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

Di Vita, Stefano; Gehrmann, Thomas; Laporta, Stefano; Mastrolia, Pierpaolo; Primo, Amedeo; Schubert, Ulrich (2019). Master integrals for the NNLO virtual corrections to $q \overline{q} \to t \overline{t}$ scattering in QCD: the non-planar graphs. Journal of High Energy Physics, 2019(6):117.

## Abstract

We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are determined from their differential equations, which are cast into a canonical form using the Magnus exponential. The analytic expressions of the Laurent series coefficients of the integrals are expressed as combinations of generalized polylogarithms, which we validate with several numerical checks. We discuss the analytic continuation of the planar and the non-planar master integrals, which contribute to $qq \to tt$ in QCD, as well as to the companion QED scattering processes $ee \to μμ$ and $eμ \to eμ$.

## Abstract

We complete the analytic evaluation of the master integrals for the two-loop non-planar box diagrams contributing to the top-pair production in the quark-initiated channel, at next-to-next-to-leading order in QCD. The integrals are determined from their differential equations, which are cast into a canonical form using the Magnus exponential. The analytic expressions of the Laurent series coefficients of the integrals are expressed as combinations of generalized polylogarithms, which we validate with several numerical checks. We discuss the analytic continuation of the planar and the non-planar master integrals, which contribute to $qq \to tt$ in QCD, as well as to the companion QED scattering processes $ee \to μμ$ and $eμ \to eμ$.

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