Michel Guidal (IPN Orsay) NPQCD2015, 21/04/2015 GPD phenomenology Michel Guidal (IPN Orsay)

y x z ep a eX (DIS) (Parton Distribution Functions: PDF)

ep a eX (DIS) ep a ep (elastic) y z (Parton Distribution x Functions: PDF) y x z ep a ep (elastic) (Form Factors: FFs)

ep a eX (DIS) ep a ep (elastic) ep a epg (DVCS) y z (Parton Distribution Functions: PDF) y x z ep a ep (elastic) (Form Factors: FFs) x z ep a epg (DVCS)

ep a eX (DIS) ep a ep (elastic) ep a epg (DVCS) ep a epX (SIDIS) y z (Parton Distribution Functions: PDF) y x z ep a ep (elastic) (Form Factors: FFs) x z ep a epg (DVCS) (Generalized Parton Distributions: GPDs) ep a epX (SIDIS) z (Transverse Momentum Dependent PDFs: TMDs) x

In the light-cone frame: x+x : relative longitudinal momentum of initial quark x-x : relative longitudinal momentum of final quark t=D2 : total squared momentum transfer to the nucleon (transverse component: )

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

(x,x ) dependence : Double Distributions (Radyushkin) Hq(x,x,0)~ db da d(x-b-ax)DDq(a,b)

(x,x ) dependence : Double Distributions (Radyushkin) 22b+1G(2b+1)(1-|b|)2b+1 Hq(x,x,0)~ db da d(x-b-ax)DDq(a,b) With : and DDq(a,b,t)=hb(a,b) q(b) hb(a,b)=G(2b+2)[(1-|b|)2-a2]b

(x,x,t ) dependence : Reggeized Double Distributions (Radyushkin, Muller, Polyakov,VdH, M.G.) DDq(a,b,t)=q (b) hb(a,b)b-a’(1-b)t x b (GeV-1) Hu(x,b ) y z Satisfies Form Factors sum rule and polynomiality

proton electromagnetic form factors HqDD(x,0,t) q(x) x-a’1(1-x)t EqDD(x,0,t) q(x)(1-x)hqx-a’2(1-x)t

DVCS data (until a few weeks ago) JLab Hall A DVCS B-pol. X-section DVCS unpol. X-section JLab CLAS DVCS BSA DVCS lTSA HERMES DVCS BSA,lTSA,tTSA,BCA

In general, 8 GPD quantities accessible (Compton Form Factors) with

Given the well-established LT-LO DVCS+BH amplitude Bethe-Heitler GPDs Can one recover the 8 CFFs from the DVCS observables? Obs= Amp(DVCS+BH) CFFs Two (quasi-) model-independent approaches to extract, at fixed xB, t and Q2 (« local » fitting), the CFFs from the DVCS observables

1/ «Brute force » fitting c2 minimization (with MINUIT + MINOS) of the available DVCS observables at a given xB, t and Q2 point by varying the CFFs within a limited hyper-space (e.g. 5xVGG) The problem can be (largely) underconstrained: JLab Hall A: pol. and unpol. X-sections JLab CLAS: BSA + TSA 2 constraints and 8 parameters ! However, as some observables are largely dominated by a single or a few CFFs, there is a convergence (i.e. a well-defined minimum c2) for these latter CFFs. The contribution of the non-converging CFF enters in the error bar of the converging ones. For instance (naive): If -10<x<10:

1/ «Brute force » fitting c2 minimization (with MINUIT + MINOS) of the available DVCS observables at a given xB, t and Q2 point by varying the CFFs within a limited hyper-space (e.g. 5xVGG) The problem can be (largely) underconstrained: JLab Hall A: pol. and unpol. X-sections JLab CLAS: BSA + TSA 2 constraints and 8 parameters ! However, as some observables are largely dominated by a single or a few CFFs, there is a convergence (i.e. a well-defined minimum c2) for these latter CFFs. The contribution of the non-converging CFF enters in the error bar of the converging ones. M.G. EPJA 37 (2008) 319 M.G. & H. Moutarde, EPJA 42 (2009) 71 M.G. PLB 689 (2010) 156 M.G. PLB 693 (2010) 17

