Generalized Parton Distributions Summary for SIR 2005Jlab Michel
Generalized Parton Distributions Summary for SIR 2005@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 § When integrated over x, one gets the coordinate space density n(p)=|ψ(p)|2 X. Ji
Wigner distributions for quarks in proton § Wigner operator (X. Ji, PRL 91: 062001, 2003) § Wigner distribution: “density” for quarks having position r and 4 -momentum k (off-shell) X. Ji
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) X. Ji Density ρ(r)
Reduced Wigner Distributions and GPDs § The 4 D reduced Wigner distribution f(r, x) is related to Generalized parton distributions (GPD) H and E through simple FT, t= – q 2 ~ qz H, E depend only on 3 variables. There is a rotational symmetry in the transverse plane. . X. Ji
Burkardt
Burkardt
observation at low energy scale : (from polarized DIS) Wakamatsu
From Holography to Tomography A. Belitsky, B. Mueller, NPA 711 (2002) 118 mirror An Apple mirror A Proton 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 detector
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 bx X. Ji by
Non-Perturbative Issues Does factorization work ? Instanton mediated processes ? Hoyer, Boer
Boer
GPDs ON A LATTICE Zanotti
Zanotti
Zanotti
Fleming
Fleming
Fleming
Fleming
GPDs for nuclei ? Liutti
Nowak
Kinematical domain E=190, 100 Ge. V Nx 2 Collider : H 1 & ZEUS 0. 0001<x<0. 01 Fixed target : JLAB 6 -11 Ge. V SSA, BCA? HERMES 27 Ge. V SSA, BCA COMPASS could provide data on : Cross section (190 Ge. V) BCA (100 Ge. V) Wide Q 2 and xbj ranges Limitation due to luminosity Burtin
Separating GPDs through polarization ep epg s+ - s Ds A = s+ + s - = 2 s = x. B/(2 -x. B) k = t/4 M 2 Polarized beam, unpolarized target: ~ Ds. LU ~ sinf{F 1 H + (F 1+F 2)H +k. F 2 E}df ~ H, H, E Kinematically suppressed Unpolarized beam, longitudinal target: Ds. UL ~ ~ sinf{F H+ (F +F )(H + … }df 1 1 2 ~ H, H Unpolarized beam, transverse target: Ds. UT ~ sinf{k(F 2 H – F 1 E) + …. . }df Burkert H, E
Nowak
GPDs – Flavor separation DVMP DVCS longitudinal only hard gluon hard vertices DVCS cannot separate u/d quark contributions. Burkert M = r/w select H, E, for u/d flavors M = p, h, K select H, E
Nowak
Nowak
Ellinghaus
Exclusive r 0 production on transverse target T AUT = - 2 D (Im(AB*))/p |A|2(1 - 2) - |B|2( 2+t/4 m 2) - Re(AB*)2 2 Q 2=5 r 0 Ge. V 2 A ~ 2 Hu + Hd B ~ 2 Eu + Ed Eu, Ed needed for angular momentum sum rule. r 0 K. Goeke, M. V. Polyakov, M. Vanderhaeghen, 2001 B Burkert
GPD Reaction ep→epγ (DVCS) Obs. Expt BSA CLAS 4. 2 Ge. V Published PRL CLAS 4. 8 Ge. V Preliminary CLAS 5. 75 Ge. V Preliminary Hall A 5. 75 Ge. V Fall 04 CLAS 5. 75 Ge. V Spring 05 (+ σ) Status ep→epγ (DVCS) TSA CLAS 5. 65 Ge. V Preliminary e(n)→enγ (DVCS) BSA Hall A 5. 75 Ge. V Fall 04 ed→edγ (DVCS) BSA CLAS 5. 4 Ge. V ep→epe+e- (DDVCS) BSA CLAS 5. 75 Ge. V under analysis ep→epρ CLAS 4. 2 Ge. V CLAS 5. 75 Ge. V under analysis CLAS 5. 75 Ge. V Accepted EPJA ep→epω σL (σL) From ep → ep. X Dedicated set-up under analysis Published PLB + other meson production channels π, η, Φ under analyses in the three Halls. M. Garcon
DVCS with a polarized target in CLAS * Detect all 3 particles in the final state (e, p, γ) to eliminate contribution from N 5. 65 Ge. V run with NH 3 longitudinally polarized target, Q 2 up to 4. 5 Ge. V 2 (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 p 0 asymmetry (two photons required) Exclusive M. Garcon S. Chen
DDVCS (Double Deeply Virtual Compton Scattering) DDVCS-BH interference generates a beam spin asymmetry sensitive to e- e- γ*T e+ e- 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
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 Lepton pair squared invariant mass or detected electron belongs to lepton pair from γ* Hyp. 2 seems the most valid → quasi-real photoproduction of vector mesons M. Garcon
Exclusive ep CLAS (4. 3 Ge. V) x. B=0. 38 Q 2 (Ge. V 2) GPD formalism approximately describes CLAS and HERMES data Q 2 > 2 Ge. V 2 Burkert epr. L 0 production HERMES (27 Ge. V) W=5. 4 Ge. V
Deeply virtual meson production Meson and Pomeron (or two-gluon) exchange … (Photoproduction) ω π, f 2, P ρ0 ω Φ (σ), f 2, P π , f 2 , P P … or scattering at the quark level ? Flavor sensitivity of DVMP on the proton: ρ0 ω Φ ρ+ 2 u+d, 9 g/4 2 u-d, 3 g/4 s, g u-d γ*L ωL
Exclusive ρ meson production: ep → epρ CLAS (4. 2 Ge. V) CLAS (5. 75 Ge. V) Regge (JML) C. Hadjidakis et al. , PLB 605 GPD (MG-MVdh) s An GPD formalism (beyond leading order) describes approximately data for x. B<0. 4, Q 2 >1. 5 Ge. V 2 is s y l ro p n s gre i a Two-pion invariant mass spectra
Exclusive r production on transverse target r 0 AUT ~ Im(AB*) AUT r+ A ~ 2 Hu + Hd B ~ 2 Eu + Ed A ~ Hu - Hd B ~ Eu - Ed Asymmetry depends linearly on the GPD E in Ji’s sum rule. r 0 and r+ measurements allow separation of Eu, Ed r 0 CLAS 12 projected K. Goeke, M. V. Polyakov, M. Vanderhaeghen, 2001 x. B Burkert
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 12 Ge. V unique).
- Slides: 43