Pion Generalized Parton Distributions with covariant and Light-front constituent quark models

TL;DR

This paper compares different covariant and light-front models to study the pion's generalized parton distributions, revealing a common underlying one-gluon-exchange mechanism and matching lattice results for gravitational form factors.

Contribution

It provides a detailed comparison of covariant and light-front approaches for pion GPDs, highlighting the shared dynamical mechanism and collinear behavior at high momentum transfer.

Findings

One-gluon-exchange dominance at short distances.

Consistent collinear behavior at high momentum transfer.

Agreement with lattice calculations of gravitational form factors.

Abstract

We investigate the model dependence of no-helicity flip generalized parton distribution of the pion upon different approaches for the quark-hadron and quark-photon vertexes, in the spacelike region. In order to obtain information on contributions from both the valence and non-valence regions, we compare results for spacelike momentum transfers obtained from i) an analytic covariant model with a bare quark-photon vertex, ii) a Light-front approach with a quark-photon vertex dressed through a microscopic vector-meson model and iii) a Light-front approach based on the Relativistic Hamiltonian Dynamics. Our comparisons lead to infer the same dynamical mechanism, the one-gluon-exchange dominance at short distances, as a source of both the electromagnetic form factor at large momentum transfer and the parton distribution close to the end-points. The expected collinear behavior of the generalized parton distributions at high momentum transfer, i.e. a maximum for $x\sim 1$, is also illustrated, independently of the different approaches. Finally a comparison with recent Lattice calculations of the gravitational form factors is presented.