A simple form for the low-x generalized parton distributions in the skewed regime

TL;DR

This paper presents a simplified relation between generalized parton distributions and usual diagonal distributions in the skewed low-x regime, improving understanding and calculation of relevant cross sections at the LHC.

Contribution

It introduces a straightforward method to relate GPDFs to diagonal distributions in the skewed regime, bypassing complex integrals and enhancing practical applications.

Findings

Simplified relation derived from the Shuvaev transform

Application to Higgs and Upsilon production at the LHC

Improved accuracy in cross section calculations

Abstract

We show that the generalized parton distributions (GPDFs) in the 'skewed' $x \approx \xi << 1$ regime can be related in a particularly simple way to the usual diagonal distributions. This follows directly from the Shuvaev transform, but bypasses a direct evaluation of the poorly convergent double integral which this relation contains, thus allowing for a more transparent understanding of the physics involved; it avoids the necessity for any further low-x approximations for the diagonal partons, as well as permitting a clearer application to cases when the GPDFs unintegrated over the parton transverse momentum are required. We consider for illustration the specific examples of the central exclusive production of a Standard Model Higgs boson, and the photoproduction of a Upsilon meson at the LHC, and show how a careful evaluation of the GPDFs, which our simple results allow, is required to correctly calculate the predicted cross sections.