q=q V +q sea q=q sea so: total sea (q+q): q sea = 2 q Kresimir Kumericki, Dieter Mueller, Nucl.Phys.B841:1-58,2010.

Belitsky A V, Mueller D and Kirchner A 2002 Nucl. Phys. B –392

H Im H Re H Im H Re HERMES x B =0.09,Q 2 =2.5 JLab (Hall A) x B =0.36,Q 2 =2.3 t (GeV 2 )

x b(GeV -1 ) H u (x,b ) y x z

VGG prediction Fit with 7 CFFs (boundaries 5xVGG CFFs) Fit with 7 CFFs (boundaries 3xVGG CFFs) Fit with ONLY H and H ~ t-dependence at fixed x B of H Im & H Im ~ Axial charge more concentrated than electromagnetic charge ?

In the non-perturbative regime the interaction of quarks and gluons is highly non-linear

 (more data existing) L.O calculation with running  s calculation with k perp effects One example:

,

Regge theory: Exchange of families of mesons in the t-channel

Regge theory: Exchange of families of mesons in the t-channel M(s,t) ~ s  (t) where  (t) (trajectory) is the relation between the spin and the (squared) mass of a family of particles M->s  (t)  tot ~1/s x Im(M(s,t=0))->s  (0)-1 [optical theorem]  tot d  /dt s t d  /dt~1/s 2 x |M(s,t)| 2 ->s  (t)-2 ->[e  (t)lns(s) ]

Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (  (0)~0.5) However, when a reaction proceeds via the exchange of vacuum quantum numbers, the cross section doesn’t decrease (even slightly increases).

However, in contrast with meson trajectories, there is no physical particles which has been identified very Conclusively for such trajectory. [QCD:glueballs] =>Introduction of a trajectory with intercept  (0) ~1 : the Pomeron [  (0) ~1.08] Each time a reaction proceeds via the exchange of a charged (meson) in the t-channel, the cross-section decreases (  (0)~0.5) However, when a reaction proceeds via the exchange of vaccuum quantum numbers, the cross section doesn’t decrease (even slightly increases).

The theory of Regge poles has been very popular a few decades ago because it could describe the main characteristics of numerous processes with a limited number of parameters Difficulty to connect Regge with quantum field theory (QCD) and the fundamental degrees of freedom (quarks, gluons)=> hadronic theory. However, relative loss of interest after: describe with precision the data and refine the theory means to go beyond the basic hypothesis and becomes very quickly complicated. For instance, other singularities than simple poles (cuts…) =>first approximation

,

,

, Q 2 >>

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Some signatures of the (asymptotic) « hard » processes:  L /  T ~Q 2  J  ~9/1/2/8  L ~1/Q 6  T ~1/Q 8  ~|xG(x)| 2 Q 2 dependence: W dependence: (for gluon handbag) Ratio of yields: (for gluon handbag) Saturation with hard scale of  P (0), b, … SCHC : checks with SDMEs

LO (w/o kperp effect) Handbag diagram calculation needs k perp effects to account for preasymptotic effects LO (with kperp effect) Same thing for 2-gluon exchange process

H1, ZEUS, Q 2 >>

H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS

H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS + « older » data from: E665, NMC, Cornell,…

H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS + « older » data from: E665, NMC, Cornell,…

Steepening W slope as a function of Q 2 indicates « hard » regime (reflects gluon distribution in the proton) W dependence

Two ways to set a « hard » scale: *large Q 2 *mass of produced VM W dependence Steepening W slope as a function of Q 2 indicates « hard » regime (reflects gluon distribution in the proton) Universality :  at large Q 2 +M 2 similar to J/ 

 P (0) increases from “soft” (~1.1) to “hard” (~1.3) as a function of scale  2 =(Q 2 +M V 2 )/4. Hardening of W distributions with  2

