Master Integrals for the two-loop, non-planar QCD corrections to top-quark pair production in the quark-annihilation channel

Abstract

We present the analytic calculation of the Master Integrals for the two-loop, non-planar topologies that enter the calculation of the amplitude for top-quark pair hadroproduction in the quark-annihilation channel. Using the method of differential equations, we expand the integrals in powers of the dimensional regulator ǫ and determine the expansion coefficients in terms of generalized harmonic polylogarithms of two dimensionless variables through to weight four.

Master integrals for the NNLO virtual corrections to $$ q\overline{q}\to t\overline{t} $$ scattering in QCD: the non-planar graphs

“…Beside these important validations, our results have been successfully compared against the computation of the master integrals relevant to the same integral topologies expressed in a different basis set, independently obtained by Becchetti, Bonciani, Casconi, Ferroglia, Lavacca and von Manteuffel [51], published in tandem to the current manuscript.…”

Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel

“…Over the last few years, motivated by the increasing demand of precise theoretical descriptions including mass dependence, there has been substantial progress in developing a complete framework for use in phenomenological applications. There are a large number of amplitude level corrections to the process which do not depend on elliptic sectors and there has been substantial effort to find a complete analytic form for the squared amplitudes [26][27][28][29][30][31][32][33].…”

Two-loop non-planar master integrals for top-pair production in the quark-annihilation channel

“…On the other hand, an analytic expression for the coefficients B qq and C qq is not yet available, since they depend on certain Feynman integrals families whose analytic solution have been obtained just recently [24,26,28,29]. In the following we consider two non-planar integral families that contribute to B qq and C qq which have been computed in [28]. They are described by the two seven-denominator two-loop topologies, which we denote with the capital letters A and B (see Figure 1):…”

“…However, since some master integrals are common to both topologies, the actual total number of master integrals is 70. For a subset of these master integrals analytic expressions in terms of MPLs were already been obtained previously [18,19,20,13,14,21,22,23,26], while for others, including the seven denominator four-point functions, analytic expressions are obtained for the first time [28].…”