General introduction to GPDsGeneral introduction to GPDs

From data to GPDs From data to GPDs

General introduction to GPDsGeneral introduction to GPDs

From data to GPDs From data to GPDs

Operator inOperator inspace coordinatesspace coordinates

Structure function inStructure function inmomentum coordinatesmomentum coordinates

pyqqp )()0( O)(),( 11 xgxfep eX

pqqp )0()0(' O)(),(),(),( 21 tGtGtFtF PAep ep

pyqqp )()0(' O),,(

~),,,(

~),,,(),,,(

txEtxH

txEtxH

ep ep

DiagrammeDiagramme ProcessProcess

(restricting myself to LT-LO, chiral even, quark sector)

H, H, E, E (x,ξ,t)~ ~

Standard 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

2Jq = x(H+E)(x,ξ,0)dx

gq LGL 21

21

(nucleon spin)

x+ξ x-ξ

tγ, π, ρ, ω…

-2ξ

: don’t appear in DIS : NEW INFORMATION

<x ><x >00

<x ><x >-1 -1

t=0t=0

<x ><x >11

DDsDDs

« D-term »« D-term »x,bx,b

GPDsGPDs

Pion cloudPion cloudLong.mom./trans.pos. correlationsLong.mom./trans.pos. correlations

F (t), G (t)F (t), G (t)1,21,2 A,PSA,PS

q(x),q(x),q(x)q(x)

R (t),R R (t),R (t)(t)AA VVJJqq

(z)(z)

p p’

H,E,H,E~ ~

x

t

Deconvolution needed !Deconvolution needed !x : mute variable

x

Hq(x,,t) but only and t accessible experimentally

d

d dtB

~ A H (x,,t)q

x-idx +B E (x,,t)

q

x-idx +….

1 1

-1 -1

2

= xB1-x /2B t=(p-p ’)2

x = xB !

/2

GPD and DVCSGPD and DVCS

1

1

1

1

),,(),,(

~),,(

~ tHidxx

txHPdx

ix

txHT DVCS

Cross-section measurementand beam charge asymmetry (ReT)

integrate GPDs over x

Beam or target spin asymmetrycontain only ImT,

therefore GPDs at x = and

(at leading order:)

General introduction to GPDsGeneral introduction to GPDs

From data to GPDs From data to GPDs

The experimental actorsThe experimental actors

p-DVCS

BSAs,lTSAs

p-DVCS

X-sec

Hall BHall A

JLab CERNCOMPASS

Vector mesons

DVCS

p-DVCS

X-sec,BCA

p-DVCS

BSA,BCA,

tTSA,lTSA

H1/ZEUSHERMES

DESY

In general, 8 GPD quantities accessible (Compton Form Factors)

DVCS : goldenChannelAnticipatedLeading Twist dominancealready at low Q2

Model-independent fit, at fixed xB, t and Q2, of DVCS observables with

MINUIT + MINOS

Given the well-established LT-LO DVCS+BH amplitude

DVCS Bethe-Heitler

GPDs

7 unknowns (the CFFs), non-linear problem, strong correlations

M.G. EPJA 37 (2008) 319 M.G. & H. Moutarde, EPJA 42 (2009) 71)

M.G. PLB 689 (2010) 156 M.G. arXiv:1005.4922 [hep-ph] (acc.PLB)

Only 3 CFFs come out from the fit with finite error bars: HIm , HIm and HRe

~

* « Shrinkage » of HIm

* HIm>HRe

As energy increases:

JLabxB=0.36,Q2=2.3

*Different t-behavior for HIm&HRe

(model dependent Fit ofD. Muller, K. KumerickiHep-ph 0904.0458

HERMES

HIm HRe

HIm HRexB=0.09,Q2=2.5

xB dependence at fixed t of HIm

VGG prediction

xB-dependence at fixed t

Fitting the CLAS & HERMES lTSAslTSAs:

of HIm

~

VGG predictionFit with 7 CFFs(boundaries 5xVGG CFFs)

Fit with 7 CFFs(boundaries 3xVGG CFFs)

JLabHERMES

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 xB

of HIm & HIm

~

Axial charge more concentrated than electromagnetic charge ?

First CFFs model independent fits First CFFs model independent fits (leading-twist/leading order (leading-twist/leading order approximation); approximation); “Minimal theoretical input”“Minimal theoretical input”

Procedure tested by Procedure tested by Monte-CarloMonte-Carlo

Procedure is working on Procedure is working on real datareal data; ; extraction of extraction of HHImIm and and HHReRe at JLab at JLab (cross sections)(cross sections)

and HERMES and HERMES (asymmetries)(asymmetries) energies energies

Relatively large uncertainties on extracted CFFsRelatively large uncertainties on extracted CFFs(due to lack of observables -and precision on data-)(due to lack of observables -and precision on data-)

Introducing more theoretical input will reduceIntroducing more theoretical input will reduceuncertainties uncertainties (but model dependency)(but model dependency)

Large flow of new observables and data expected soon;Large flow of new observables and data expected soon;will bring much more experimental constraints to extractwill bring much more experimental constraints to extractCFFs with minimum theoretical inputCFFs with minimum theoretical input