Approaching handbag prediction of n=6 (Q 2 not asymptotic, fixed W vs fixed x B,  tot vs  L, Q 2 evolution of G(x)…) Q 2 dependence  L ~  /Q 6 => Fit with  ~1/(Q 2 +M V 2 ) n Q 2 >0 GeV 2 => n=2+/ Q 2 >10 GeV 2 => n=2.5+/ Q 2 >0 GeV 2 => n= / /  J  (S. Kananov) Q 2 dependence is damped at low Q 2 and steepens at large Q 2

t dependence b decreases from “soft” (~10 GeV -2 ) to “hard” (~4-5 GeV -2 ) as a function of scale  2 =(Q 2 +M V 2 )/4

Ratios  J  ~ 9/1/2/8 (SU(4) universality)    1/sqrt(2){|uu>-|dd>}  1/sqrt(2){|uu>+|dd>}   Ratio  =9

L/TL/TL/TL/T (almost) compatible with handbag prediction (damping at large Q 2 )

SDMEs HERMES H1 (almost) no SCHC violation

At high energy (W>5 GeV), the general features of the kinematics dependences and of the SDMEs are relatively/qualitatively well understood Good indications that the “hard”/pQCD regime is dominant for for  2 =(Q 2 +M V 2 )/4 ~ 3-5 GeV 2. Data are relatively well described by GPD/handbag approaches

H1, ZEUS, Q 2 >> H1, ZEUS CLAS HERMES COMPASS

Exclusive  0,   electroproduction on the CLAS6 on the CLAS6 S. Morrow et al., Eur.Phys.J.A39:5-31,2009 (  J. Santoro et al., Phys.Rev.C78:025210,2008 ( L. Morand et al., Eur.Phys.J.A24: ,2005 ( C. Hadjidakis et al., Phys.Lett.B605: ,2005 (  GeV) K. Lukashin et al., Phys.Rev.C63:065205,2001 ( GeV) } e1-b (1999) } e1-6 ( ) A. Fradi, Orsay Univ. PhD thesis (  GeV) } e1-dvcs (2005)

e1-6 experiment (E e =5.75 GeV) (October 2001 – January 2002)

ep  ep  + (  - ) Mm(epX) Mm(ep  + X) e p ++  - )

1) Ross-Stodolsky B-W for  0 (770), f 0 (980) and f 2 (1270) with variable skewedness parameter, 2)  ++ (1232)  +  - inv.mass spectrum and  +  - phase space. Background Subtraction

   (  * p  p  0 ) vs W

L. Morand et al., Eur.Phys.J.A24: ,2005 ( C. Hadjidakis et al., Phys.Lett.B605: ,2005 (  GeV) K. Lukashin, Phys.Rev.C63:065205,2001 ( GeV) J. Santoro et al., Phys.Rev.C78:025210,2008 ( S. Morrow et al., Eur.Phys.J.A39:5-31,2009 (      A. Fradi, Orsay Univ. PhD thesis, 2009 ( 

GK  L LL ep->ep     

GPDs parametrization based on DDs (VGG/GK model) Strong power corrections… but seems to work at large W…

VGG GPD model +

GK GPD model

H, H, E, E (x,ξ,t) ~~ x+ξx-ξ t γ, π, ρ, ω… -2ξ x ξ-ξ-ξ +1 0 Quark distribution q q Distribution amplitude Antiquark distribution “ERBL” region“DGLAP” region W~1/  ERBLDGLAP

DDs + “meson exchange” DDs w/o “meson exchange” (VGG) “meson exchange”

VMs (  0,  ) the only exclusive process [with DVCS] measured over a W range of 2 orders of magnitude (  L,T, d  /dt, SDMEs,…) At high energy (W>5 GeV), transition from “soft” to “hard” (  2 scale) physics relatively well understood (further work needed for precision understanding/extractions) At low energy (W<5 GeV), large failure of “hard” approach. This is not understood. Is the GPD/handbag approach setting at much larger Q 2 or is the widely used GPD parametrisation in the valence region completely wrong ? A lot of new data expected soon from COMPASS (transv. target), HERA new analysis,…

Interpretation “a la Regge” : Laget model  *p  p  0  *p  p   *p  p  Free parameters: *Hadronic coupling constants: g MNN *Mass scales of EM FFs: (1+Q 2 /  2 ) -2

Regge/Laget  L (  * L p  p  L 0 ) Pomeron ,f 2

Comparison with   