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

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.