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Marc Vanderhaeghen College of William & Mary / JLab

Report from the GPD workshop. Marc Vanderhaeghen College of William & Mary / JLab. QCD and Hadron Physics Town Meeting Rutgers, January 12-14, 2007. GPD workshop, Univ. Maryland, Oct 29-30, 2006. “Extraction” of GPDs from data. What has been done

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Marc Vanderhaeghen College of William & Mary / JLab

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  1. Report from the GPD workshop Marc Vanderhaeghen College of William & Mary / JLab QCD and Hadron Physics Town Meeting Rutgers, January 12-14, 2007

  2. GPD workshop, Univ. Maryland, Oct 29-30, 2006 “Extraction” of GPDs from data What has been done very encouraging first experimental results coming out from JLab 6 GeV (and HERMES) where the analysis techniques are developed/tested Future facilities JLab @ 12 GeV (valence quark structure of nucleon)and EIC (gluon imaging) are ultimate facilities for full study / definite extraction white paper in progress

  3. Generalized Parton Distributions * Qhard2 large t = Δ2 low –t process : -t << Qhard2 Ji , Radyushkin (1996) x + ξ x - ξ P - Δ/2 P + Δ/2 GPD (x, ξ ,t) (x + ξ) and(x - ξ): longitudinal momentum fractions of quarks at large Q2 : QCD factorizationtheorem hard exclusive process can be described by 4 transitions(GPDs) : ~ Vector :H (x, ξ ,t) Tensor :E (x, ξ ,t) Axial-Vector :H (x, ξ ,t) Pseudoscalar :E (x, ξ ,t) ~

  4. Δ P - Δ/2 P + Δ/2 known information on GPDs forward limit : ordinaryparton distributions unpolarized quark distr polarized quark distr : do NOT appear in DIS new information first moments : nucleonelectroweak form factors Dirac Pauli axial ξ independence : Lorentz invariance pseudo-scalar

  5. Why GPDs are interesting Unique tool to explore the internal landscape of the nucleon : 3D quark/gluon imaging of nucleon Access to static properties : constrained (sum rules) by precision measurements of charge/magnetization orbital angular momentum carried by quarks

  6. GPDs : 3D quark/gluon imaging of nucleon Fourier transform of GPDs : simultaneous distributions of quarks w.r.t. longitudinal momentum x P and transverse positionb ( Burkardt ) theoretical parametrization needed : double distributions, dual param. (Guzey), conformal param. (Müller)

  7. Generalized Parton Distributions yield 3-dim quark structure of nucleon Elastic Scattering transverse quark distribution in Coordinate space DIS longitudinal quark distribution in momentum space DES (GPDs) Fully-correlated quark distribution in both coordinate and momentum space

  8. electromagnetic form factors PROTON NEUTRON world data (2006) modified Regge GPD parametrization Regge GPD parametrization

  9. GPDs : transverse image of the nucleon (tomography) Hu(x, b? ) x b?(fm)

  10. orbital angular momentumcarried by quarks : solving thespin puzzle with Ji (1997) evaluated at μ2 = 2.5 GeV2

  11. t g* g,M,... x~xB x ~ ~ H,E,H,E p p’ Beam or target spin asymmetries contain only ImT, i.e. GPDs at x = x and -x Cross sections and charge asymmetries measurements (ReT) Integral of GPDs over x link GPDs and observables

  12. Ds 2s ep epg s+ - s- s+ + s- A = = Polarized beam, unpolarized target: ~ ~ x = xB/(2-xB) DsLU~ sinf{F1H+ x(F1+F2)H+kF2E}df H(x,x,t),H(x,x,t), E(x,x,t) k = -t/4M2 (BSA) Kinematical suppression Unpolarized beam, long. pol. target: ~ ~ H, H DsUL~ sinf{F1H+x(F1+F2)(H+ … }df (l)TSA Unpolarized beam, trans. pol. target: H, E DsUT~ sinf{k(F2H – F1E) + …..}df (t)TSA extracting GPDs from data global analysis : X-sec, asymm, (p,n), (g,M)

  13. DVCS : beam spin asymmetry DVCS Bethe-Heitler ALU ~ (BH) * Im(DVCS) * sin Φ Process under theoretical control including twist-3 corrections Extract twist-2 component and map out GPDs at x = ξ curves : twist-2 + twist-3 HERMES, JLab

