DVCS & DVCS & Generalized Parton Distributions

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

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

Final state constrained :  New generation of machines : - high energy - high duty cycle + spectrometers : - large acceptance - high resolution }accessible now ! now ! e  p e’ p’  DEEP INELASTIC ( EXCLUSIVE ) ~~ e  e’ p p’  H,E,H,E ~~ x t 

p p’(=p+  )  H,E(x, ,t) ~~ x-  t  x+  GPD formalism  {   [N(p’)  + N(p) + N(p’)i  +    N(p)] {   [H q (x, ,t)N(p’)  + N(p) + E q (x, ,t)N(p’)i  +    N(p)]  5   [N(p’)  +  5 N(p) + N(p’)     N(p)]}  5   [H q (x, ,t)N(p’)  +  5 N(p) + E q (x, ,t)N(p’)     N(p)]} 2M2M2M2M _ ~~ 2M2M2M2M _ _ _ Vector Ms : H,E Large Q 2, small t PS Ms : H,E ~~ (Ji, Radyushkin, Collins, Strikman, Frankfurt)  :  T lead. twist Mesons :  L

H, H, E, E (x,ξ,t) ~~ “Ordinary” parton distributions H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~ x Elastic form factors  H(x,ξ,t)dx = F(t) (  ξ) x Ji’s sum rule 2J q =  x(H+E)(x,ξ,0)dx (nucleon spin) x+ξx-ξ t γ, π, ρ, ω… GPDs are not completely unknown -2ξ

y x z Transverse localisation of the partons in the nucleon (independently of their longitudinal momentum) Form Factors y x z Longitudinal momentum distribution (no information on the transverse localisation) Parton Distribution (Belitsky et al.)

y x z The GPDs contain information on the longitudinal AND transverse distributions of the partons in the nucleon Generalized Parton Distributions 3-D picture of the nucleon (femto-graphy of the nucleon)

GPDs probe the nucleon at amplitude level q(x)~ q(x)~ H(x,  )~ H(x,  )~ pp’ x+  x-  z 0101 z p p’ x+  x-  x<  : x>  : DIS : DES : pp’ x xx x x xx x pp’ x+  x- 

0 t=0 1 DDs « D-term » k GPDs Pion cloud Trans. Mom. of partons F (t), G (t) 1,2 A,PS q(x),  q(x) R (t),R  (t) A V J q  (z)

e  e’ p p’  H,E,H,E ~~ Access experimentally the GPDs through the measurement of the angular and energy distributions of EXCLUSIVE reactions q’q H,E,H,E(x, ,t) : GPDs ~~ H E q spin average H E q spin diff. ~~ p spin no flip p spin flip

 p p’  H,E,H,E ~~ x t Deconvolution needed ! x : mute variable  x  H q (x, ,t) but only  and t accessible experimentally dd dQ d  dt 2 B ~A H (x, ,t,Q ) 2 q x-ix-i dxdx +B+B E (x, ,t,Q ) 2 q x-ix-i dx +… == x B 1-x /2 B t=(p-p ’) 2 x = x B ! /2

GPD and DVCS Cross-section measurement and beam charge asymmetry (ReT) integrate GPDs over x Beam or target spin asymmetry contain only ImT, therefore GPDs at x =  and  (at leading order:) (M. Vanderhaeghen)

- “Trivial” kinematical corrections - Quark transverse momentum effects (modification of quark propagator) - Other twist-4 …… DES: finite Q 2 corrections (real world ≠ Bjorken limit) DES: finite Q 2 corrections (real world ≠ Bjorken limit) GPD evolution O (1/Q) O (1/Q 2 ) Dependence on factorization scale μ : Kernel known to NLO - 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). (here for DVCS)

The actors JLab Hall AHall BHall C p-DVCS n-DVCS Vector mesons p-DVCS d-DVCS Pseudoscalar mesons DESY HERMESZEUS/H1 Vector & PS mesons DVCS CERN COMPASS Vector mesons DVCS + theory (almost) everywhere

JLab(E e =6 GeV):CLAS/Hall B ( ) and Hall A (2004) HERA (E e =27 GeV) : HERMES and ZEUS/H1 (up to 2006) CERN (E  =200 GeV) : COMPASS (2007 ?) « DES » in the world

e  p e’ p’  The ep  ep  process The ep  ep  process DVCS e  p e’ p’  e  p e’ p’ Bethe-Heitler GPDs

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

e  p e’ p’  The ep  ep  process The ep  ep  process DVCS e  p e’ p’  e  p e’ p’ Bethe-Heitler Interference between the 2 processes : if the electron beam is polarised => beam spin asymmetry GPDs

