Extracting the Asymptotic Behavior of S-matrix Elements from their Phases

TL;DR

This paper introduces a method to extract rapidity anomalous dimensions from the phase of the S-matrix, simplifying calculations of asymptotic behaviors in quantum field theory without requiring rapidity regulators.

Contribution

It generalizes previous work by showing how to reconstruct rapidity anomalous dimensions via complex boosts from S-matrix phases, avoiding the need for rapidity regulators.

Findings

Derived rapidity anomalous dimensions for the Sudakov form factor

Calculated rapidity anomalous dimensions for the two-parton soft function

Determined the Regge trajectory in QCD

Abstract

The asymptotic kinematic limits of S-matrices are dominated by large logarithms which, roughly speaking, fall into two categories: those which are controlled by a renormalization group (RG) scale, which we may think of as logs involving ratios of invariant mass scales, and those which are functions of ratios of rapidities, so called "rapidity logs". It has been pointed out by Caron-Huot and Wilhlem [1] that RG anomalous dimension can be extracted from the phase of the S-matrix, which can greatly simplify calculations via unitarity methods. In this paper we generalize the results of [1] to show that the phase can be used to reconstruct rapidity anomalous dimensions, by performing a complex boost. The methodology introduced here also allows one to calculate without the need for a rapidity regulator. We demonstrate the use of this method to derive the rapidity anomalous dimensions in the Sudakov form factor, the two parton soft function and the Regge trajectory in QCD.