The Gravitational Form Factor of the Pion and Proton and the Conformal Anomaly

TL;DR

This paper investigates the gravitational form factors of hadrons using QCD and conformal symmetry, revealing insights into quark and gluon angular momentum and proposing a parameterization for future experimental measurements at the Electron-Ion Collider.

Contribution

It introduces a conformal field theory approach to analyze gravitational form factors and their relation to the conformal anomaly in QCD, with a new parameterization for experimental applications.

Findings

Identification of a dilaton interaction in the $t$-channel at $O(\a_s^2)$

Connection between GFFs and quark/gluon angular momentum

Parameterization relevant for future Electron-Ion Collider experiments

Abstract

We analyze the hard scattering amplitude of gravitational form factors (GFFs) of hadrons within QCD factorization at large momentum transfers, focusing on their conformal field theory (CFT) description. These form factors are key to studying quark and gluon angular momentum in hadrons, connected to Mellin moments of Deeply Virtual Compton Scattering (DVCS). The analysis uses diffeomorphism invariance and conformal symmetry in momentum space. A non-Abelian $TJJ$ 3-point function at $O(\alpha_s^2)$ reveals a dilaton interaction in the $t$-channel. We present a parameterization relevant for future DVCS/GFF experiments at the Electron-Ion Collider.