Evaluating master integrals in non-factorizable corrections to $t$-channel single-top production at NNLO QCD

TL;DR

This paper computes master integrals for two-loop non-factorizable corrections in t-channel single-top production at NNLO QCD, using differential equations and polylogarithms, with insights into elliptic sectors.

Contribution

It introduces a systematic method to evaluate master integrals with uniform transcendental basis for complex two-loop diagrams in single-top production.

Findings

Master integrals expressed in Goncharov polylogarithms.

Complete basis constructed using canonical differential equations.

Discussion on potential elliptic sector diagrams.

Abstract

We studied the two-loop non-factorizable Feynman diagrams for the $t$-channel single-top production process in quantum chromodynamics. We present a systematic computation of master integrals of the two-loop Feynman diagrams with one internal massive propagator in which a complete uniform transcendental basis can be built. The master integrals are derived by means of canonical differential equations and uniform transcendental integrals. The results are expressed in the form of Goncharov polylogarithm functions, whose variables are the scalar products of external momenta, as well as the masses of the top quark and the $W$ boson. We also gave a discussion on the diagrams with potential elliptic sectors.