Anomalous dimensions for exclusive processes

TL;DR

The paper tackles the challenge of determining the anomalous dimension matrix (ADM) for leading-twist operators in non-forward kinematics, which governs the scale evolution of non-perturbative generalized parton distributions. It compares two complementary methods: (i) a conformal-symmetry approach using the critical dimension $D=4-2\varepsilon$ and the conformal anomaly to reconstruct the off-diagonal ADM elements, and (ii) a consistency-relations approach based on renormalization of total-derivative operators that yields all-order recursive identities relating off-diagonal to forward anomalous dimensions. The conformal method benefits from the anomaly known up to two loops to enable reconstruction up to three loops, while the consistency-relations method provides exact, all-order constraints, with caveats about operator mixing beyond one loop. Together these methods offer a robust framework for obtaining the evolution kernels of generalized parton distributions in hard exclusive processes.

Abstract

We give an overview of recent developments in the computation of the anomalous dimension matrix of composite operators in non-forward kinematics. The elements of this matrix set the evolution of non-perturbative parton distributions such as the generalized parton distribution functions. The latter provide important information about hadronic structure and are accessible experimentally in hard exclusive scattering processes. We focus our discussion on a recent method that exploits consistency relations for the anomalous dimensions which follow from the renormalization structure of quark and gluon operators.