Realistic parameterization of GPDs and its

applications

Simonetta Liuti

University of Virginia

Jlab Theory Group SeminarNovember 10th, 2008.

Collaborations

Gary Goldstein (Tufts University)

Leonard Gamberg (Penn State, Berks)

Eric Voutier (Grenoble)

AHLT: Saeed Ahmad (U. Wisconsin), Heli Honkanen

(Iowa State), S.L., Swadhin Taneja

Graduate Students: Osvaldo Gonzalez, Chuanzhe Lin,

Huong Nguyen, Dan Perry

Outline

Unpolarized GPDs from proton and neutron data sets

New results using Jlab data constraints!

Access to Chiral-Odd GPDs

Practical method for the extraction of both

tensor charge: q “Burkardt's moment”: Tq

Nuclei: DVCS and p0 electroproduction on 4He

Conclusions/Outlook

1. Extraction from data needs a reliable GPD model

No longer simple models (D. Muller)

Include Q2 dependence (M. Diehl)

Include all constraints from data DVCS, DVMP... (S.L.)

Include new data as they become available... (S.L.)

Use Lattice + Chiral Extrapolations (P. Hägler, A. Schaefer)

Connect various experiments, separate valence from sea,

flavors separation (T. Feldman)...

New! Representation in terms of dispersion relation only

necessary to measure imaginary part? Stronger polynomiality

constraint (Anikin, Teryaev, Diehl, Ivanov, Vanderhaeghen)

A more advanced phase of extracting GPDs from data

(a bit of summary from ECT*, June'08, and Jlab Hall B meeting, Aug.’08)

A similar program exists for TMDs (simpler partonic interpretation than

GPDs) see e.g. M. Anselmino and collaborators

GPDs give access to orbital angular momentum of partons!

DVCS and Generalized Parton Distributions

GPDs are hybrids of PDFs and FFs: describe simultaneously

x and t-dependences !

GPDs give access to spatial d.o.f. of partons !

“Generalized Parton Distributions Correlator”

t= 2

X. Ji

DVCS Cross Section

What goes into a theoretically motivated

parametrization...?

The name of the game: Devise a form combining

essential dynamical elements with a flexible model

that allows for a fully quantitative analysis

constrained by the data

Hq(X, t)= R(X, t) G(X, t)

“Regge” Quark-Diquark

Q2 Evolution is an essential element!!

S. Ahmad, H. Honkanen, S. Liuti and S.K. Taneja,

Phys. Rev. D 75, 094003 (2007)

Two different time orderings/pole structure!

Quark anti-quark pair describes similar physics (dual to) Regge t-channel exchange!!

DGLAP ERBL

X> X<

t

In DGLAP region partonic picture

PX

+

P'+=(1- )P+

k+=XP+k'+=(X- )P+

q q+

k' =k -k

P+

ReggeQuark-Diquark

Formulae extended to >0 in AHLT2 (arXiv:0708.0268).

Constraints on

parameters...

= 0 Nucleon Form Factors

Parton Distribution Functions

Notice! GPD parametric

form is given at Q2=Qo2

and evolved to Q2 of data.

Notice! We provide a

parametrization for

GPDs that

simultaneously fits

the PDFs:

q(x) = Hq(x,0,0)

Polynomiality

For higher moments (n=2,3,...) use lattice results

(consistency with data can be checked Juvs. J

d)

n=2

n=3

P. Haegler

Use information from Lattice QCD:

(1) lattice results follow dipole behavior for n=1,2,3

Chiral Extrapolations

Dorati, Gail and Hemmert (2007)

Wang, Thomas, Young (2008)Ashley et al. (2003)

-t (GeV2)

Sensible predictions for kT

vs. xBj

Sensible predictions for r2 = b2/(1-xBj

) vs. xBj

(M. Burkardt)

Dominance of large xBj

at large t

Summary of Constraints

Constraints from Form Factors

Dirac

Pauli

Constraints from PDFs

Further Theoretical Constraints:

● Sensible prediction for hadron shape at x 1

● Sensible prediction for kT

dependence (connection with TMDs!)

(SL and Taneja, 2004)

Constraints from Polynomiality

On the connection between TMDs and GPDs

Liuti and Taneja, PRD (2004)

AHLT Parameterization

v1

v2

7 + 1 (Qo) parameters

10 + 1 (Qo) parameters

More details in AHLT, PRD 2007

0

use v1 for DGLAP region (X > )

0

Hq(x,0,t) E

q(x,0,t)

u d u d

Comparison with similar parametrizations at =0 (Diehl et al.)

Comparison with similar parametrizations at =0 (Guidal et al.)

The ERBL Region…partonic interpretation is not obvious

We know the area from

n=1 moment + constrained

DGLAP

We extract it from lattice QCD results

Hybrid Model (Dieter Mueller)

Weighted Average Value

Location of X-bin

Dispersion (error in X)

We know n 3 moments

Reconstruct GPDs from Bernstein moments

Test with known, previously evaluated GPD, at 0

ERBL Region AHLT arXiv:0708.0268

Determined from lattice moments up to n=3

Comparison with Jlab Hall A data (proton)Munoz Camacho et al. (2006)

Im H from asymmetry

Note!!

