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M. Guidal, IPN Orsay

Varenna , 05/07/2011. Lecture 1: Deep Virtual Compton Scattering: From data to GPDs (CFFs). M. Guidal, IPN Orsay. A few basic definitions/features of GPDs. Extracting the GPDs (CFFs). Review of the data (JLab, HERMES). ~. First extractions of the H Re , H Im and H Im CFFs.

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M. Guidal, IPN Orsay

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  1. Varenna, 05/07/2011 Lecture 1: Deep Virtual Compton Scattering: From data to GPDs (CFFs) M. Guidal, IPN Orsay

  2. A few basic definitions/features of GPDs Extracting the GPDs (CFFs) Review of the data (JLab, HERMES) ~ First extractions of the HRe, HImandHImCFFs

  3. A few basic definitions/features of GPDs Extracting the GPDs (CFFs) Review of the data (JLab, HERMES) ~ First extractions of the HRe, HImandHImCFFs

  4. Process Diagramme Structure function Interpretation z x y ep a ep z y x z ep a epg x ep a eX (restrictingmyself to LT-LO, chiral even, quark sector)

  5. x /2 2 t=(p-p ’) x= B 1-x /2 B x = xB! ds 1 1 2 q q H (x,x,t) E (x,x,t) dx dx +…. ~ A +B 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 x and t accessible experimentally g* t g,M,... x~xB x p p’

  6. (at leading order:) 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

  7. Inputs of Radyushkin (DDs), Weiss&Polyakov (D-term), Kivel (twist-3), Pentinen&Polyakov (pion pole contributionE),… ~ Models GPDs and calculates amplitudes/observables (stot, ds/dx, BSA, BCA,…) for eNaeNg, eNaeNM(r0,m,p0,m,h,…), eNaeDp,… The VGG model/code M. Vanderhaeghen, P. Guichon, M.G., PRL80, 5064 (98) M. Vanderhaeghen, P. Guichon, M.G., PRD 60, 094017 (99) K. Goeke, M. Polyakov, M. Vanderhaeghen, PPNP 47, 401 (01) M. G., M. Polyakov, A. Radyushkin, M. Vanderhaeghen, PRD 72, 054013 (05)

  8. Hq(x,x,0)~ db da d(x-b-ax)DDq(a,b) With : DDq(a,b,t)=hb(a,b) q(b) and hb(a,b)=G(2b+2)[(1-|b|)2-a2]b 22b+1G(2b+1)(1-|b|)2b+1 (x,x ) dependence : Double Distributions (Radyushkin,VGG model) Satisfies relations with DIS and polynomiality

  9. y Hu(x,b ) z x x (GeV-1) b Satisfies Form Factors sum rule and polynomiality (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

  10. Extracting GPDs from DVCS observables g ~ Polarized beam, unpolarizedtarget (BSA) : Im{Hp, Hp, Ep} f e’ ~ DsLU~ sinfIm{F1H+ x(F1+F2)H-kF2E}df e leptonic plane N’ ~ ~ Unpolarized beam, longitudinaltarget (lTSA) : Polarized beam, longitudinaltarget (BlTSA) : hadronic plane Re{Hp, Hp} Im{Hp, Hp} ~ ~ DsUL ~ sinfIm{F1H+x(F1+F2)(H+ xB/2E) –xkF2E+…}df DsLL~ (A+Bcosf)Re{F1H+x(F1+F2)(H+ xB/2E)…}df Unpolarized beam, transversetarget (tTSA) : Im{Hp, Ep} DsUT~ cosfIm{k(F2H– F1E) + …..}df x= xB/(2-xB) k=-t/4M2 ProtonNeutron ~ Im{Hn, Hn, En} ~ ~ Im{Hn, En, En} ~ Re{Hn, En, En} Im{Hn}

  11. A few basic definitions/features of GPDs Extracting the GPDs (CFFs) Review of the data (JLab, HERMES) ~ First extractions of the HRe, HImandHImCFFs

  12. Given the well-established LT-LO DVCS+BH amplitude Obs=Amp(DVCS+BH) CFFs DVCS Bethe-Heitler GPDs Can one recover the CFFs from data ? Model-independent fit, at fixed xB, t and Q2, of DVCS observables with MINUIT + MINOS 8unknowns (the CFFs), non-linearproblem, strongcorrelations

  13. In general, 8 GPD quantities accessible (Compton FormFactors) DVCS : golden Channel Anticipated Leading Twist dominance already at low Q2 ~ (in practice, EIm set to 0)

  14. Given the well-established LT-LO DVCS+BH amplitude Obs=Amp(DVCS+BH) CFFs Only3CFFs come out from the fit withfiniteerror bars: HIm , HImand HRe ~ 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 DVCS Bethe-Heitler GPDs Can one recover the CFFs from data ? Model-independent fit, at fixed xB, t and Q2, of DVCS observables with MINUIT + MINOS 7 unknowns (the CFFs), non-linear problem, strong correlations

  15. Otherapproach: Assume a functionnal shape and fit someparameters *D. Mueller & K. Kumericki *H. Moutarde *VGG by the HERMES and n-DVCS Hall A coll. (slidefrom K. Kumericki, Photons11)

  16. The experimental actors DESY HERMES H1/ZEUS p-DVCS BSA,BCA, tTSA,lTSA,BlTSA p-DVCS X-sec,BCA JLab Hall A Hall B p-DVCS (Bpol.) X-sec p-DVCS BSAs,lTSAs

