On operator relations for gravitational form factors of a spin-0 hadron

TL;DR

This paper explores the relations and symmetries of gravitational form factors for spin-0 hadrons, revealing their connection to internal hadron structure and quark-gluon dynamics through QCD principles.

Contribution

It derives and clarifies the symmetry and equation-of-motion relations for quark gravitational form factors of scalar hadrons, linking them to higher-twist effects and generalized parton distributions.

Findings

Relations between gravitational form factors and QCD symmetries

Connections to higher-twist quark-gluon correlations

Insights into hadron internal pressure and shear forces

Abstract

The gravitational form factors for a hadron, the form factors for the hadron matrix element of the QCD energy-momentum tensor, not only describe the coupling of the hadron with a graviton, but also serve as unique quantities for describing the shape inside the hadron reflecting dynamics of quarks and gluons, such as the internal shear forces acting on the quarks/gluons and their pressure distributions. We consider the quark contribution to the gravitational form factors for a (pseudo)scalar hadron, and derive and clarify the relations satisfied by them as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal the connections between the gravitational form factors and the higher-twist quark-gluon correlation effects inside the hadrons.