Analytic results for the planar double box integral relevant to top-pair production with a closed top loop

TL;DR

This paper provides an analytic method to compute the master integrals for a specific Feynman diagram relevant to top-pair production, enabling systematic calculations to all orders in dimensional regularisation.

Contribution

It introduces a systematic approach to solve the differential equations for the integrals, transforming them into a form linear in epsilon with explicit iterated integral solutions.

Findings

Explicit all-order epsilon expansion of the integrals.

Transformation of differential equations into epsilon-linear form.

Explicit iterated integral expressions for NNLO calculations.

Abstract

In this article we give the details on the analytic calculation of the master integrals for the planar double box integral relevant to top-pair production with a closed top loop. We show that these integrals can be computed systematically to all order in the dimensional regularisation parameter $\varepsilon$. This is done by transforming the system of differential equations into a form linear in $\varepsilon$, where the $\varepsilon^0$-part is a strictly lower triangular matrix. Explicit results in terms of iterated integrals are presented for the terms relevant to NNLO calculations.