Dilaton Sum Rules of Gravitational Form Factors in QCD at Order $\alpha_s$

TL;DR

This paper develops a QCD-based framework for hadronic gravitational form factors using conformal limit techniques, revealing a dilaton-like interpretation and anomaly-driven features.

Contribution

It introduces a novel partonic description of gravitational form factors in QCD, incorporating conformal methods and sum rules to understand anomaly effects.

Findings

The anomaly form factor obeys a mass-independent dispersive sum rule.

In the light-cone limit, anomaly-related structures dominate the form factors.

A dilaton-like interpretation emerges from the anomaly contributions.

Abstract

We formulate a partonic description of hadronic gravitational form factors within QCD, focusing on the three-point function of the energy-momentum tensor and two gluon currents. Despite the lack of exact conformal symmetry in QCD, the correlator may be organized around the conformal limit through momentum-space CFT methods, suitably adjusted for gauge-fixing effects. This yields a tensor decomposition into spin-2, spin-1, and spin-0 sectors, with the spin-0 contribution governed by the conformal anomaly. The corresponding anomaly form factor satisfies a mass-independent dispersive sum rule and allows a dilaton-like interpretation. In the light-cone limit, this term and an additional traceless structure become dominant, indicating an effective anomaly-mediated description relevant to hadronic gravitational form factors.