Strategies to extract gpds from data
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Simonetta Liuti University of Virginia & Gary Goldstein Tufts University INT, 14-19 September 2009 APS DNP Meeting Saturday, October 25th, 2008. Oakland, USA. Strategies to extract GPDs from data. Introduce a step by step analysis Step 1, Step 2, Step 3, Step 4

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Strategies to extract GPDs from data

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Simonetta Liuti

University of Virginia


Gary Goldstein

Tufts University

INT, 14-19 September 2009

APS DNP Meeting

Saturday, October 25th, 2008.

Oakland, USA

Strategies to extract GPDs from data

Introduce a step by step analysis

Step 1, Step 2, Step 3, Step 4

Interesting applications: Access Chiral-Odd GPDs, Nuclei: DVCS and 0 electroproduction on 4He



With the new experimental analyses at HERMES, Jlab, Compass… we are entering a new, more advanced phase of extracting GPDs from data

Many concerns have been raised recently:

No longer simple parametrizations (K. Kumericki, D. Muller)

Q2 dependence (M. Diehl et al.)

What type of information and accuracy from simultaneous measurements of different observables? (M. Guidal, H. Moutarde)

How can one use Lattice + Chiral Extrapolations (P. Hägler, S.L.)

How can one connect various experiments, separate valence from sea, flavors separation (P. Kroll, T. Feldman)...

Use of dispersion relation: is it only necessary to measure imaginary part of DVCS, DVMP? (Anikin & Teryaev, Diehl & Ivanov, Vanderhaeghen, Goldstein & S.L.)

Global analysis exists for TMDs (simpler partonic interpretation than

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

DVCS Cross Section (Belitsky, Kirchner, Muller, 2002)


Angle between transverse spin and final state plane

Azimuthal angle between planes

Comtpon Scattering and Bethe Heitler Processes


Look for instance at DVCS-BH Interference

Off forward Parton Distributions (GPDs) are embedded in

soft matrix elements for deeply virtual Compton scattering (DVCS)






P’+=(1- )P+



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)



+ Q2 Evolution

Quark-Diquark model: two different time orderings/pole structure!

DGLAP: quark off shell, spectator on shell

ERBL: quark on shell, spectator off-shell



Quark anti-quark pair describes similar physics (dual to) Regge

t-channel exchange (JPC quantum numbers)

Vertex Structures



P’+=(1- )P+




S=0 or 1

Focus e.g. on S=0

Vertex function 



O. Gonzalez Hernandez, S.L.

Fixed diquark mass formulation

DGLAP region

ERBL region

Reggeized diquark mass formulation

Diquark spectral function


 (MX2)


DIS  Brodsky, Close, Gunion ‘70s

  • Fitting Procedure

  • Fit at=0, t=0  Hq(x,0,0)=q(X)

    • 3 parameters per quark flavor (MXq, q, q) + initial Qo2

  • Fit at=0, t0 

    • 2 parameters per quark flavor (, p)

  • Fit at 0, t0 DVCS, DVMP,… data (convolutions of GPDs with Wilson coefficient functions) + lattice results (Mellin Moments of GPDs)

  • Note! This is a multivariable analysis  see e.g. Moutarde,

    Kumericki and D. Mueller, Guidal and Moutarde

  •  additional parameters (how many?)

  • t




    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:

    Hq(X,,t)= R(X,,t) G(X,,t)



    Nucleon Form Factors

    = 0, t0

    S. Ahmad, H. Honkanen, S. L., S.K. Taneja, PRD75:094003,2007

    Parameters from PDFs

    Parameters from FFs

    Some results…



    S. Ahmad, H. Honkanen, S. L., S.K. Taneja, (AHLT), PRD75:094003,2007

    , t S. Ahmad et al., EPJC (2009)

     we were able to extend the parametrization to 

    taking into account lattice results on n=2,3 moments of GPDs

     the new parametrization is valid for valence quarks only

    (not expected to be extended sensibly, “as it is”, into

    HERA/HERMES region: need sea quarks + gluons)

     it works fine at Jefferson Lab kinematics

    Use information from Lattice QCD:

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

     

     Extract dipole masses from

    lattice data

     Relate dipole mass to “radius”


     Chiral extrapolation of dip. mass

    Polynomiality from lattice results up to n=3



    Results of Chiral Extrapolations

    proton form factor

     Ashley et al. (2003)

     Ahmad et al. (2008)

    -t (GeV2)

    New Developments (H.Nguyen)

    We repeated the calculation with improved lattice results

    (Haegler et al., PRD 2007, arXiv:0705:4295)


    Results are comparable (up to n=2) to our

    “phenomenological” extrapolation

    We are investigating the impact of different chiral extrapolation

    methods: “direct” extrapolation applicable up to n=2 only

    M. Dorati, T. Gail and T. Hemmert (NPA 798, 2008)

    (Also using P. Wang, A. Thomas et al. )

    New Results are more precise and compatible with other chiral extrapolations

    A20u-d vs. (-t)

    Nguyen, S.L.


