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Probing Generalized Parton Distributions (GPDs) in Exclusive Processes

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

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Probing Generalized Parton Distributions (GPDs) in Exclusive Processes

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  1. 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

  2. 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 1960-1990: What is the internal structure of the proton? • Deeply inelastic scattering • discover quarks in ‘scaling’ of structure functions • quark longitudinal momentum distribution • quark helicity distribution Nobel prize 1990 - J. Friedman, H. Kendall, R. Taylor Today: How are these representations of the proton, form factors and quark distributions, connected?

  3. .. X. Ji, D. Muller, A. Radyushkin .. A. Belitsky and D. Muller, Nucl.Phys.A711(2002)118 (Infinite momentum frame) GPDs connect form factors and parton distribution Quark longitudinal momentum & helicity distributions Proton form factors, transverse charge & current distributions Form factors, parton distributions, and GPDs

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

  5. x Link to DIS at =t=0 = - - q H ( x , 0 , 0 ) q ( x ), q ( x ) ~ = D D - q ( x , 0 , 0 ) q ( x ), q ( x ) H ~ ~ x q q q q H , E , H , E ( x , , t ) Access to quark angular momentum (Ji’s sum rule) [ ] 1 1 1 ò = - JG = x + x q q q J xdx H ( x , , 0 ) E ( x , , 0 ) 2 2 - 1 X. Ji, Phy.Rev.Lett.78,610(1997) Link to DIS and Elastic Form Factors Link to form factors (sum rules) ] [ 1 å ò x = q dx H ( x , , t ) F1 ( t ) Dirac FF q ] [ 1 å ò x = q dx E ( x , , t ) F2 ( t ) Pauli FF q 1 1 ~ ~ ò ò x = x = q q dx H ( x , , t ) G ( t ) , dx E ( x , , t ) G ( t ) , , A q P q - - 1 1

  6. DIS only measures at x=0 Quark distribution q(x) Accessed by beam/target spin asymmetry -q(-x) Accessed by cross sections t=0 Modeling Generalized Parton Distributions

  7. 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 scaling cross section for photons dominates at high Q2 over meson production.

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

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

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

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

  12. DVMP CLAS • ro, w production at W > 2 GeV, Q2 = 1.0 - 4.5 GeV2 • p0/h, p+production New equipment, full reconstruction of final state The JLab Program @ 6 GeV • DVCS CLAS and Hall A Full reconstruction of final state ep epg ALU,Dsfor 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

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

  14. Quark distributions in transverse coordinates ep epg* e+e- DDVCS:Allows access to x = x kinematics DDVCS: Hard baryon spectroscopyep egD, (egN*) 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

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

  16. 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

  17. 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

  18. 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

  19. 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

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

  21. <xB> = 0.35 <-t> = 0.30 sL stot sT Deeply Virtual r0 Production at 11 GeV CLAS++ • 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

  22. L=1035cm-2s-1 2000hrs sL dominance DQ2=1 Q2= 5GeV2, -t = 0.5GeV2 Dt = 0.2 K. Goeke, M.V. Polyakov, M. Vanderhaeghen CLAS++ - r0/wproduction with transverse target 2 D (Im(AB*))/p Asymmetry depends linearly on the GPDE,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) w has similar sensitivity to proton quark spin

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

  24. 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

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

  26. 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.

  27. 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.

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

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

  30. ~ N N = F1H+ (F1+F2) - F2E H ALU = sinf D • Dominant contribution to H is Im(H) 1 D = [4(1-xB)( + H H* B (2-xB)2 V.Korotkov, W.D.Novak NPA711 (2002) 175 ~ ~ - (x2 +(2-xB)2 )EE* - x2 ] B B E* E xB 1 - xB ~ ~ (2-xB) = 4 ( ImH )2 + …. H H*) - x2(HE* + EH* + .. ) ( 2 - xB )2 t t t 4M2 4M2 4M2 At small xB, t, ALU and N measureIm(H(x,x,t)) from whichSe2(Hq(x,x,t)-Hq(-x,x,t)) may be extracted q Extraction of GPD Hq(x,x,t) @ small t, xB

  31. Partial wave expansion techniques (Polyakov, A. Shuvaev). • generalized quark distributions given by sum over t-channel exchanges dxxH (x,x,t) = [B12(t)- (B12(t) -2B10(t))x2] First moment: S H(x,x,t) =(1-x2) An(x,t)C3/2 (x) n From Ji’s sum rule: n=1 1 3 6 5 6 5 JQ = (B10(0) + C10(0)) JQ can be extracted from S-wave exchange in t-channel! 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

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

  33. g* g D eeply V irtual C ompton S cattering ( DVCS ) xB g x = 2 - xB (in the Bjorken regime) t 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) .. Deeply Virtual Exclusive Processes Inclusive Scattering Forward Compton Scattering q,Dq q,Dq q = 0

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

  35. H, E M = r, w H, E M = p, h, K 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 DVMP DVCS 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 • In hard scattering, photons dominate at high Q2 Need to isolate g*L

  36. 2001/2002 data E=5.75GeV sinf sinf AUL AUL not for distribution 2001/2002 data E=5.75GeV g,p0 sinf AUL xB (25% data sample)

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

  38. CLAS 4.3GeV Coverage for deeply virtual exclusive experiments

  39. (taken through a low resolution microscope) How do we obtain model- independent information? quark spin valence quarks meson cloud In DIS experiments we probe one-dimensional projections of the nucleon quark longitudinal/ transverse momentum sea quarks orbital angular momentum correlations Longitudinal quark momentum and helicity distribution We need to map out the full nucleon wave function to understand the internal dynamics q + q q - q x 1 0.5 0 eliminate ? Snapshot of a Nucleon

  40. 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.

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