Two-Loop Master Integrals for the Planar QCD Massive Corrections to Di-photon and Di-jet Hadro-production
Matteo Becchetti, Roberto Bonciani
TL;DR
The paper delivers a complete analytic determination of the two-loop master integrals needed for planar massive QCD corrections to di-photon and di-jet hadroproduction, cast in a canonical differential-equations framework. Most master integrals are expressible in Goncharov polylogarithms via a rational alphabet, while a subset requires one- or two-fold numeric integrations due to non-linearizable square roots. The authors construct a canonical basis for 37 MIs (12 new) and provide explicit pre-canonical to canonical mappings, boundary conditions, and integration paths, with numerical cross-checks against FIESTA4. This work enables the leading-color massive corrections to di-jet production and lays out a path toward incorporating heavy-quark loops into NNLO QCD predictions for relevant LHC processes, with di-photon results pending inclusion of crossed diagrams in future work.
Abstract
We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.