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DVCS & Generalized Parton Distributions

DVCS & Generalized Parton Distributions. MENU04, 02/09/04. M. Guidal, ORSAY. Compton Scattering. “DVCS” (Deep Virtual Compton Scattering). }. f. f ,. 2. 1. 2. 2. Bjorken scaling (Q >1 GeV ) : pointlike objects. : spin ½ objects. 1/2 momentum carried by quarks.

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DVCS & Generalized Parton Distributions

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  1. DVCS & Generalized Parton Distributions MENU04, 02/09/04 M. Guidal, ORSAY

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

  3. } f f , 2 1 2 2 Bjorken scaling (Q >1 GeV ) : pointlike objects : spin ½ objects 1/2 momentum carried by quarks Bjorken Sum Rule : 1/4 spin carried by quarks (INCLUSIVE) DEEP INELASTIC ) e’ ( ( ) e g q ( ) p

  4. DEEP INELASTIC e’ e g,p,w,r,h,... g } New generation of machines : - high energy - high duty cycle + spectrometers : - large acceptance - high resolution p p’ accessible now ! e’ g,p,w,r,h,... e g* x t x ~ ~ H,E,H,E p p’ ~ ~ (EXCLUSIVE) Final state constrained : s

  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 GPD formalism (Ji, Radyushkin, Collins, Strikman, Frankfurt) t g* g,M,... -2x x+x x-x p’(=p+D) p

  6. “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) ~ GPDs are not completely unknown t γ, π, ρ, ω… -2ξ x+ξ x-ξ ~ ~ H, H, E, E (x,ξ,t)

  7. 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)

  8. Generalized Parton Distributions 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

  9. x+x x-x x+x x-x x<x : x>x : p’ p p’ p z 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 ’>

  10. 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

  11. ~ ~ H,E,H,E(x,x,t): GPDs H E q spin average ~ ~ H E q spin diff. p spin no flip p spin flip ~ ~ H,E,H,E Access experimentally the GPDs through the measurement of the angular and energy distributions of EXCLUSIVE reactions e’ g,r,w,h,p,... e g q q’ p p’

  12. x /2 2 t=(p-p ’) x= B 1-x /2 B 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 x and t accessible experimentally g* t g,M,... x~xB x p p’

  13. GPD and DVCS (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 (M. Vanderhaeghen)

  14. 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 ……

  15. The actors

  16. « 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 ?)

  17. 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

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

  19. 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

  20. 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

  21. 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)

  22. D.E.S.: an experimental challenge Missing mass MX2 ep  epX MAMI 850 MeV ep  epX Hall A 4 GeV • Resolution • Exclusivity • Luminosity γ π0 ep  epX CLAS 4.2 GeV are the key issues for this physics! N N+π ep  eγX HERMES 28 GeV

  23. g e’ A typical DVCS event in CLAS p

  24. ep→epX (CLAS at 4.2 GeV) : X = γ or π0 ? Only 2-parameter fit: Ng and Np0 Ng

  25. Add EM calorimeter at forward angles Add solenoid Moller shield around target A typical epa epg event in CLAS e’ g p

  26. JLab/ITEP/ Orsay/Saclay/UVA collaboration Dynamical range : 50 MeV < Eg < 5 GeV(s~5%/sqrt(Eg)) Counting rates ~ 1 MHz Magnetic field environment : B~ 1 T ~400 PbWO4 crystals : ~10x10 mm2, l=160 mm (18 l’s) Read-out : APDs +preamps

  27. 0 mass peak σ 21 MeV (with online calibration)

  28. Projected results 60 days of beam time in spring’05 Experiment E01-113 : V. Burkert, L. Edouardrihi, M. Garçon, S. Stepanyan et al. Run March-May 2005 About 380 bins in f, xB, t

  29. Veto detector added n-DVCS : to the p-DVCS set-up DVCS in Hall A Experiment E00-110 : P. Bertin, C.E. Hyde-Wright, R. Ransome and F. Sabatié. To run mid-september • High Resolution Hall A spectrometer for electron detection • 100-channel scintillator array for proton detection • 132-block PbF2 electromagnetic calorimeter for photon detection • Detection of all 3 final-state particles ensures exclusivity Also HERMES & COMPASS

  30. 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

  31. Deeply virtual ω production at 5.75 GeV (CLAS) Q2 from 1.6 to 5.6 GeV2 Ludyvine Morand’s thesis xB from 0.16 to 0.70 ω peak in MM[epX] for (Q2,xB) bins Analysis of ω polarizationfrom ep → epπ+π-X configurations (for the first time for this channel above Q2 ~ 1 GeV2) Evidence for unnatural parity exchange  0 exchange dominating even up to large Q2 (see also J.-M. Laget, hep-ph/0406153) SCHC does not seem to hold → not possible to extract σL handbag diagram estimated to contribute only about 1/5 of measured cross sections ω more challenging/difficult channel to access GPD s

  32. 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,...)

  33. THEORY : Q2 evolution worked out to NLO, twist-3 contributions to DVCS estimated, first lattice calculations have been recently published,... (f (x), g (x), F (t), G (t), F(z), pion cloud,…) 1 1 1 A Further higher twists –mesons–, deconvolution issues,.... EXPERIMENT : First experimental signatures very encouraging Up to 2005: definitely sign the validity of the approach (factorization, scaling,...) Beyond : systematically measure and extract the GPDs (JLab@11 GeV) Summary The most complete information on the structure of the nucleon : GPDs

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