Generalized parton distributions from hadronic observables: non-zero skewness

Abstract

We propose a physically motivated parametrization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, ζ. Our approach follows a previous detailed study of the ζ = 0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non singlet sector. Additional constraints at ζ = 0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards an extraction of generalized distributions based on a global fit of the available data within the given set of constraints.

Flexible parametrization of generalized parton distributions from deeply virtual Compton scattering observables

“…By inspecting Eqs. (27), (29) and (48) one can see that for t = 0 and ζ = 0, the only parameters that enter are: As already noticed in [24][25][26], the diquark model based parametrization corresponds to a low initial scale, Q 2 o . Parametric forms are then evolved to the Q 2 of the data using LO Perturbative QCD (PQCD) evolution equations [37].…”

“…The number of parameters used is consistent with the one used in fits of the nucleon form factors data. These require four parameters for G q and E q from [24,25] at the scale Q 2 o , is also shown. In Fig.7 we show H u,d (X, ζ, t; Q 2 ) evaluated at Q 2 = 2 GeV 2 and for a variety of ranges in ζ ≡ x Bj and Q 2 .…”

“…[24,25] where we considered both the S = 0 (scalar) and S = 1 (axial vector) configurations for the diquark. This allows one to obtain distinct predictions for the u and d quarks.…”

Generalized parton distributions for the proton in position space: Nonzero skewness

“…In this work, we investigate a recent parametrization [18] of the GPDs in position space for non-zero ζ. GPDs for zero skewness have been parametrized in a similar way in [19]. At the input scale they are parametrized by a spectator model term multiplied by a Regge motivated term.…”

Generalized Parton Distributions in Deeply Virtual Lepton Scattering Processes

“…Initial work [4] in constructing a spectator model for the chiral even GPDs, H q (X, ζ ,t) and E q (X, ζ ,t), showed considerable promise in incorporating constraints and in confronting data. This approach was extended to include all four of the chiral even valence quark GPDs, in conjunction with Deeply Virtual Compton Scattering (DVCS), in a series of papers that developed the "flexible model", which is a "Reggeized diquark model" (R x Dq) [5,6].…”