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

,

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) ]

,

, Q 2 >>

,

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

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,…

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

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…

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) F.-X. Girod

Exclusive  0 electroproduction

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

IM(p  + )

IM(p  - )

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

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

 +f 0 + f 2  all (incl.  0 ) Good description of CLAS,SLAC data Laget model: Photoproduction

Laget model: Electroproduction CLAS data Laget model

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

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

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

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

Longitudinal cross section  L  (  * L p  p  L 0 )

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

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

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:

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

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)

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

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

Exclusive  electroproduction

ep->ep       

cos(  cm ) distribution  cm distribution

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

Cross section  (  * p  p  Comparison with GPD calculation (VGG)

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

++ e  - ) (p)   One event in CLAS e p  e’ [n]    e’ [n]  +  0  e’ [n]    Channel selection IC EC

Invariant mass IM(  +  0 )

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

Invariant mass IM(  +  0 )

PRELIMINARY Total cross section  Q 2,x B )  +

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

“Hadronic approach”: Laget model ++ 00

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

(*) “Partonic approach”: GPDs GPDs 00 VGG GPD model GK GPD model ++ GPDs p n LL  e e’e’

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

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

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)

Comparison of t-slope for    channels at 6 GeV

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

W~1/  GPDs/handbag GPDs/handbag ???

BACKUP SLIDES

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”

   (  * p  p  0 ) vs W

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

Exclusive  electroproduction

ep->ep     

GK  L LL Laget  T +  L W=2.9 GeV W=2.45 GeV W=2.1 GeV

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

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

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

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

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

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

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

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

 L (    L (    b  d  L  dt (   d  L  dt (    b  Longitudinal cross sections PRELIMINARY

 e  e  Q ~ MeV  Q >>GeV  Increasing Q 2 : Q 2 >>

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

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

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 V 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    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

HERMES Cornell CLAS

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

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

(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 :

C. Weiss:

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