Gravitational and higher-order form factors of the pion in chiral quark models

TL;DR

This paper evaluates the gravitational form factor of the pion using chiral quark models, compares results with lattice QCD data, and explores relations between gravitational and electromagnetic form factors, including higher-order moments.

Contribution

It provides a comparison of chiral quark model predictions with lattice QCD data for pion form factors and derives a simple relation between gravitational and electromagnetic form factors.

Findings

Good agreement of the Spectral Quark Model with lattice data

Derived relation: gravitational radius is half the electromagnetic radius

Higher-order form factors at t=0 agree with lattice results

Abstract

The gravitational form factor of the pion is evaluated in two chiral quark models and confronted to the recent full-QCD lattice data. We find good agreement for the case of the Spectral Quark Model, which builds in the vector-meson dominance for the charge form factor. We derive a simple relation between the gravitational and electromagnetic form factors, holding in the considered quark models in the chiral limit. The relation implies that the gravitational mean squared radius is half the electromagnetic one. We also analyze higher-order quark generalized form factors of the pion, related to higher moments in the symmetric Bjorken X-variable of the generalized parton distribution functions, and discuss their perturbative QCD evolution, needed to relate the quark-model predictions to the lattice data. The values of the higher-order quark form factors at t=0, computed on the lattice, also agree with our quark model results within the statistical and method uncertainties.