A glimpse into pion gravitational form factor

TL;DR

This paper introduces a new method to calculate the pion's gravitational form factor using the Bethe-Salpeter equation with contact interactions, highlighting the roles of intrinsic quarks and bound states.

Contribution

It presents a symmetry-preserving approach to compute the pion's gravitational form factor, explicitly including contributions from intrinsic quarks and bound states.

Findings

Explicit calculation of the pion's D-term in the soft-pion limit.

Demonstration of the importance of bound states in the form factor.

A versatile method applicable to various physical processes.

Abstract

We provide a novel approach to calculate the gravitational form factor of pion under the ladder approximation of the Bethe-Salpeter equation, with contact interactions. Central to this approach is a symmetry-preserving treatment of the dressed $\pi\pi$ amplitude, which shows explicitly the contributions from intrinsic quarks and bound states, the latter being necessary to produce the $D$-term of pion in the soft-pion limit. The approach we provide in this work can be applied to many processes of physical significance.