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Generalized Parton Distributions Summary for SIR2005@Jlab

Generalized Parton Distributions Summary for SIR2005@Jlab. Michel Garçon (Saclay) Pervez Hoodbhoy (Islamabad) Wolf-Dieter Nowak (DESY) 20 May 2005. Wigner parton distributions (WPD). When integrated over p, one gets the coordinate space density ρ (x)=| ψ (x)| 2

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Generalized Parton Distributions Summary for SIR2005@Jlab

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  1. Generalized Parton DistributionsSummary for SIR2005@Jlab Michel Garçon (Saclay) Pervez Hoodbhoy (Islamabad) Wolf-Dieter Nowak (DESY) 20 May 2005

  2. Wigner parton distributions (WPD) • When integrated over p, one gets the coordinate space density ρ(x)=|ψ(x)|2 • When integrated over x, one gets the coordinate space density n(p)=|ψ(p)|2 X. Ji

  3. Wigner distributions for quarks in proton • Wigner operator (X. Ji,PRL91:062001,2003) • Wigner distribution: “density” for quarks having position r and 4-momentum k(off-shell) X. Ji

  4. Wigner parton distributions & offsprings Mother Dis. W(r,p) q(x, r, k) Red. Wig. q(x,r) • TMDPD q (x, k) PDF q(x) Density ρ(r) X. Ji

  5. Reduced Wigner Distributions and GPDs • The 4D reduced Wigner distribution f(r,x) is related toGeneralized parton distributions (GPD)H and E through simple FT, t= – q2  ~ qz H,E depend only on 3 variables. There is a rotational symmetry in the transverse plane.. X. Ji

  6. Burkardt

  7. Burkardt

  8. observation at low energy scale : (from polarized DIS) Wakamatsu

  9. A. Belitsky, B. Mueller, NPA711 (2002) 118 An Apple A Proton detector From Holography to Tomography mirror mirror mirror mirror By varying the energy and momentum transfer to the proton we probe its interior and generate tomographic images of the proton (“femto tomography”). Burkert

  10. Imaging quarks at fixed Feynman-x • For every choice of x, one can use the Wigner distributions to picture the nucleon in 3-space; quantum phase-space tomography! z by bx X. Ji

  11. Non-Perturbative Issues Does factorization work ? Instanton mediated processes ? Hoyer, Boer

  12. Boer

  13. GPDs ON A LATTICE Zanotti

  14. Zanotti

  15. Zanotti

  16. Fleming

  17. Fleming

  18. Fleming

  19. Fleming

  20. GPDs for nuclei ? Liutti

  21. Nowak

  22. E=190, 100GeV Kinematical domain Nx2 Collider : H1 & ZEUS0.0001<x<0.01 Fixed target : JLAB 6-11GeV SSA,BCA? HERMES 27 GeV SSA,BCA COMPASScould provide data on : Cross section (190 GeV) BCA (100 GeV) Wide Q2 and xbj ranges Limitation due to luminosity Burtin

  23. Ds 2s ep epg s+ - s- s+ + s- A = = x = xB/(2-xB) k = t/4M2 Separating GPDs through polarization Polarized beam, unpolarized target: ~ ~ DsLU~ sinf{F1H+ x(F1+F2)H+kF2E}df H, H, E Kinematically suppressed Unpolarized beam, longitudinal target: ~ ~ H, H DsUL~ sinf{F1H+x(F1+F2)(H+ … }df Unpolarized beam, transverse target: H, E DsUT~ sinf{k(F2H – F1E) + …..}df Burkert

  24. Nowak

  25. GPDs – Flavor separation DVMP DVCS longitudinal only hard gluon hard vertices DVCS cannot separate u/d quark contributions. M = r/w select H, E, for u/d flavors M = p, h, K select H, E Burkert

  26. Nowak

  27. Nowak

  28. Ellinghaus

  29. Q2=5 GeV2 Exclusiver0 production on transverse target 2D (Im(AB*))/p T AUT = - |A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2 A~ 2Hu + Hd r0 B~ 2Eu + Ed Eu, Edneeded for angular momentum sum rule. r0 K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 B Burkert

