Relations Between Anomalous Dimensions in the Regge Limit

TL;DR

This paper develops a new formalism linking anomalous dimensions in high-energy scattering to cut amplitudes, simplifying calculations of Regge trajectories and enabling bootstrap of operator anomalous dimensions.

Contribution

It introduces a novel approach combining EFT factorization and unitarity to relate anomalous dimensions to cut amplitudes, including explicit two-loop calculations.

Findings

Derived expressions for Regge trajectories using the new formalism.

Computed one and two-loop Regge trajectories explicitly.

Showed how to determine operator anomalous dimensions from simpler cases.

Abstract

We extend the recent formalism developed for computing rapidity anomalous dimension of form factors using unitarity to the problem of high-energy near forward scattering. By combining the factorization of $2\rightarrow 2$ scattering in the effective field theory (EFT) for Glauber operators with definite signature amplitudes, we derive an expression that relates anomalous dimensions (including Regge trajectories) to cut amplitudes, leading to significant computational simplifications. We demonstrate this explicitly by computing the one and two-loop Regge trajectories. Our formalism can also be used to bootstrap anomalous dimensions of operators not related by symmetries. As an example, we show that the full anomalous dimensions (including both the Regge pole and cut pieces) of the two Glauber operator anti-symmetric octet operator, can be determined from the anomalous dimension of the single Glauber exchange operator. Many other such relations exist between other color channels at each order in $\alpha$.