2/ Mapping and linearization If enough observables measured, one has a system of 8 equations with 8 unknowns Given reasonable approximations (leading-twist dominance, neglect of some 1/Q2 terms,...), the system can be linear (practical for the error propagation) ~ DsLU ~ sinf Im{F1H + x(F1+F2)H -kF2E}df ~ ~ DsUL ~ sinfIm{F1H+x(F1+F2)(H + xB/2E) –xkF2 E+…}df K. Kumericki, D. Mueller, M. Murray, arXiv:1301.1230 hep-ph, arXiv:1302.7308 hep-ph

Other approaches: Assume a functionnal shape and fit some parameters *D. Mueller & K. Kumericki *H. Moutarde *VGG by the HERMES and n-DVCS Hall A coll. Les 2 precedentes methodes sont « quasi » independantes de modele, i.e. elles ne necessitent pas de supposer une forme fonctionelle avec des parametres a fitter. Les methodes qui sont sur ce slide supposent que les GPDs ont déjà une forme particuliere.

Hall A : s & DsLU , xB=0.36,Q2=2.3,t=.17,.23,.28,.33 c2=1.01 c2=0.92

unpol.sec.eff. + beam pol.sec.eff. c2 minimization Avec « ma » methode, extraction obtenue pour Him en fittant les sec.eff. (pol. et non-pol.) du Hall A c2 minimization

unpol.sec.eff. + beam pol.sec.eff. beam spin asym. + long. pol. tar. asym Avec « ma » methode, extraction obtenue pour Him en fittant les BSA et les TSA (Shifeng) de CLAS c2 minimization

unpol.sec.eff. + beam pol.sec.eff. beam spin asym. + long. pol. tar. asym beam charge asym. + beam spin asym … Avec la methode de KM et la mienne, extraction obtenue pour Him en fittant les asymetries d’HERMES. c2 minimization linearization

unpol.sec.eff. + beam pol.sec.eff. beam spin asym. + long. pol. tar. asym beam charge asym. + beam spin asym … Compilation de toutes les methodes c2 minimization linearization Moutarde 10 model/fit VGG model KM10 model/fit

the t-slope reflects the size of the probed object (Fourier transf.) HIm: (~H(x,x,t) ) the t-slope reflects the size of the probed object (Fourier transf.) Resultats pour HtildeIm The sea quarks (low x) spread to the periphery of the nucleon while the valence quarks (large x) remain in the center

Resultats pour HtildeIm ~ The axial charge (~Him) appears to be more « concentrated » than the electromagnetic charge (~Him)

From CFFs to spatial densities How to go from momentum coordinates (t) to space-time coordinates (b) ? (with error propagation) Burkardt (2000) Applying a (model-dependent) “deskewing” factor: and, in a first approach, neglecting the sea contribution

} 1/Smear the data according to their error bar 2/Fit by Aebt 3/Fourier transform (analytically) 4/Obtain a series of Fourier transform as a function of b 5/For each slice in b, obtain a (Gaussian) distribution which is fitted so as to extract the mean and the standard deviation ~1000 times

CLAS data (xB=0.25) “skewed” HIm “deskewed” HIm (fits applied to « deskewed » data) “deskewed” HIm

HERMES data (xB=0.09) “skewed” HIm “deskewed” HIm (fits applied to « deskewed » data) “deskewed” HIm

xB=0.25 xB=0.09

GPDs contain a wealth of information on nucleon structure and dynamics: space-momentum quark correlation, orbital momentum, pion cloud, pressure forces within the nucleon,…

