One-Loop QCD Corrections to $\bar{u}d \rightarrow t\bar{t}W$ at $\mathcal{O}(\varepsilon^2)$

TL;DR

This paper computes one-loop QCD corrections to top-quark pair production with a W boson, including higher-order epsilon terms, as a step towards NNLO accuracy, and introduces a structured analytic and semi-numerical framework.

Contribution

It provides the first calculation of one-loop QCD corrections including epsilon^2 terms for this process, aiding future NNLO computations.

Findings

Explicit analytic form factors up to epsilon^0

Structured tensor decomposition with special functions

Semi-numerical solutions via series expansion

Abstract

We present a computation of the one-loop QCD corrections to top-quark pair production in association with a $W$ boson, including terms up to order $\varepsilon^2$ in dimensional regularization. Providing a first glimpse into the complexity of the corresponding two-loop amplitude, this result is a first step towards a description of this process at next-to-next-to-leading order (NNLO) in QCD. We perform a tensor decomposition and express the corresponding form factors in terms of a basis of independent special functions with compact rational coefficients, providing a structured framework for future developments. In addition, we derive an explicit analytic representation of the form factors, valid up to order $\varepsilon^0$, expressed in terms of logarithms and dilogarithms. For the complete set of special functions required, we obtain a semi-numerical solution based on generalized power series expansion.