  30. GPD Reaction Obs. Expt Status ep→epγ (DVCS)BSA CLAS 4.2 GeV Published PRL CLAS 4.8 GeV Preliminary CLAS 5.75 GeV Preliminary (+ σ) Hall A 5.75 GeV Fall 04 CLAS 5.75 GeV Spring 05 ep→epγ (DVCS)TSA CLAS 5.65 GeV Preliminary e(n)→enγ (DVCS)BSA Hall A 5.75 GeV Fall 04 ed→edγ (DVCS)BSA CLAS 5.4 GeV under analysis ep→epe+e- (DDVCS)BSA CLAS 5.75 GeV under analysis ep→epρσL CLAS 4.2 GeV Published PLB CLAS 5.75 GeV under analysis ep→epω (σL) CLAS 5.75 GeV Accepted EPJA + other meson production channels π, η, Φ under analyses in the three Halls. From ep → epX Dedicated set-up M.Garcon

  31. Exclusive DVCS with a polarized target in CLAS * Detect all 3 particles in the final state (e,p,γ) to eliminate contribution from N (but calorimeter is at too large angles) , * Apply kinematical cuts to suppress ep→epπ0 contribution. * Remaining Φ-dependent π0 contribution (10-40%) extracted from MC. * π0 asymmetry measured 5.65 GeV run with NH3 longitudinally polarized target, Q2 up to 4.5 GeV2 p0 asymmetry (two photons required) S. Chen M.Garcon

  32. DDVCS (Double Deeply Virtual Compton Scattering) DDVCS-BH interference generates a beam spin asymmetry sensitive to e+ e- e- e- γ*T γ*T p p The (continuously varying) virtuality of the outgoing photon allows to “tune” the kinematical point (x,ξ,t) at which the GPDs are sampled (with |x | < ξ). M. Guidal & M. Vanderhaeghen, PRL 90 A. V. Belitsky & D. Müller, PRL 90 M.Garcon

  33. DDVCS: first observation of ep → epe+e- * Positrons identified among large background of positive pions * ep→epe+e- cleanly selected (mostly) through missing mass ep→epe+X * Φ distribution of outgoing γ* and beam spin asymmetry extracted (integrated over γ* virtuality) but… A problem for both experiment and theory: * 2 electrons in the final state → antisymmetrisation was not included in calculations, → define domain of validity for exchange diagram. * data analysis was performed assuming two different hypotheses either detected electron = scattered electron or detected electron belongs to lepton pair from γ* Hyp. 2 seems the most valid → quasi-real photoproduction of vector mesons Lepton pair squared invariant mass M.Garcon

  34. HERMES (27GeV) W=5.4 GeV GPD formalism approximately describes CLAS and HERMES data Q2 > 2 GeV2 Exclusiveep epr0production L CLAS (4.3 GeV) xB=0.38 Q2 (GeV2) Burkert

  35. Deeply virtual meson production Meson and Pomeron (or two-gluon) exchange … (Photoproduction) ω π, f2, P …or scattering at the quark level ? Flavor sensitivity of DVMP on the proton: ωL γ*L

  36. Exclusive ρ meson production: ep → epρ CLAS (4.2 GeV) CLAS (5.75 GeV) Regge (JML) GPD (MG-MVdh) Analysis in progress C. Hadjidakis et al., PLB 605 GPD formalism (beyond leading order) describes approximately data for xB<0.4, Q2 >1.5 GeV2 Two-pion invariant mass spectra M.Garcon

  37. AUT r0 xB Exclusiver production on transverse target A~ 2Hu + Hd r0 AUT ~ Im(AB*) B~ 2Eu + Ed A~ Hu - Hd B ~ Eu - Ed r+ Asymmetry depends linearly on the GPDEin Ji’s sum rule. r0and r+ measurements allow separation of Eu, Ed CLAS12 projected K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001 Burkert

  38. GPD CHALLENGES • Goal: map out the full dependence on • Develop models consistent with known forward distributions, form factors, polynomiality constraints, positivity,… • More lattice moments, smaller pion masses, towards unquenched QCD,… • Launch a world-wide program for analyzing GPDs perhaps along the lines of CTEQ for PDFs. • High energy, high luminosity is needed to map out GPDs in deeply virtual exclusive processes such as DDVCS (JLab with 12GeV unique).

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