Chiral and trace anomalies in Deeply Virtual Compton Scattering

TL;DR

This paper investigates chiral and trace anomalies in Deeply Virtual Compton Scattering by calculating one-loop quark box diagrams, revealing anomaly-related poles and their cancellations, and exploring implications for QCD factorization and gravitational form factors.

Contribution

It provides a detailed calculation of anomalies in DVCS, linking them to GPDs, and proposes a cancellation mechanism for trace anomaly poles involving gluon condensates.

Findings

Re-derivation of the axial anomaly pole in polarized DIS.

Identification of trace anomaly remnants in unpolarized DIS.

Proposal of a cancellation mechanism involving gluon condensates.

Abstract

Inspired by recent work by Tarasov and Venugopalan, we calculate the one-loop quark box diagrams relevant to polarized and unpolarized Deep Inelastic Scattering (DIS) by introducing off-forward momentum $l^\mu$ as an infrared regulator. In the polarized case, we rederive the pole $1/l^2$ related to the axial (chiral) anomaly. In addition, we obtain the usual logarithmic term and the DIS coefficient function. We interpret the result in terms of the generalized parton distributions (GPDs) $\tilde{H}$ and $\tilde{E}$ and discuss the possible violation of QCD factorization for the Compton scattering amplitude. Remarkably, we also find poles in the unpolarized case which are remnants of the trace anomaly. We argue that these poles are cancelled by the would-be massless glueball poles in the GPDs $H$ and $E$ as well as in their moments, the nucleon gravitational form factors $A,B$ and $D$. This mechanism sheds light on the connection between the gravitational form factors and the gluon condensate operator $F^{\mu\nu}F_{\mu\nu}$.