Chiral theory of nucleons and pions in the presence of an external gravitational field

TL;DR

This paper extends chiral effective theory to include gravitational interactions, calculating loop corrections and pion-production amplitudes, which could impact the interpretation of lattice QCD data on nucleon gravitational form factors.

Contribution

It introduces a gravitationally coupled chiral Lagrangian and computes novel one-loop and tree-level corrections relevant for nucleon and pion interactions in gravitational fields.

Findings

New expressions for nucleon gravitational form factors differ from previous literature.

Revises the understanding of chiral corrections in gravitational form factors.

Potential implications for lattice QCD data analysis.

Abstract

We extend the standard second order effective chiral Lagrangian of pions and nucleons by considering the coupling to an external gravitational field. As an application we calculate one-loop corrections to the one-nucleon matrix element of the energy-momentum tensor to fourth order in chiral counting, and next-to-leading order tree-level amplitude of the pion-production in an external gravitational field. We discuss the relation of the obtained results to experimentally measurable observables. Our expressions for the chiral corrections to the nucleon gravitational form factors differ from those in the literature. That might require to revisit the chiral extrapolation of the lattice data on the nucleon gravitational form factors obtained in the past.