Minimal model of the dual parameterization of nucleon GPDs

V. Guzey and T. Teckentrup, Phys. Rev. D 74, 054027 (2006) (2006)
V. Guzey and T. Teckentrup, Phys. Rev. D. 79 , 017501 (2009) [arXiv:0810.3899 [hep-ph]]

Description of the model

Comparison to DVCS data

Compton Form Factors
of proton and neutron
(with downloads)

DVCS asymmetries
ALU, AC and AUT
of proton and neutron
(with downloads)

Nuclear GPDs and nuclear
DVCS asymmetries
(with downloads)






Back to V.Guzey at PNPI 		IMPORTANT: A factor of two in front of the DVCS amplitude was missing in our original paper [V. Guzey and T. Teckentrup, Phys. Rev. D 74, 054027 (2006)]. In other words, the GPDs had the forward limit, which is 1/2 of the conventional one.

This was explained and corrected in our recent paper (V. Guzey and T. Teckentrup, Phys. Rev. D. 79 , 017501 (2009) [arXiv:0810.3899 [hep-ph]]).
As a result, the good agreement with the high-energy DVCS data (H1 and ZEUS) is no longer possible in the minimal model of the dual parameterization.

All expressions, plots, data files (grids) and Fortran codes given below are up-to-date, i.e. with the restored factor of two and the correct forward limit of the generalized parton distributions.

Description of the model

The dual parameterization of nucleon Generalized Parton Distributions (GPDs) is built as a formal infinite and divergent series reproducing Mellin moments of the nucleon GPDs. The parameterization is called dual because its derivation is based on the hypothesis of duality: the resulting nucleon GPDs are presented as infinite sums of t-channel exchanges. The advantages of the dual parameterization include:

  • simple (forward) QCD evolution
  • weak model-dependence for xB<0.2
  • simple expressions for Compton form factors.

    • The dual parameterization for the nucleon GPDs H and E reads (the singlet combination which has the quark+antiquark sum in the forward limit):

    dual_formula_2009
    where Bnl and Cnl are unknown form factors (with the known QCD µ2 evolution);
    Cn3/2 are Gegenbauer polynomials; Pl are Legendre polynomials;
    i is the quark flavor.

    The way to work with the above divergent series is to introduce the generating functions Qk and Rk (Shuvaev transform):

    dual_formula2

    With this trick, the expressions for the GPDs become explicitly finite:

    dual_formula4_2009

    The expressions for the GPDs H and E are organized as series in terms of xikQk. Therefore, at sufficiently small xi, the series can be truncated.

    The minimal model of the dual parameterization consists in keeping only the generating functions Q0 and Q2 for H and R0 and R2 for E.
    The generating functions Q0 and R0 are expressed in terms of the following forward distributions:

    dual_formula3
    The generating functions Q2 and R2 can be modeled in terms of Q0 and R0 and the the so-called D-term.

    Within the dual parameterization, the t-dependence of the GPDs should be modeled separately. Two models were considered:
  • non-factorized Regge-motivated
    (preferred)
    		• dual_formula7

    		dual_formula8

    		dual_formula9
  • factorized exponential
    		•  dual_formula5

    		dual_formula6

    The Compton form factors (CFFs) have a simple form in terms of the generating functions:

    dual_formula10_2009
    In the sums above, only the terms with k=0,2 are kept in the minimal model.
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