect the charge & current distributions with the forward quark distributions measured in DIS. Current data demonstrate the applicability of the GPD framework at modest Q2. A program to study the proton GPDs has been developed for the CEBAF 12 GeV upgrade covering a broad range of kinematics and reactions. This program will provide fundamental insights into the internal quark dynamics of the proton.

The program of Deeply Exclusive Experiments at Jefferson Lab is continuing the breakthrough experiments to study the internal nucleon structure at a new level. It has the potential to revolutionize hadronic physics with electromagnetic probes.

Measurement of exclusive DVCS with CLAS Beam/target spin asymmetry 2000 data, E=5.65GeV, 10% sample ALL = N++-N-+-(N+--N--) N+++N-+ +N+--N-- Beam-target double spin asymmetry: e p epg <xB> = 0.25 <Q2> = 1.6 GeV2 <-t> = 0.25 GeV2 0.9 ALL 0.6 Asymmetry dominated by Bethe-Heitler, modulated by DVCS (GPD) (~15%) 0.3 uncorrected data not for distribution fg*g(o) A. Belitsky et al., hep-ph/0112108 xB=0.25, Q2=2GeV2,-t=0.25GeV2

Separated Cross section for ep e p+n Rosenbluth separation for s / s L T x = 0.4-0.5 + many other bins at B -t = 0.2-0.4GeV 2 the same time Measure pp0, ph, KL,.. simultaneously s L s TOT s T

Extraction of GPD Hq(x,x,t) @ small t, xB ~ ALU = sinf t 4M2 N D N = F1H + (F1+F2) - F2E xB (2-xB) Dominant contribution to H is Im(H) [4(1-xB)( H H* ~ H*) - x2(HE* + EH* + .. ) + - (x2 +(2-xB)2 )EE* - x2 ] t 4M2 E E* 1 (2-xB)2 D = B = 4 ( ImH )2 + …. 1 - xB ( 2 - xB )2 V.Korotkov, W.D.Novak NPA711 (2002) 175 At small xB, t, ALU and N measure Im(H(x,x,t)) from which Se2(Hq(x,x,t)-Hq(-x,x,t)) may be extracted q

From Observables to GPDs Procedures to extract GPDs from experimental data are currently under intense development. Fit parametrizations of GPDs to large sets of data. Constraint by “forward” parton distribution Polynomiality conditions Approximations for certain kinematics (small x, t), allow extraction of dominant GPDs (e.g. H(x,x,t)) directly Partial wave expansion techniques (Polyakov, A. Shuvaev). generalized quark distributions given by sum over t-channel exchanges H(x,x,t) = (1-x2) An(x,t)C3/2 (x) S n n=1 dxxH (x,x,t) = [B12(t)- (B12(t) -2B10(t))x2] 1 3 First moment: 6 5 6 5 JQ = (B10(0) + C10(0)) From Ji’s sum rule: JQ can be extracted from S-wave exchange in t-channel!

Holographic Images of Objects An Apple A. Belitsky, B. Mueller, NPA711 (2002) 118 detector The Proton By measuring the t- dependence we may generate a tomographic image of the proton

Deeply Virtual Exclusive Processes Inclusive Scattering Forward Compton Scattering q,Dq q,Dq q = 0 D eeply V irtual C ompton S cattering ( DVCS ) t g x = xB 2 - xB (in the Bjorken regime) g* Probe the internal nucleon dynamics through interferences of amplitudes, H(x,x,t) , E(x,x,t). …. (GPDs) ( D. Muller et al. (1994), X. Ji (1997), A. Radyushkin (1997) ..

ò ò DVCS and GPDs ~ ~ ~ ~ g GPDs : H, E unpolarized , H, E polarized g * ) ( x + P ) ( x - P ò H q (x, x GPD’s , t, Q 2 ) dx e.g. H ( x , t, Q 2 ) = x- x + i e ò H q (x, x , t, Q 2 ) dx = + i p H q ( x , x , t, Q 2 ) x- x imaginary part cross section real part difference d 3 s ~ ~ = f ( H , E , H , E ) dQ 2 dx dt B H q : Probability amplitude for N to emit a parton q with x+ x and N’ to absorb it with x- x .

Access GDPs in Deeply Virtual Exclusive Processes Scaling cross sections for photon and meson production M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017 DVCS DVMP hard gluon hard vertices 1/Q6 1/Q6 N*,D 1/Q4 DVCS depends on all 4 GPDs and u, d quarks DVMP allows separation of un(polarized) H, E (H, E) GPDs, and contributions of u, d quarks g M = r, w H, E M = p, h, K H, E In hard scattering, photons dominate at high Q2 Need to isolate g*L

g,p0 AUL not for distribution xB 2001/2002 data E=5.75GeV sinf AUL 2001/2002 data E=5.75GeV g,p0 AUL sinf xB (25% data sample)

Deeply Virtual Meson Production Final state selects the quark flavors u, d, s => probes the GPD structure complementary to DVCS Filter for spin-(in)dependent GPDs

Coverage for deeply virtual exclusive experiments CLAS 4.3GeV

Snapshot of a Nucleon eliminate ? x (taken through a low resolution microscope) valence quarks sea quarks correlations meson cloud quark spin orbital angular momentum quark longitudinal/ transverse momentum x 1 0.5 In DIS experiments we probe one-dimensional projections of the nucleon Longitudinal quark momentum and helicity distribution q + q q - q How do we obtain model- independent information? We need to map out the full nucleon wave function to understand the internal dynamics

Summary Knowledge of GPDs will allow to construct “tomographic” respresentations of the nucleon’s quark and spin distributions in transverse space and infinite momentum frame. GPDs can be accessed in deeply virtual exclusive processes at moderately high Q2. Broad theoretical support is available to extract the fundamental physics. DVCS + DVMP (r, w) give access to the total quark contributions to the nucleon spin. A broad program for DVCS and DVMP is proposed for Jlab covering a wide range of kinematics in several channels, largely inaccessible at other labs. The upgrade energy of 12 GeV allows to reach high Q2. We can make use of asymmetry and cross section measurements to determine GPDs. Data from zero’th generation experiments show feasibility of the program.