Master integrals for the NNLO virtual corrections to $$ q\overline{q}\to t\overline{t} $$ scattering in QCD: the non-planar graphs
Stefano Vita (INFN, Sezione di Milano, Via Celoria 16, Milano, 20133, Italy); Thomas Gehrmann (Department of Physics, University of Zürich, Wintherturerstrasse 190, Zürich, CH-8057, Switzerland); Stefano Laporta (Dipartimento di Fisica ed Astronomia, Università di Padova, Via Marzolo 8, Padova, 35131, Italy, INFN, Sezione di Padova, Via Marzolo 8, Padova, 35131, Italy); Pierpaolo Mastrolia (Dipartimento di Fisica ed Astronomia, Università di Padova, Via Marzolo 8, Padova, 35131, Italy, INFN, Sezione di Padova, Via Marzolo 8, Padova, 35131, Italy); Amedeo Primo (Department of Physics, University of Zürich, Wintherturerstrasse 190, Zürich, CH-8057, Switzerland); et al - Show all 6 authors
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 q q → tt in QCD, as well as to the companion QED scattering processes ee → μμ and eμ → eμ.
