Massive planar and non-planar double box integrals for light Nf contributions to gg->tt

TL;DR

The paper delivers analytic, two-loop master integrals for the light-$N_f$ contributions to $gg \to t\bar{t}$, covering planar and non-planar double-box topologies with a single massive propagator. Using differential equations in $\epsilon=(4-d)/2$ and a careful choice of master integral basis, the authors obtain results in terms of multiple polylogarithms and fix integration constants via Mellin-Barnes representations and symmetry constraints. A key advance is the analytical treatment of the challenging non-planar sector with mass, where a coproduct-augmented symbol approach yields compact representations and reveals simplifications in the pole structure. These results complete the analytic toolkit needed for NNLO predictions of top-quark pair production in gluon fusion and demonstrate the power of symbol/coproduct techniques to simplify high-weight polylogarithms in multi-loop QCD.

Abstract

We present the master integrals needed for the light fermionic two-loop corrections to top quark pair production in the gluon fusion channel. Via the method of differential equations we compute the results in terms of multiple polylogarithms in a Laurent series about d=4, where d is the space-time dimension. The most involved topology is a non-planar double box with one internal mass. We employ the coproduct-augmented symbol calculus and show that significant simplifications are possible for selected results using an optimised set of multiple polylogarithms.

Figures (1)

• Figure 1: Physical region of phase space bounded by $u\,t=1$ and possible threshold singularities at $s=0$, $s=4m^2$, $t=m^2$ and $u=m^2$.