    Lattice results are used to model/fit the ERBL Region…

    We know the area from n=1 moment + constrained DGLAP

    Reconstruction of GPDs from Bernstein moments

    Weighted Average Value

    Location of X-bin

    Dispersion (error in X)


    * Algebra a bit more complicated for  to transformation, details in EPJC(2009)

    Test with known, previously evaluated GPD, at 0

    ERBL Region

    Ahmad et al., EPJC (2009)

    Determined from lattice moments up to n=3

    New Analysis

    • Results are more accurate one can see trends

    • both isovector and isoscalar terms

    Summary of first three steps towards parametrization


    7 + 1 (Qo) parameters


    10 + 1 (Qo) parameters


    use v1 for DGLAP region(X >  )


    use lattice calculations for ERBL region(X <  )

    BSA data are predicted at this stage

    Munoz Camacho et al., PRL(2006)

    Hall B (one binning, 11 more)

    Comparison with Jlab Hall A data (neutron)

    Mazouz et al. (2007)


    Fit to JLAB data: real part of CFF from d+ + d-

    Real Part(work with S.Ahmad, H. Nguyen)


    Fitted directly at Q2 of data

    Cusp from reggeized ERBL  (-X)

    either from phenom.“DA type” shape, or diquark model

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

    • Consistent with lattice determination!

    Dispersion Relations (brief parenthesis…)






    G.Goldstein and S.L.,arXiv:0905.4753 [hep-ph]

    Dispersion relations cannot be directly applied to DVCS because one misses a

    fundamental hypothesis: “all intermediate states need to be summed over”

    This happens because “t” is not zero  t-dependent threshold cuts out

    physical states

    It is not an issue in DIS (see your favorite textbook, LeBellac, Muta,

    Jaffe’s lectures…) because of optical theorem

    From DR

    to Mellin moments expansion


    One proceeds backwards, from polynomiality  analytic properties (Teryaev)

    But here one is forced to look into the nature of intermediate states because there is no optical theorem

    t-dependent thresholds are important: counter-intuitively as Q2 increases the DRs start failing because the physical threshold is farther away from the continuum one (from factorization)

    Is the mismatch between the limits obtained from factorization and the physical limits from DRs a signature of the “limits of standard kinematical approximations”? (Collins, Rogers, Stasto and Accardi, Qiu)

    Dispersion Relations (brief parenthesis…)






    G.Goldstein and S.L.,



    Simple Ansatz

    h1(x,Q2) = q f1(x,Q2)


    HT(x, , t,Q2) = q H(x, , t,Q2)


    ET(x,  , t,Q2) = TqHT(x, , t,Q2)

    Related to Boer-Mulders function


    GPDs & hadron tensor for Spin 0 nuclear target(Liuti and Taneja, PRC 2005)Exclusive o production from 4He (with G. Goldstein)

    OAM sum rule in deuterium (with S.K. Taneja)

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

    S.L. and E. Voutier

    Spatial structure of quarks and gluons in nuclei


    impact parameter

    quark's position

    in nuclei

    New! Test OAM SR in Spin 1 system: Deuteron

    (S.L. and S. Taneja)

    Conclusions and Outlook

    • Approaching “Global Analysis” for GPDs is a more complex problem than for PDFs and TMDs:

      • combinations of GPDs enter simultaneously the physical observables

      • dependence on several kinematical variables: X,,t,Q2 of which…

      • …X always appears integrated over

    • Strategies to extract GPDs from data are based on multistep analyses: we propose one of such analyses using a physically motivated parametrization + lattice results

    • Focus of the present work was on H and E in “valence” region

      • Several applications and extensions: extraction of tensor charge and transverse anomalous moment from neutral pion production data, studies of spatial structure of nuclei…

    • …but analysis is underway that takes into account all GPDs

    • This analysis is possible thanks to the flexibility offered by our parametrization/model

    , , , ..

    b1, h1



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