Master integrals of a planar double-box family for top-quark pair production

Long-Bin Chen,Jian Wang

doi:10.1016/j.physletb.2019.03.030

Abstract

We calculate analytically the master integrals of a planar double-box family for top-quark pair production using the method of differential equations. With a proper choice of the bases, the differential equations can be transformed to the d-log form. The square roots of the kinematic variables in the differential equations can be rationalized by defining two dimensionless variables. We find that all the boundary conditions can be fully fixed either by simple integrals or regularity conditions at some special kinematic points. The analytic results for thirty-three master integrals at general kinematics are all expressed in terms of multiple polylogarithms up to transcendental weight four.

Highlights

The top-quark pair production is one of the most important processes at a hadron collider, such as the LHC
We have examined all the Feynman integrals relevant to the NNLO corrections to top-quark pair production, and found six planar and seven non-planar double-box integral families remaining to be calculated analytically
As proposed in ref. [22], a proper choice of the basis can lead to a rather simple form of differential equations for the master integrals. In this case the differential equations can be transformed to the d-log form, and as a consequence we can present the results of master integrals in terms of multiple polylogarithms

Summary

Introduction

The top-quark pair production is one of the most important processes at a hadron collider, such as the LHC. The total cross sections and differential distributions of the top-quark pair production have been calculated up to next-tonext-to-leading order (NNLO) [3,4,5,6,7]. [14], the authors calculated the master integrals for the light fermionic two-loop QCD corrections to top-quark pair production in the gluon fusion channel. The planar double-box integrals for top-quark pair production with a closed top-quark loop have been calculated [17,18], of which the results contain elliptic integrals. We have examined all the Feynman integrals relevant to the NNLO corrections to top-quark pair production, and found six planar and seven non-planar double-box integral families remaining to be calculated analytically. We calculate one of the analytically unknown planar double-box integrals, i.e., P 1, for top-quark pair production. The analytic results as well as the rational matrices are provided in ancillary files along with this paper

Canonical basis and differential equations

Boundary conditions and analytic results

Conclusions