Pion gravitational form factors in a relativistic theory of composite particles

TL;DR

This paper develops a relativistic quantum mechanical model to calculate the gravitational form factors of pions, incorporating constituent quarks and satisfying quantum field theory constraints, with results aligning well with existing data.

Contribution

It extends a relativistic approach to include gravitational form factors of hadrons, introducing a new parameter for constituent quarks and providing first-principle calculations.

Findings

Calculated pion gravitational form factors agree with known results.

The model satisfies quantum field theory constraints.

The gravitational mean-square radius is consistent with expectations.

Abstract

We extend our relativistic theory of electroweak properties of composite systems to describe simultaneously the gravitational form factors of hadrons. The approach is based on a version of the instant-form relativistic quantum mechanics and makes use of the modified impulse approximation. We exploit the general method of the relativistic invariant parametrizaton of local operators to write the energy-momentum tensor of a particle with an arbitrary spin. We use the obtained results to calculate the gravitational form factors of the pion assuming point-like constituent quarks. All but one parameters of our first-principle model were fixed previously in works on electromagnetic form factors. The only free parameter, $D_{q}$, is a characteristic of the gravitational form factor of a constituent quark. The derived form factors of the pion satisfy the constraints given by the general principles of the quantum field theory of hadron structure. The calculated gravitational form factors and gravitational mean-square radius are in a reasonable agreement with known results.