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 q q → tt in QCD, as well as to the companion QED scattering processes ee → μμ and eμ → eμ.
Highlights
Production matrix elements could not be derived due to incomplete knowledge on the relevant two-loop Feynman integrals
The integrals are determined from their differential equations, which are cast into a canonical form using the Magnus exponential
We presented the analytic expressions of the master integrals for a set of non-planar two-loop Feynman graphs, with two quark currents exchanging massless gauge bosons
Summary
We complete the determination of the Feynman integrals for the qq → ttscattering process q(p1) + q(p2) → t(p3) + t(p4) ,. The full set of two-loop three-point integrals that are involved in the process has been known for some time [53,54,55,56,57,58,59,60], as well all the relevant planar four-point functions [12, 13, 24] On top of these contributions, the evaluation of the full double-virtual matrix element requires the computation of two-loop non-planar Feynman diagrams. The MIs for the QED-like family A1 are already available in the literature, as they have been studied in the context of the NNLO QED corrections to eeμμ processes (with suitable redefinitions of the momenta and of the Mandelstam invariants) They have been first computed in [25] (in an unphysical region, to be analytically continued), and later in [43] (directly in the heavy-fermion-production kinematic region). The two-loop tadpole integral 2I[4−2 ](0, 2, 0, 0, 0, 2, 0, 0, 0) is normalized to 1
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