# Operator Relations for Gravitational Form Factors

## TL;DR

This paper explores the properties and relations of gravitational form factors in QCD, revealing their connection to internal hadron dynamics, symmetries, and higher-twist effects, enhancing understanding of hadron structure and QCD anomalies.

## Contribution

It derives and clarifies the relations of gravitational form factors based on QCD symmetries and equations of motion, linking them to higher-twist effects and trace anomalies.

## Key findings

- Relations between gravitational form factors and QCD symmetries
- Connection of form factors to higher-twist quark-gluon correlations
- Link between form factors and QCD trace anomaly

## Abstract

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 as the ``gravitational form factors'', 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 gravitational form factors for a hadron, in particular, for a (pseudo)scalar hadron and for the nucleon. We derive and clarify the relations satisfied by the gravitational form factors as direct consequences of the symmetries and the equations of motion in QCD, and connections to the generalized parton distributions. Our results reveal that the gravitational form factors are related to the higher-twist quark-gluon correlation effects inside the hadrons and also to QCD trace anomaly.