Generic modelling of non-perturbative quantities and a description of hard exclusive $\pi^+$ electroproduction

TL;DR

This paper develops empirical models for generalized parton distributions based on Regge-inspired and counting rule arguments, and compares them with experimental data on hard exclusive pion electroproduction, revealing limitations of minimalist models.

Contribution

It introduces new GPD models incorporating a hypothetical master trajectory and tests their validity against experimental data, highlighting the challenges of minimalist GPD approaches.

Findings

Minimalist GPD models are disfavored at leading order.

The proposed GPDs on the cross-over line describe HERMES and JLAB data well.

Inclusion of a hypothetical master trajectory improves data description.

Abstract

Based on Regge-inspired arguments and counting rules, we formulate empirical models for zero-skewness generalized parton distributions (GPDs) ${\widetilde H}^{(3)}$ and ${\widetilde E}^{(3)}$ in the iso-vector sector. If a hypothetical $a_1/\rho_2$ master trajectory is taken into account, we find that the polarized deep inelastic structure function $g_1^{(3)}$, axial-vector form factor, pseudoscalar form factor, and lattice data are well described. Thereby, we use a symmetric valence scenario in which the `spin puzzle' in the iso-vector sector is trivially resolved. Utilizing a minimalist `holographic' GPD principle, tying the $t$-channel angular momentum and collinear conformal spin together, we build skewness dependent GPD models. Confronting these models with HERMES and JLAB measurements of hard exclusive $\pi^+$ electroproduction within the collinear factorization approach, we might conclude that minimalist GPD models are disfavored at leading order. We provide then a set of GPDs on the cross-over line that fairly describes both HERMES and JLAB measurements.