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

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.