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

Claudio Corianò, Stefano Lionetti, Dario Melle, Leonardo Torcellini

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.

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.

Paper Structure

This paper contains 12 sections, 41 equations, 3 figures.

Table of Contents

  1. Introduction
  2. DVCS, generalized parton distributions and gravitational form factors
  3. QCD in curved spacetime and the trace anomaly
  4. The reconstruction of the quark and gluon sectors in QCD
  5. Momentum-space CFT and the role of gauge fixing
  6. Tensor decomposition of the $TJJ$ correlator
  7. Spectral density and dispersive sum rule
  8. On-shell limit and pole dominance
  9. Relation to anomaly effective actions
  10. Physical interpretation and relation to hadronic observables
  11. Why the sum rule matters for GFFs
  12. Conclusions

Figures (3)

  • Figure 1: Leading (left) and NLO contributions to the GFF of the pion.
  • Figure 2: Typical quark and gluon contributions contributions to the non-Abelian $TJJ$.
  • Figure 3: Perturbative expansion of the hard scattering of the GFF in the proton case. The dooubly wiggled line denotes a graviton.