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Generalized Parton Distributions

Generalized Parton Distributions. Duality'05, 08/06/05. M. Guidal, IPN Orsay. 1/ Generalized Parton Distributions. H,E( x , x , t ) H,E( x , x , t ). ~. ~. GPDs. (Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt). t= D 2. g*. g,M,. -2x. x+ x. x- x. p - D /2.

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Generalized Parton Distributions

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  1. Generalized Parton Distributions Duality'05, 08/06/05 M. Guidal, IPN Orsay

  2. 1/ Generalized Parton Distributions

  3. H,E(x,x,t) H,E(x,x,t) ~ ~ GPDs (Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt) t=D2 g* g,M,... -2x x+x x-x p-D/2 p’(=p+D/2) light-cone dominance, nμ(1, 0, 0, -1) / (2 P+)

  4. Large Q2, small t Vector Ms : H,E ~ ~ PS Ms : H,E g : sT lead. twist Mesons : sL H,E(x,x,t) H,E(x,x,t) _ _ ~ ~ {g-[Hq(x,x,t)N(p’)g+N(p) + Eq(x,x,t)N(p’)is+kDkN(p)] 2M _ _ ~ ~ +g5 g-[Hq(x,x,t)N(p’)g+ g5 N(p) +Eq(x,x,t)N(p’)g5D+N(p)]} 2M GPDs (Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt) t=D2 g* g,M,... -2x x+x x-x p-D/2 p’(=p+D/2) light-cone dominance, nμ(1, 0, 0, -1) / (2 P+)

  5. Large Q2, small t Vector Ms : H,E ~ ~ PS Ms : H,E g : sT lead. twist Mesons : sL H,E(x,x,t) H,E(x,x,t) _ _ ~ ~ {g-[Hq(x,x,t)N(p’)g+N(p) + Eq(x,x,t)N(p’)is+kDkN(p)] 2M _ _ ~ ~ +g5 g-[Hq(x,x,t)N(p’)g+ g5 N(p) +Eq(x,x,t)N(p’)g5D+N(p)]} 2M GPDs (Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt) t=D2 g* g,M,... -2x x+x x-x p-D/2 p’(=p+D/2) light-cone dominance, nμ(1, 0, 0, -1) / (2 P+)

  6. t “Ordinary” parton distributions Elastic form factors Ji’s sum rule 2Jq =  x(H+E)(x,ξ,0)dx x x (nucleon spin)  H(x,ξ,t)dx = F(t)( ξ) H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~ x +1 -1 -ξ 0 ξ : do NOT appear in DISNEW INFORMATION quark distribution anti-quark distribution q q distribution amplitude γ, π, ρ, ω… -2ξ x+ξ x-ξ ~ ~ H, H, E, E (x,ξ,t)

  7. t g* x~xB g,M,... x ~ ~ H,E,H,E p p’ Beam or target spin asymmetry contain only ImT, therefore GPDs at x = x and -x Cross-section measurement and beam charge asymmetry (ReT) integrate GPDs over x (M. Vanderhaeghen)

  8. Extensions RCS : gp->gp (intermediate t)(Radyushkin, Dihl, Feldman, Jakob, Kroll) tDVCS : gp->pg* (e+e-) (Berger, Pire, Diehl,...) tDDVCS : ep->epg* (e+e-) (M.G., Vanderhaeghen, Belitsky, Muller,...) sDDVCS : ep->ep (Vanderhaeghen, Gorschtein,...) _ IDVCS : pp->gg (Freund, Radyushkin,Shaeffer,Weiss) DVCS : ep->eDg(Frankfurt, Polyakov, Strikman, Vanderhaeghen) N-DVCS : eA->eAg (Scopetta, Pire, Cano, Polyakov, Muller, Kirschner, Berger....) Hybrids, pentaquarks,... (Pire, Anikin,Teryaev,...)

  9. DES: finite Q2 corrections (real world ≠ Bjorken limit) GPD evolution O (1/Q) O(1/Q2) Dependence on factorization scale μ : Kernel known to NLO (here for DVCS) • Gauge fixing term • Twist-3: contribution from γ*L may be expressed in terms of derivatives of (twist-2) GPDs. • - Other contributions such as small (but measureable effect). • “Trivial” kinematical corrections • Quark transverse momentum effects (modification of quark propagator) • Other twist-4 ……

  10. H(x,0,b )=FT H(x,0,t) (Burkhardt) 2/ Study on the (x,t) correlation of the GPDs (in coll. with M. Vanderhaeghen, A. Radyushkin & M. Polyakov)

  11. GPDs in impact parameter space (Belitsky) y z x The GPDs contain information on the longitudinalAND transversedistributions of the partons in the nucleon (femto-graphy of the nucleon) 3-D picture of the nucleon

  12. evaluate for ξ = 0 : model and LOW -t ( -t < 1 GeV2 ) : Regge model Goeke, Polyakov, Vanderhaeghen (2001) Regge trajectory : valence model for E t = 0 : t ≠ 0 : 2 free parameters : a’1,a’2 Fit 4 form factors : G E,Mp,n GPDs : t dependence ( small –t )

  13. 1 0 proton & neutron charge radii r 21,p =-6a’ lnx(euuv+eddv)dx F1u = uv(x)1/(x a’t)dx GPV Regge model experiment Regge slope

