General introduction to GPDs From data to GPDs

General introduction to GPDs From data to GPDs

Operator in Operator in space coordinates Structure function in Structure function in momentum coordinates ep  eX ep  ep ep  ep  Diagramme Diagramme Process Process (restricting myself to LT-LO, chiral even, quark sector)

H, H, E, E (x,ξ,t) ~~ Standard Parton Distributions H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~ x Elastic Form Factors  H(x,ξ,t)dx = F(t) (  ξ) x Ji’s sum rule 2J q =  x(H+E)(x,ξ,0)dx (nucleon spin) x+ξx-ξ t γ, π, ρ, ω… -2ξ : don’t appear in DIS : NEW INFORMATION

0 t=0 1 DDs « D-term » x,b GPDs Pion cloud Long.mom./trans.pos. correlations F (t), G (t) 1,2 A,PS q(x),  q(x) R (t),R  (t) A V J q  (z)

 p p’  H,E,H,E ~~ x t Deconvolution needed ! x : mute variable xx H q (x, ,t) but only  and t accessible experimentally dd d  dt B ~A H (x, ,t) q x-ix-i dxdx +B E (x, ,t) q x-ix-i dx +… == x B 1-x /2 B t=(p-p ’) 2 x = x B ! /2

GPD and DVCS Cross-section measurement and beam charge asymmetry (ReT) integrate GPDs over x Beam or target spin asymmetry contain only ImT, therefore GPDs at x =  and  (at leading order:)

General introduction to GPDs From data to GPDs

The experimental actors p-DVCS BSAs,lTSAs p-DVCS X-sec Hall BHall A JLab CERN COMPASS Vector mesons DVCS p-DVCS X-sec,BCA p-DVCS BSA,BCA, tTSA,lTSA H1/ZEUSHERMES DESY

In general, 8 GPD quantities accessible (Compton Form Factors) DVCS : golden Channel Anticipated Leading Twist dominance already at low Q 2

Model-independent fit, at fixed x B, t and Q 2, of DVCS observables with MINUIT + MINOS Given the well-established LT-LO DVCS+BH amplitude DVCSBethe-Heitler GPDs 7 unknowns (the CFFs), non-linear problem, strong correlations M.G. EPJA 37 (2008) 319M.G. & H. Moutarde, EPJA 42 (2009) 71) M.G. PLB 689 (2010) 156M.G. arXiv: [hep-ph] (acc.PLB) Only 3 CFFs come out from the fit with finite error bars: H Im, H Im and H Re ~

* « Shrinkage » of H Im * H Im >H Re As energy increases: JLab x B =0.36,Q 2 =2.3 *Different t-behavior for H Im &H Re (model dependent Fit of D. Muller, K. Kumericki Hep-ph HERMES H Im H Re H Im H Re x B =0.09,Q 2 =2.5

x B dependence at fixed t of H Im VGG prediction

x B -dependence at fixed t lTSAs Fitting the CLAS & HERMES lTSAs: of H Im ~ VGG prediction Fit with 7 CFFs (boundaries 5xVGG CFFs) Fit with 7 CFFs (boundaries 3xVGG CFFs) JLab HERMES

VGG prediction Fit with 7 CFFs (boundaries 5xVGG CFFs) Fit with 7 CFFs (boundaries 3xVGG CFFs) Fit with ONLY H and H ~ t-dependence at fixed x B of H Im & H Im ~ Axial charge more concentrated than electromagnetic charge ?

First CFFs model independent fits (leading-twist/leading order approximation); “Minimal theoretical input” Procedure tested by Monte-Carlo Procedure is working on real data; extraction of H Im and H Re at JLab (cross sections) and HERMES (asymmetries) energies Relatively large uncertainties on extracted CFFs (due to lack of observables -and precision on data-) Introducing more theoretical input will reduce uncertainties (but model dependency) Large flow of new observables and data expected soon; will bring much more experimental constraints to extract CFFs with minimum theoretical input