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0, , + exclusive electroproduction on the proton at CLAS on the proton at CLAS

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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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,

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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 (or x B ) 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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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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Ratios J ~ 9/1/2/8 1/sqrt(2){|uu>-|dd>} 1/sqrt(2){|uu>+|dd>} Ratio =9

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For W>5 GeV, good indications that the “hard”/pQCD regime is reached/dominant for is reached/dominant for 2 =(Q 2 +M V 2 )/4 ~ 3-5 GeV 2. Data are relatively well described by GPD/handbag approaches Great, one can hope to learn about the gluon (transverse) spatial distribution in the nucleon, the gluon orbital momentum contribution to the nucleon spin, etc…

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

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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) F.-X. Girod

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Exclusive 0 electroproduction

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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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IM(p + )

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IM(p - )

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V. Mokeev 2 e-prod model Working up to W=1.6 GeV up to Q 2 ~1 GeV 2

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J-M. Laget 2 e-prod model +f 0 + f 2

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+f 0 + f 2 all (incl. 0 ) Good description of CLAS,SLAC data Laget model: Photoproduction

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Laget model: Electroproduction CLAS data Laget model

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At the time of the analysis (~2008), radiative corrections were treated as averaged over M + -, i.e. only as a function of (x B, Q 2 ) Relatively small effect on 0 cross sections as the “distortion” of the M + - spectrum was “absorbed” in the effective + - continuum background subtraction (also ~25% syst. uncertainty was included) M + - (GeV) However, current more refined re-analysis of these data (B. Garillon, aimed at f 0 and f 2 analysis, see talk on Saturday) show that there is a M + - -dependence f0f0 f2f2

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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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d /dt ( * p p 0 ) Fit by e bt Large t min ! (1.6 GeV 2 )

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Angular distribution analysis, cos cm Relying on SCHC (exp. check to the ~25% level)

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Longitudinal cross section L ( * L p p L 0 )

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

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Comparison of cross sections is model-dependent: k perp dependence ansatz, model for GPDs,… L / T ~Q 2 L ~1/Q 6 T ~1/Q 8 Q 2 dependence: Saturation with hard scale of b SCHC : checks with SDMEs J ~9/1/2/8 ~|xG(x)| 2 W (or x B ) dependence: Ratio of yields: Some signatures available for gluon handbag are not relevant for quark handbag: Model-independent features:

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GeV S. Morrow et al., Eur.Phys.J.A39:5-31,2009 (

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b (from e bt ) as a function of Q 2 (be careful of correlation with W) L / T as a function of Q 2 (be careful of correlation with W)

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Exclusive electroproduction at CLAS12 CLAS12 proposal PR Q 2 range at 6 GeV Q 2 range at 12 GeV

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decay angular distribution (polar angle cm ) CLAS12 proposal PR purely statistical error bars statistical error bars +10% systematic

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Exclusive electroproduction

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ep->ep

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cos( cm ) distribution cm distribution

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Laget Regge model for *p p Cross section ( * p p Laget T + L Laget L VGG L (H&E) Issue with GPD approach if 0 exchange dominant : 0 ->E E subleading in handbag for VM production (GK includes 0 exchange with k perp effects) ~ ~ while DESY data CORNELL data

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Cross section ( * p p Comparison with GPD calculation (VGG)

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Exclusive + electroproduction (A. Fradi’s thesis) Slow but steady progress towards publication ! towards publication !

