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.
Highlights
Intensive computations require two-loop 2 → 2, one-loop 2 → 3 and tree-level 2 → 4 partonic amplitudes to be combined using a consistent UV and IR subtraction scheme to obtain a finite result
We present a complete set of analytic helicity amplitudes for top quark pair production via gluon fusion at two-loops in QCD
That we have identified the various elliptic curves entering the computation, let us turn to the computation of the master integrals J21 and J22, which are not known from the literature
Summary
Intensive computations require two-loop 2 → 2, one-loop 2 → 3 and tree-level 2 → 4 partonic amplitudes to be combined using a consistent UV and IR subtraction scheme to obtain a finite result. The helicity amplitudes presented contain complete information about top quark decays in the narrow width approximation This helicity amplitude technique has been used successfully at one-loop [40,41,42,43]. We construct a rational parametrisation of the on-shell kinematics via momentum twistors and obtain helicity amplitudes via projecting onto a basis of independent spinor structures, accounting for the freedom in the top quark spin states. This method defines a set of on-shell, gauge invariant sub-amplitudes that can be computed using on-shell top-quark kinematics. We check these results against previous computations for the interference
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