  17. ep epg DVCS@JLab HALL A Scattered Electron Left HRS LH2 / LD2 target Polarized Electron Beam g Charged Particle Tagger Electromagnetic Calorimeter N NucleonDetector

  18. H(e,e’)X DVCS : exclusivity HRS+calorimeter ep -> ep ep -> ep0 0-> ep -> ep0 ep -> ep0N … H(e,e’)X - H(e,e’’)X' H(e,e’p) HRS+calorimeter + proton array H(e,e’)N • Good resolution : no need for the proton array • Remaining contamination 1.7%

  19. DVCS Bethe-Heitler GPDs Difference of (beam-)polarized cross sections Unpolarized cross sections JLab Hall A Collaboration, PRL 97:262002,2006

  20. Hall A : s & Dsz0, xB=0.36,Q2=2.3,t=.17,.23,.28,.33 c2=1.01 c2=0.92 c2=1.44 c2=2.31

  21. HIm HRe Result of the (model independent) fit Bounds (for ALL CFFs): {-3,3}, {-5,5}, {-7,7} x VGG M.G. EPJA 37 (2008) 319

  22. HIm HRe Result of the (model independent) fit M.G. EPJA 37 (2008) 319 VGG prediction

  23. g DVCS@JLab e’ HALL B epa epg p JLab/ITEP/ Orsay/Saclay collaboration 420 PbWO4crystals: ~10x10 mm2, l=160 mm Read-out : APDs +preamps

  24. Without the electromagneticcalorimeter: ep  epX CLAS 4.2 GeV Phys.Rev.Lett.87:182002,2001 γ π0

  25. Selection of the DVCS final state epp0→epg(g) background calculated with Monte Carlo simulation and experimental epp0→epggdata: 5% on average • Exclusivity cuts: • PXT < 90 MeV/c (150 MeV/c) [ep→epgX] • Cone angle (X’) <1.2° (2.7°) [epepX’] • Coplanarity angle between (p) et (*p)<±1.5° (±3°) • EX < 300 MeV (500 MeV)

  26. x~0.16,-t~0.31,Q2~1.82 CLAS DVCS lTSAs CLAS DVCS BSAs Can weextract (in a model-independentway) someCFFsfromfitting(simultaneously) the CLAS DVCS BSAs and TSAs ? (atapproximativelythe samekinematics)

  27. x~0.16,-t~0.31,Q2~1.82 (average) CLAS DVCS lTSAs CLAS DVCS BSAs Can weextract (in a model-independentway) someCFFsfromfitting(simultaneously) the CLAS DVCS BSAs and TSAs ? (atapproximativelythe samekinematics)

  28. x~0.16,-t~0.31,Q2~1.82 (average) CLAS DVCS lTSAs CLAS DVCS BSAs Can we extract (in a model-independent way) some CFFs from fitting (simultaneously) the CLAS DVCS BSAs and TSAs ? (at approximately the same kinematics)

  29. x~0.16,-t~0.31,Q2~1.82 (average) CLAS DVCS lTSAs CLAS DVCS BSAs Can we extract (in a model-independent way) some CFFs from fitting (simultaneously) the CLAS DVCS BSAs and TSAs ? (at approximately the same kinematics)

  30. t-dependence at fixedxB ~ of HIm& HIm Axial charge more concentrated than electromagnetic charge ? Fit with 7 CFFs (boundaries 3xVGG CFFs) Fit with 7 CFFs (boundaries 5xVGG CFFs) ~ Fit with ONLYH and H VGG prediction M.G. PLB 689 (2010) 156

  31. p-DVCSBSA, BCA, lTSA, tTSA, BlTSA A. Airapetian et al., JHEP 0806, 066 (2008) A. Airapetian et al., JHEP 0911, 083 (2009) A. Airapetian et al., JHEP 1006, 019 (2010)

  32. p-DVCSBSA, BCA, lTSA, tTSA, BlTSA A. Airapetian et al., JHEP 0806, 066 (2008) A. Airapetian et al., JHEP 0911, 083 (2009) Analysis of data withrecoil detector in progress A. Airapetian et al., JHEP 1006, 019 (2010) (slidefrom M. Murray, Baryons10)

  33. 17out of 23 F moments Result of fit VGG prediction

  34. Averagekinematics xB=0.09,Q2=2.5 Bounds: {-3,3} x VGG {-5,5} x VGG {-7,7} x VGG {-10,10} x VGG M.G. & H. Moutarde EPJA 37 (2008) 319 Bounds: {-5,5} x VGG {-3,3} x VGG VGGprediction M.G. PLB 693 (2010) 17

  35. (model dependent Fit of D. Muller, K. Kumericki Hep-ph 0904.0458 Fitting the Hall A s,Ds& HERMESBSAs&BCAs: HIm HRe JLab (Hall A) xB=0.36,Q2=2.3 As energy increases: * « Shrinkage » of HIm HIm HRe HERMES * HIm>HRe xB=0.09,Q2=2.5 *Different t-behavior for HIm&HRe

  36. y Hu(x,b ) z x x (GeV-1) b

  37. xB dependence at fixed t

  38. xB dependence at fixed t

  39. xB dependence at fixed t

  40. xB dependence at fixed t

  41. xB dependence at fixed t

  42. xBdependenceatfixed t

  43. (slidefrom K. Kumericki, Photons11)

  44. Procedure tested by Monte-Carlo 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 Procedure is working on real data; extraction of Him , HReand HImat JLab(cross sections) and HERMES (asymmetries) energies ~ First CFFs model independent fits (leading-twist/leading order approximation); “Minimal theoretical input”

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