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++ e - ) (p) One event in CLAS e p e’ [n] e’ [n] + 0 e’ [n] Channel selection IC EC

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Invariant mass IM( + 0 )

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Invariant mass IM(n 0 ) Invariant mass IM(n + )

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Invariant mass IM( + 0 )

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PRELIMINARY Total cross section Q 2,x B ) +

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Laget Regge “hadronic” approach Laget Regge “hadronic” approach + ++ ++ ++ n ++ n GPD “partonic” approach GPD “partonic” approach +L+L H, E ρ0ρ0ρ0ρ0 e u H u - e d H d e u E u - e d E d e u H u + e d H d e u E u + e d E d ρ+ρ+ρ+ρ+ H u - H d E u - E d

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“Hadronic approach”: Laget model ++ 00

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“Hadronic approach” Laget model does not reproduce the drop of d /dt for t →0 PRELIMINARY

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(*) “Partonic approach”: GPDs GPDs 00 VGG GPD model GK GPD model ++ GPDs p n LL e e’e’

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GPDs model agrees fairly with the data at low x B (high W) GPDs model misses the data at high x B (low W) (*) “Partonic approach”: GPDs Only H in this calculation

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(*) Hint of GPD E dominance The GPD E reproduces the drop of d /dt for t →0

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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 ( (preliminary)

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Comparison of t-slope for channels at 6 GeV

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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 low energy (W<5 GeV), success of “hard” approach for the channel ( nucleon gluon imaging) but large failure for the 0, + channels. This is not understood. Why the GPD/handbag approach sould set at much larger Q 2 for valence quarks ? Are the widely used GPD parametrisations in the valence region completely wrong ? JLab12 PR proposal: broader phase space, check when Q 2 independence settles for a variety of observables At high energy (W>5 GeV), transition from “soft” to “hard” ( 2 scale) physics relatively well understood (further work needed for precision understanding/extractions) handbag interpretation and nucleon imaging handbag interpretation and nucleon imaging

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W~1/ GPDs/handbag GPDs/handbag ???

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BACKUP SLIDES

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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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( * p p 0 ) vs W

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

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Exclusive electroproduction

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ep->ep

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GK L LL Laget T + L W=2.9 GeV W=2.45 GeV W=2.1 GeV

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100% acceptance & integrated over all variables but (x B,Q 2 ) 6 GeV e fixed p target Counting rates for 1000 hours at cm -2 s -1 Limitation comes from phase space

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100% acceptance & integrated over all variables but (x B,Q 2 ) 6 GeV e fixed p target Counting rates for 100 hours at cm -2 s -1 Limitation comes from phase space

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100% acceptance & integrated over all variables but (x B,Q 2 ) 11 GeV e fixed p target Counting rates for 1000 hours at cm -2 s -1 Limitation comes from phase space

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100% acceptance & integrated over all variables but (x B,Q 2 ) 11 GeV e fixed p target Counting rates for 1000 hours at cm -2 s -1 Limitation comes from phase space

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100% acceptance & integrated over all variables but (x B,Q 2 ) Counting rates for 1000 hours at cm -2 s GeV e 60 GeV p Limitation comes from luminosity

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100% acceptance & integrated over all variables but (x B,Q 2 ) Counting rates for 1000 hours at cm -2 s GeV e 60 GeV p Limitation comes from luminosity

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6 GeV e fixed p target 11 GeV e fixed p target 11 GeV e 60 GeV p

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d /dt ( * p p 0 ) Fit by e bt Large t min ! (1.6 GeV 2 )

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L ( L ( b d L dt ( d L dt ( b Longitudinal cross sections PRELIMINARY

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e e Q ~ MeV Q >>GeV Increasing Q 2 : Q 2 >>

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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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d /dt ( * p p 0 ) Fit by e bt Large t min ! (1.6 GeV 2 )

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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 V 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+/ 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

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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 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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HERMES Cornell CLAS

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LL ep->ep GK L CLAS HERMES HERA

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Exclusive electroproduction: gluon imaging of the proton x<0.01: measured at H1/ZEUS x>0.1: practically unknown: with CLAS12

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(A. Kubarovsky’s simulations) Extract t–slope of d L /dt up to Q 2 ~7 GeV2 As a function of Q 2 : check when Q 2 -independence settles As a function of x B (or W): first 3D-gluon imaging at large x Exclusive electroproduction: gluon imaging of the proton CLAS12 proposal PR :

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C. Weiss:

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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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