  14. proton electromagnetic form factors GPV Regge model forward parton distributions atm2 = 1 GeV2 (MRST2002 NNLO)

  15. neutron electromagnetic form factors GPV Regge model

  16. GPDs : t dependence ( large –t ) 1/ exp(- α΄ t lnx) -> exp(- α΄ (1 – x) t lnx) if q(x)->(1-x)n then FF->1/t(n+1)/2(Drell-Yan-West relation) M. Burkardt (2002) 2/ Large x behavior of E should be different from H : extra (1-x) power hq for q(x) modified Regge model : M.G., Polyakov, Radyushkin, Vanderhaeghen (2004) F1(t)->1/t2, F2(t)->1/t4 (t>>) Hq(x,0,t)=q(x)x-a t=q(x)e-a t ln(x) Large t power behavior is fixed by large x (->1) behavior if q(x) ~ (1-x)n then FF->1/t(n+1)

  17. proton electromagnetic form factors GPRV modified Regge model GPV Regge model a’ = 1.105 GeV-2 h u= 1.713 h d= 0.566

  18. neutron electromagnetic form factors GPRV modified Regge model GPV Regge model

  19. proton Dirac & Pauli form factors GPRV modified Regge model GPV Regge model

  20. b x (fm)

  21. N -> Δtransition form factors in large Nc limit GPRV modified Regge model GPV Regge model

  22. quark contribution to proton spin with M1 : valence models for eq(x) : M2 :

  23. orbital angular momentum carried by quarks evaluated at μ2 = 2.5 GeV2

  24. Summary Generalized Parton Distributions (GPDs) x-tcorrelations andnucleon form factors 3 parameters (a’,hu,hd) GPDs describe all existing data (GE,Mp,n) spin of nucleon / lattice QCD

  25. The actors

  26. « DES » in the world JLab(Ee=6 GeV):CLAS/Hall B(2001+2005) and Hall A(2004) HERA (Ee=27 GeV) :HERMES and ZEUS/H1(up to 2006) CERN (Em=200 GeV) :COMPASS(2007 ?)

  27. Bethe-Heitler g e’ e’ e g e g* g* p p’ p p’ The epa epg process DVCS e’ e g g* p p’ GPDs

  28. Energy dependence BH DVCS Calculation (M.G.&M.Vanderhaeghen)

  29. Bethe-Heitler g e’ e’ e g e g* g* p p’ p p’ Interference between the 2 processes : if the electron beam is polarised => beam spin asymmetry The epa epg process DVCS e’ e g g* p p’ GPDs

  30. First observations of DVCS charge asymmetry (HERMES) Magnitude and Q2 dependence of DVCS X-section (H1/ZEUS) All in basic agreement with theoretical predictions First experimental signatures DVCS First observations of DVCS beam asymmetries CLAS HERMES Phys.Rev.Lett.87:182002,2001

  31. 0.15 < xB< 0.4 1.50 < Q2 < 4.5 GeV2 -t < 0.5 GeV2 PRELIMINARY PRELIMINARY 5.75 GeV data(H. Avakian & L. Elhouadrhiri) CLAS/DVCS at 4.8 and 5.75 GeV PRELIMINARY GPD based predictions (BMK) 4.8 GeV data(G. Gavalian)

  32. Mesons σL(ep->epr) ρ γ*L Regge (Laget) Handbag diagram calculation (frozen as) can account for CLAS and HERMES data on σL(ep->epr) W=5.4 GeV GPD (MG-MVdh) Q2(GeV2) CLAS 4.2 GeV data(C. Hadjidakis, hep-ex/0408005) HERMES (27GeV) A. Airapetian et al., EPJC 17

  33. 1 0 proton & neutron charge radii r 21,p =-6a’ lnx(euuv+eddv)dx F1u = uv(x)1/(x a’t)dx GPV Regge model experiment Regge slope

  34. Trans. Mom. of partons Pion cloud F (t), G (t) k 1,2 A,PS « D-term » 0 <x > GPDs F(z) DDs t=0 -1 <x > q(x),D q(x) 1 <x > J R (t),R (t) q A V

  35. g* t g,M,... x~xB x /2 2 t=(p-p ’) x= B 1-x /2 x B p p’ x = xB ! ds 1 1 2 q q 2 2 H (x,x,t,Q ) E (x,x,t,Q ) dx dx +…. ~ A +B 2 dQ d x dt x-x+ie x-x+ie B -1 -1 Deconvolution needed ! x : mute variable ~ ~ H,E,H,E Hq(x,x,t) but only xand t accessible experimentally

  36. Compton Scattering “DVCS” (Deep Virtual Compton Scattering)

  37. z 0 1 0 1 GPDs probe the nucleon at amplitude level DIS : DES : x x x+x x-x p p’ p p’ H(x,x)~<p|F(x-x)F(x+x)|p ’> q(x)~<p|F(x)F(x)|p ’> x+x x-x x+x x-x x<x : x>x : p’ p p’ p z

  38. y (Belitsky et al.) y Parton Distribution z x Longitudinalmomentum distribution (no information on the transverse localisation) Form Factors z x Transverse localisation of the partons in the nucleon (independentlyof their longitudinal momentum)

  39. [s(x)-s(x)]dx=0 1 1 -1 -1 Nucleon strangeness : F1s _ _ But : F1s (t)= [s(x)-s(x)]/ (x a’t)dx=0 /

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