GPDs contain a wealth of information on nucleon structure and dynamics: space-momentum quark correlation, orbital momentum, pion cloud, pressure forces within the nucleon,… Many more DVCS data coming with JLab 6 GeV: Cross sections on p, BSA for DVCS on He4,…

To be published in 2015, on ArXiv CLAS (courtesy H.S. Jo) To be published in 2015, on ArXiv

GPDs contain a wealth of information on nucleon structure and dynamics: space-momentum quark correlation, orbital momentum, pion cloud, pressure forces within the nucleon,… Many more DVCS data coming with JLab 6 GeV: Cross sections on p, BSA for DVCS on He4,… DVMP data also provide access to GPDs: PS mesons transversity GPDs,… First new insights on nucleon structure already emerging from current data with new fitting algorithms Large flow of new observables and data expected soon (JLab6,JLab12,COMPASS) will allow a precise nucleon tomography in the valence region (Other DVCS-related processes planned for JLab 12 GeV (TCS, DDVCS) Theory developments: higher twists, target mass corrections, NLO corrections, …

Double beam-target spin asym. Long. target spin asym. Double beam-target spin asym. CLAS (courtesy S. Niccolai) To be published in 2014

Mass corrections in propagators – In lightcone frame, q and P collinear along z-axis using lightcone vectors pµ, nµ along + and – z direction and ξ and ξ' = + component of ∆ and q ~ ~ ~ – Kinematical variables: experimentaly accessible Light-cone momentum fraction, include mass terms At asymptotic limit:

Gauge invariance correction We have: qµHµνLO = ½ (∆⊥)κHκνLO and q'νHµνLO = – ½ (∆⊥)λHκλLO Restore gauge invariance: qµHµν = qνHµν ≡ 0 twist 2 vector part

Hard scattering amplitude of TCS - - - - - -

1) The HERMES Recoil detector. A. Airapetian et al, e-Print: arXiv:1302.6092 2) Beam-helicity asymmetry arising from deeply virtual Compton scattering measured with kinematically complete event reconstruction A. Airapetian et al, JHEP10(2012)042 3) Beam-helicity and beam-charge asymmetries associated with deeply virtual Compton scattering on the unpolarised proton A. Airapetian et al, JHEP 07 (2012) 032 Many analysis at JLab in progress (CLAS X-sections and lTSA, new Hall A X-sections at different beam energies, proton and neutron channels,… with publications planned for 2013/2014

HIm:the t-slope reflects the size of the probed object (Fourier transf The sea quarks (low x) spread to the periphery of the nucleon while the valence quarks (large x) remain in the center

~ The axial charge (~Him) appears to be more « concentrated » than the electromagnetic charge (~Him)

~ New A_UL and A_LL CLAS data Confirms the apparent Phys.Rev. D91 (2015) 5, 052014 Les nouvelles donnees de CLAS pour A_UL et A_LL. Confirms the apparent « xB-independence » and flatter « t-dependence » of HIm ~

~ Im{Hp, Hp, Ep} ~ ~ Im{Hp, Hp} Re{Hp, Hp} Im{Hp, Ep} f g e’ e N’ leptonic plane hadronic plane N’ e’ e x= xB/(2-xB) k=-t/4M2 DsLU ~ sinf Im{F1H + x(F1+F2)H -kF2E}df ~ Polarized beam, unpolarized target (BSA) : Im{Hp, Hp, Ep} Unpolarized beam, longitudinal target (lTSA) : DsUL ~ sinfIm{F1H+x(F1+F2)(H + xB/2E) –xkF2 E+…}df ~ Im{Hp, Hp} nDVCS complements pDVCS for the different sensitivity to GPDs of the various observables Polarized beam, longitudinal target (BlTSA) : DsLL ~ (A+Bcosf)Re{F1H+x(F1+F2)(H + xB/2E)…}df ~ Re{Hp, Hp} Unpolarized beam, transverse target (tTSA) : DsUT ~ cosfIm{k(F2H – F1E) + ….. }df Im{Hp, Ep}