First experimental signatures Magnitude and Q 2 dependence of DVCS X-section (H1/ZEUS) First observations of DVCS beam asymmetries CLAS HERMES DVCS First observations of DVCS charge asymmetry (HERMES) All in basic agreement with theoretical predictions Phys.Rev.Lett.87:182002,2001

4.8 GeV data (G. Gavalian) GPD based predictions (BMK) PRELIMINARY 0.15 < x B < < Q 2 < 4.5 GeV 2 -t < 0.5 GeV 2 PRELIMINARY 5.75 GeV data (H. Avakian & L. Elhouadrhiri) CLAS/DVCS at 4.8 and 5.75 GeV

Resolution Exclusivity Luminosity ep  epX MAMI 850 MeV ep  epX Hall A 4 GeV ep  eγX HERMES 28 GeV N+πN Missing mass M X 2 ep  epX CLAS 4.2 GeV π0π0 γ D.E.S.: an experimental challenge are the key issues for this physics!

e’ p  A typical DVCS event in CLAS

NN Only 2-parameter fit: N  and N  0 ep→epX (CLAS at 4.2 GeV) : X = γ or π 0 ?

e’ p  A typical ep  ep  event in CLAS Add EM calorimeter at forward angles Add solenoid Moller shield around target

Dynamical range : 50 MeV < E  < 5 GeV (  ~5%/sqrt(E  )) Counting rates ~ 1 MHz Magnetic field environment : B~ 1 T ~400 PbWO 4 crystals : ~10x10 mm 2, l=160 mm (18 ’s) Read-out : APDs +preamps JLab/ITEP/ Orsay/Saclay/ UVA collaboration

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

About 380 bins in , x B, t 60 days of beam time in spring’05 Experiment E : V. Burkert, L. Edouardrihi, M. Garçon, S. Stepanyan et al. Run March-May 2005 Projected results

High Resolution Hall A spectrometer for electron detection 100-channel scintillator array for proton detection 132-block PbF 2 electromagnetic calorimeter for photon detection Detection of all 3 final-state particles ensures exclusivity Experiment E : P. Bertin, C.E. Hyde-Wright, R. Ransome and F. Sabatié. To run mid-september DVCS in Hall A to the p-DVCS set-up n-DVCS : Veto detector added Also HERMES & COMPASS

γ* L ρ Handbag diagram calculation (frozen  s ) can account for CLAS and HERMES data on σ L (ep->ep  ) Q 2 (GeV 2 ) CLAS 4.2 GeV data (C. Hadjidakis, hep-ex/ ) W=5.4 GeV HERMES (27GeV) A. Airapetian et al., EPJC 17 σ L (ep->ep  ) Regge (Laget) GPD (MG-MVdh) Mesons

Ludyvine Morand’s thesis Analysis of ω polarization from ep → epπ + π - X configurations (for the first time for this channel above Q 2 ~ 1 GeV 2 ) Evidence for unnatural parity exchange   0 exchange dominating even up to large Q 2 (see also J.-M. Laget, hep-ph/ ) SCHC does not seem to hold → not possible to extract σ L handbag diagram estimated to contribute only about 1/5 of measured cross sections ω more challenging/difficult channel to access GPD Q 2 from 1.6 to 5.6 GeV 2 x B from 0.16 to 0.70 ω peak in MM[epX] for (Q 2,x B ) bins Deeply virtual ω production at 5.75 GeV (CLAS) s

Extensions RCS :  p->  p (intermediate t) (Radyushkin, Dihl, Feldman, Jakob, Kroll)  VCS : ep->e  (Frankfurt, Polyakov, Strikman, Vanderhaeghen) tDDVCS : ep->ep  * (e + e - ) (M.G., Vanderhaeghen, Belitsky, Muller,...) IDVCS : pp->  (Freund, Radyushkin,Shaeffer,Weiss)  tDVCS :  p->p  * (e + e - ) (Berger, Pire, Diehl,...) N-DVCS : eA->eA  (Scopetta, Pire, Cano, Polyakov, Muller, Kirschner, Berger....) Hybrids, pentaquarks,... (Pire, Anikin,Teryaev,...) sDDVCS : ep->ep (Vanderhaeghen, Gorschtein,...) _

The most complete information on the structure of the nucleon : GPDs Summary (f (x), g (x), F (t), G (t),  (z), pion cloud,…)111A Q 2 evolution worked out to NLO, twist-3 contributions to DVCS estimated, first lattice calculations have been recently published,... THEORY : Further higher twists –mesons–, deconvolution issues,.... First experimental signatures very encouraging Up to 2005: definitely sign the validity of the approach (factorization, scaling,...) Beyond : systematically measure and extract the GPDs GeV) EXPERIMENT :