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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.

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Belitsky A V, Mueller D and Kirchner A 2002 Nucl. Phys. B629 323–392

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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 )

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

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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 ?

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

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(more data existing) L.O calculation with running s calculation with k perp effects One example:

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,

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

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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) ]

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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).

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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).

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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

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,

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,

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, Q 2 >>

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,

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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

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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

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H1, ZEUS, Q 2 >>

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

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

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

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

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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/

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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

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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+/- 0.01 Q 2 >10 GeV 2 => n=2.5+/- 0.02 Q 2 >0 GeV 2 => n=2.486 +/- 0.08 +/-0.068 J (S. Kananov) Q 2 dependence is damped at low Q 2 and steepens at large Q 2

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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

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Ratios J ~ 9/1/2/8 (SU(4) universality) 1/sqrt(2){|uu>-|dd>} 1/sqrt(2){|uu>+|dd>} Ratio =9

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

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SDMEs HERMES H1 (almost) no SCHC violation

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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

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

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Exclusive 0, electroproduction on the proton @ CLAS6 on the proton @ CLAS6 S. Morrow et al., Eur.Phys.J.A39:5-31,2009 ( 0 @5.75GeV) J. Santoro et al., Phys.Rev.C78:025210,2008 ( @5.75GeV) L. Morand et al., Eur.Phys.J.A24:445-458,2005 ( @5.75GeV) C. Hadjidakis et al., Phys.Lett.B605:256-264,2005 ( 0 @4.2 GeV) K. Lukashin et al., Phys.Rev.C63:065205,2001 ( @4.2 GeV) } e1-b (1999) } e1-6 (2001-2002) A. Fradi, Orsay Univ. PhD thesis ( @5.75 GeV) } e1-dvcs (2005)

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

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ep ep + ( - ) Mm(epX) Mm(ep + X) e p ++ - )

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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

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( * p p 0 ) vs W

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L. Morand et al., Eur.Phys.J.A24:445-458,2005 ( @5.75GeV) C. Hadjidakis et al., Phys.Lett.B605:256-264,2005 ( 0 @4.2 GeV) K. Lukashin, Phys.Rev.C63:065205,2001 ( @4.2 GeV) J. Santoro et al., Phys.Rev.C78:025210,2008 ( @5.75GeV) S. Morrow et al., Eur.Phys.J.A39:5-31,2009 ( 0 @5.75GeV) A. Fradi, Orsay Univ. PhD thesis, 2009 ( @5.75GeV)

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GK L LL ep->ep

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

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VGG GPD model +

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GK GPD model

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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

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

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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 JLab@11GeV, COMPASS (transv. target), HERA new analysis,…

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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

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Regge/Laget L ( * L p p L 0 ) Pomeron ,f 2

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Comparison with

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