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Abstract We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals.

Abstract We present the two-loop master integrals relevant to the O $$ \mathcal{O} $$ (αα s )-corrections to the decay H → b b ¯ $$ b\overline{b} $$ through a H t t ¯ $$ Ht\overline{t} $$ -coupling. We keep the full dependence on the heavy particle masses, but neglect the b-quark mass. The occurring square roots can be rationalised and the result is expressed in terms of multiple polylogarithms.

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 ε. This is done by transforming the system of differential equations into a form linear in ε, where the ε 0-part is a strictly lower triangular matrix. Explicit results in terms of iterated integrals are presented for the terms relevant to NNLO calculations.

We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD. For the first time, we include corrections due to massive fermion loops which give rise to integrals over elliptic curves. We present the results of the missing master integrals needed to compute the amplitude and obtain an analytic form for the finite remainders in terms of iterated integrals using rationalised kinematics and finite field sampling. We also study the numerical evaluation of the iterated integrals. [ABSTRACT FROM AUTHOR]

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 ε. This is done by transforming the system of differential equations into a form linear in ε, where the ε0-part is a strictly lower triangular matrix. Explicit results in terms of iterated integrals are presented for the terms relevant to NNLO calculations. [ABSTRACT FROM AUTHOR]