The Gravitational Form Factors of Hadrons from CFT in Momentum Space and the Dilaton in Perturbative QCD

TL;DR

This paper explores the gravitational form factors of hadrons using conformal field theory and QCD, revealing an effective dilaton interaction and providing a framework for future experimental analysis at the Electron-Ion Collider.

Contribution

It introduces a momentum space CFT approach to analyze GFFs in QCD, highlighting the role of the trace anomaly and dilaton interactions in hard scattering amplitudes.

Findings

Identification of a massless anomaly pole in the $TJJ$ correlator.

Decomposition of the scattering amplitude into transverse traceless, longitudinal, and trace parts.

Parameterization of the amplitude for future experimental studies at EIC.

Abstract

We analyze the hard scattering amplitude of the gravitational form factors (GFFs) of hadrons at one-loop, in relation to their conformal field theory (CFT) description, within the framework of QCD factorization for hard exclusive processes at large momentum transfers. These form factors play an essential role in studying the quark and gluon angular momentum of the hadrons due to their relation to the Mellin moments of the Deeply Virtual Compton Scattering (DVCS) invariant amplitudes. Our analysis is performed using a diffeomorphism invariant approach, applying the formalism of the gravitational effective action and conformal symmetry in momentum space for the discussion of the quark and gluon contributions. The interpolating correlator in the hard scattering of any GFF is the non-Abelian $TJJ$ (stress-energy/gluon/gluon) 3-point function at $O(\alpha_s^2)$, revealing an effective dilaton interaction in the $t$-channel due to the trace anomaly, in the form of a massless anomaly pole in the QCD hard scattering. We investigate the role of quarks, gauge-fixing and ghost contributions in the reconstruction of the hard scattering amplitude mediated by this interaction, performed in terms of its transverse traceless, longitudinal, and trace decomposition, as identified from CFT in momentum space (CFT$_p$). We present a convenient parameterization of the hard scattering amplitude relevant for future experimental investigations of the DVCS/GFF amplitudes at the Electron-Ion Collider at BNL.