Re H from x-section

Comparison with Jlab Hall A data (neutron)Mazouz et al. (2007)

AHLT, PRD75:094003 (2007)

From fit to form factors

From fit to PDFs

VGG: crisis or not?

Cannot reproduce both!

Im F

Re

F

Guidal (2008)

Polyakov and Vanderhaeghen

(2008)

Real Part (S.Ahmad, S.L., preliminary)

Are the exclusive data “telling” us something?

vanishes at X=0 as X

cusp

Fitted directly at Q

of data

(X- ) “DA type” shape needed to fit

“t”-dependence of Jlab data!!!

●Behavior determined by Jlab data on Real Part and Q2 dependence

S. Ahmad

●Consistent with lattice determination!

Orbital Angular Momentum

AHLT includes only

valence contribution!

Jq=(

q+1)A

20(0)

Dispersion Relations(Anikin, Teryaev, Diehl, Ivanov,…)

Q2

2

H(x,x,t) + C

Viewed this way a quark + spectator cannot be on their

mass shell but hadronic jets must have some threshold.

This threshold (“physical threshold”) is much higher than what

required for the dispersion relations to be valid

Where is threshold?

Continuum starts at s =(M+m )2 lowest hadronic threshold.

How to fill the gap? Analytic continuation?

t

0 physical

phys ifmasses in the two-body

scattering problem are different!

Q2=1.0 GeV2Q2=2.0 GeV2

Q2=5.5 GeV2

-t -t

-t

-2.4>t>-7.4 GeV2

Physical region

has no gap for Q2=5.5 GeV2

-1.1>t>-2.7 GeV2

Physical region

has no gap for Q2=2.0 GeV2

-0.60>t>-1.34 GeV2

Physical region

has no gap for Q2=1.0 GeV2

Gaps in dispersion integrals

From Gary Goldstein, SPIN 2008

When deeply virtual processes involve directly final states

- like in exclusive or semi-inclusive processes - “standard kinematic

approximations should be questioned” (Collins, Rogers, Stasto, 2007)

Transversity

u

dET(x, , t,Q2) = T

q HT(x, , t,Q2)

h1(x,Q2) = q f1(x,Q2)

HT(x, , t,Q2) = q H(x, , t,Q2)

Related to Boer-Mulders function: h1

Simple Ansatzh1

2. Electroproduction Observables and GPDs*

*S. Ahmad, Gary Goldstein, S.L., arXiv:0805.3568 hep-ph

Exclusive o electroproduction

h1

LAB

e'

e

t= 2

“Quark-Hadron” Helicity Amplitudes (Marcus Diehl)

helicity amps.

Dual Representation?

Comparison between Regge and “Partonic” approaches

Q2 dependence at pion vertex

q oq' cross section

Chiral Odd Generalized Form Factors

JPC=1-- JPC=1+-

JPC=1--, 1+-

, ...HT, E

T, ...

Only chiral-odd GPDs!!!

JPC=1++, ... (a1-type exchange) H, E, ... ~ ~

What goes into the quark-hadron

amplitudes?

Generalized Form Factors

HT(X,0,0) = h

1(X) = transversity

h1(X,Q2) dX = q= tensor charge

h1

(X) dX d2k

T ~ -

T (A.Metz)

E2(X,0,0) dX =

T = Burkardt's moment

Observables are sensitive to both q and T!

... and more ...!!!

Q2 dependence

t-channel exchange

vertex

modeled as F (pseudoscalar-

meson transition form factor)

, b1, h

1

, , b1, h

1

JPC=1--

(3S

1)

JPC=1+-

(1P

1)

JPC=0-+

quark content:

Distinction between and b1, h

1exchanges

JPC=1--

JPC=1+-

o: qqbar from S, L S=0, L L

o: qqbar from (S=0, L=1) (S=0,L=0) L =1

“Vector” exchanges no change in OAM

“Axial-vector” exchanges change 1 unit of OAM!

Main Result: Tensor Charge and Anomalous Transverse Moment treated as

free parameters to be extracted from data

Fixed u

and d

3. Nuclei: Spin 0 and Spin 1

GPDs & hadron tensor for Spin 0 nuclear target

(S.L. and SwadhinTaneja, PRC 2005)o production

(with G. Goldstein)

Jefferson Lab approved experiment, H. Egiyan, F.X Girod, K. Hafidi,

S.L. and E. Voutier

Spatial structure of quarks and gluons in nuclei

Burkardt-Soper

impact parameterquark's position

in nuclei

New! Test OAM SR in Spin 1 system: Deuteron

(S.L. and S. Taneja)

4He

o

0

0

+1/2

+1/2

-1/2

0

f 0,00(s,t,Q2) = g +,0- A0+,0 -

analogue of HT

JPC= 1+- exchange b1, h1

&

JPC= 1- - exchange 0,

mquark=0 has to flip helicity

for q +q and q q 0.

o

00

+1,0

b1 & h10 &

4He

0

4He 4Hestructure of p p

A+i(p +p) B 2 invariant amps,

2 independent helicity amps

o electro-production from 4He

Conclusions and OutlookComparison between GPD models and data is indeed possible...GPD extraction is possible!!!

Approaching “Global Analysis”

Interesting connections between TMDs and GPDs

Proposed extraction of tensor charge and transverse anomalous moment from neutral pion production data

Spatial structure of Nuclei

JPC=1-- JPC=1+-, , , .. b1, h

1