General introduction to GPDs From data to GPDs

General introduction to GPDs From data to GPDs

General introduction to GPDs From data to GPDs

Process Diagramme Structure function in Operator in momentum coordinates space coordinates ep a e. X ep a epg (restricting myself to LT-LO, chiral even, quark sector)

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

Pion cloud Long. mom. /trans. pos. correlations F 1, 2 (t), GA, PS(t) x, b « D-term » GPDs F(z) DDs <x 0 > t=0 <x 1 > Jq <x -1> RA (t), RV (t) q(x), D q(x)

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

GPD and DVCS (at leading order: ) Cross-section measurement and beam charge asymmetry (Re. T) integrate GPDs over x Beam or target spin asymmetry contain only Im. T, therefore GPDs at x = x and -x

General introduction to GPDs From data to GPDs

The experimental actors DESY HERMES H 1/ZEUS p-DVCS BSA, BCA, t. TSA, l. TSA p-DVCS X-sec, BCA CERN JLab Hall A Hall B p-DVCS X-sec p-DVCS BSAs, l. TSAs COMPASS Vector mesons DVCS

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

Given the well-established LT-LO DVCS+BH amplitude DVCS Bethe-Heitler GPDs Model-independent fit, at fixed x. B, t and Q 2, of DVCS observables with MINUIT + MINOS 7 unknowns (the CFFs), non-linear problem, strong correlations Only 3 CFFs come out from the fit with finite error bars: ~ HIm , HIm and HRe M. G. EPJA 37 (2008) 319 M. G. & H. Moutarde, EPJA 42 (2009) 71) M. G. PLB 689 (2010) 156 M. G. ar. Xiv: 1005. 4922 [hep-ph] (acc. PLB)

HIm JLab HRe x. B=0. 36, Q 2=2. 3 (model dependent Fit of D. Muller, K. Kumericki Hep-ph 0904. 0458 As energy increases: HIm HERMES x. B=0. 09, Q 2=2. 5 HRe * « Shrinkage » of HIm * HIm>HRe *Different t-behavior for HIm&HRe

x. B dependence at fixed t of HIm VGG prediction

Fitting the CLAS & HERMES l. TSAs: l. TSAs x. B-dependence at fixed t ~ of HIm HERMES Fit with 7 CFFs (boundaries 5 x. VGG CFFs) Fit with 7 CFFs (boundaries 3 x. VGG CFFs) JLab VGG prediction

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

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 HIm and HRe 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