# Soft anomalous dimensions for single-top production at three loops

## TL;DR

This paper computes three-loop soft anomalous dimensions for single-top production processes, enabling more precise soft-gluon resummation and higher-order corrections in top-quark physics.

## Contribution

It provides the first three-loop calculations of soft anomalous dimensions for various single-top production channels, including processes with new physics.

## Key findings

- Calculated three-loop cusp anomalous dimension with one massive and one massless line.
- Derived three-loop soft anomalous dimensions for $tW$, $tZ$, $t\,gamma$, and $tH^-$ production.
- Presented results for soft anomalous dimension matrices in $s$-channel and $t$-channel single-top production.

## Abstract

I present results for soft anomalous dimensions in single top-quark production processes through three loops. I first discuss the cusp anomalous dimension with one massive and one massless line at three loops. I then calculate the three-loop soft anomalous dimension for $tW$ production and for related processes with new physics such as $tZ$, $t\gamma$, and $tH^-$ production. This is followed by results at two and three loops for the soft anomalous dimension matrix in $s$-channel single-top production and, finally, in $t$-channel single-top production. These new results are needed for soft-gluon resummation at N$^3$LL accuracy and for calculations of soft-gluon corrections at N$^3$LO.