Anomalous Dimensions from Soft Regge Constants

TL;DR

This paper uses an effective field theory approach to analyze forward scattering amplitudes in the Regge limit, revealing universal soft functions and deriving higher-order contributions to the Regge trajectory.

Contribution

It introduces a novel EFT formalism for factorizing scattering amplitudes in the Regge limit, enabling simplified calculations of the Regge trajectory and its higher-order matter-dependent terms.

Findings

The one-loop soft function relates to two-loop anomalous dimensions.

A simple EFT-based calculation of the two-loop Regge trajectory is provided.

Maximally matter dependent contributions to the Regge trajectory are derived to all loop orders.

Abstract

Using an effective field theory (EFT) formalism for forward scattering, we reconsider the factorization of $2\to 2$ scattering amplitudes in the Regge limit. Expanding the amplitude in gauge invariant operators labelled by the number of Glauber exchanges, allows us to further factorize the standard impact factors into separate collinear and soft functions. The soft functions are universal, and describe radiative corrections to the Reggeized gluon states exchanged by the collinear projectiles. Remarkably, we find that the one-loop soft function for the single Reggeized gluon state is given to $\mathcal{O}(\epsilon)$ in terms of the two-loop cusp and two-loop rapidity anomalous dimensions. We argue that this iterative structure follows from the simple action of crossing symmetry in the forward scattering limit, which in the EFT allows us to replace the divergent part of a soft loop by a much simpler Glauber loop. We use this correspondence to provide a simple calculation of the two-loop Regge trajectory using the EFT. We then explore its implications at higher perturbative orders, and derive the maximally matter dependent contributions to the Regge trajectory to all loop orders, i.e.~the terms $\sim \alpha_s^{k+1}n_f^k$ for any $k$, where $n_f$ is the number of massless flavors. These simplifications suggests that the EFT approach to the Regge limit will be helpful to explore and further understand the structure of the Regge limit.