  14. Bethe-Heitler DVCS on protonJLab/Hall A @ 6 GeV DVCS GPDs Difference of polarized cross sections Unpolarized cross sections thesis C. Muñoz-Camacho (Saclay), A. Camsonne (Clermont) : 2006

  15. DVCS on proton : JLab/Hall A @ 6 GeV • Twist-2terms dominate the cross section and are independent ofQ2in the explored kinematical domain • The contribution to the cross section oftwist-3terms issmalland isindependent of Q2in the limit of error bars Strong indication in favor of factorization already from Q2=2 GeV2 in the valence region

  16. DVCS cross section on proton :JLab/CLAS @ 6 GeV thesis H.S. Jo (Orsay) 0.2<-t<0.4 0.4<-t<0.6 0.09<-t<0.2 PRELIMINARY 0.6<-t<1 1<-t<1.5 1.5<-t<2

  17. DVCS on neutron Voutier, thesis M. Mazouz (Grenoble) 0 because F1(t) is small 0 because of cancelation of u and d quarks n-DVCSgives access to the least known and constrained GPD,E JLab /Hall A (E03-106) : preliminary data

  18. High xB only reachable with high luminosity H1, ZEUS Upgraded JLab has complementary & unique capabilities Large phase space(x,t,Q2) and High luminosity required Valence region Sea/gluon region EIC JLab12 JLab Upgrade

  19. e p epg L = 1x1035 T = 2000 hrs DQ2 = 1 GeV2 Dx = 0.05 exclusive DVCS : BSA @ JLab 12 GeV Projected results E = 11 GeV DsLU~sinfIm{F1H+..}df Selected Kinematics Avakian

  20. Projected precision in extractionof GPD H at x = ξ spatial image Projected results upgraded CLAS @ JLab12GeV Avakian, Weiss

  21. L = 2x1035 cm-2s-1 T = 1000 hrs DQ2 = 1GeV2 Dx = 0.05 e p epg CLASexclusive DVCS data PRL97, 072002 (2006) exclusive DVCS on longitudinaltarget @ JLab 12 GeV Projected results Longitudinally polarized target ~ Ds~sinfIm{F1H+x(F1+F2)H...}df

  22. Projected results e p epg E = 11 GeV Q2=2.2 GeV2, xB = 0.25, -t = 0.5GeV2 • Asymmetry highly sensitive to the u-quark contributions to proton spin. exclusive DVCS on transversetarget @ JLab 12 GeV Transverse polarized target Ds ~ sinfIm{k1(F2H– F1E) +…}df AUTx Target polarization in scattering plane AUTy Target polarization perpedicular to scattering plane Avakian

  23. Q2=5 GeV2 exclusive ρ0 production on transversetarget 2D (Im(AB*))/p T AUT = - |A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2 A ~ 2Hu + Hd r0 B ~ 2Eu + Ed Projected results A~ Hu - Hd B ~ Eu - Ed r+ r0 Eu, Ed needed for angular momentum sum rule. data Goeke, Polyakov, Vdh (2001)

  24. ≤ ≤ ­ small x : Gluon imaging of proton exclusive J/Ψ production : unique tool to access gluon GPDs data t-dependence maps transverse spatial distribution of gluons in proton Frankfurt, Strikman, Weiss (2005)

  25. Gluonic transverse size of proton : x dependence gluonic transverse size increases with decreasing x Pion cloud contributes for x < mπ/MN logarithmic growth for very small x Strikman, Weiss (2003)

  26. Feasibility studies with collider (eRHIC) HE setup: e+/-(10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s-1 38 pb-1/day LE setup: e+/-( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s-1 13 pb-1/day Precision of DVCS unpolarized cross sections data for one out of 6 Q2 intervals (8 < Q2 < 15 GeV2) σ(γ*p →γ p) [nb] <Q2> = 10.4 GeV2 Projected results W[GeV] • eRHIC measurements of cross section will provide significant constraints and significantly extend the range towards small W Sandacz

  27. GPDs depend on 3 variables (x,ξ,t) and only 2 are experimentally accessible (ξ,t): extraction involves -> synergy exp / phenom. / lattice QCD Need to measure over a large phase space several channels and observables which mutually constrain the GPDs parametrizations Very encouraging first experimental results coming out from JLab 6 GeV (twist-2 dominance, first constraints on GPD models, first –very preliminary- extractions of Ju, Jd,… ) Ultimate facilities :JLab@12 GeV(valence quarkregion) andEIC(gluonsandsea quarkregion) Summary

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