Abstract
We consider Feynman integrals with algebraic leading singularities and total differentials in $\ensuremath{\epsilon}\text{ }\mathrm{d}\text{ }\mathrm{ln}$ form. We show for the first time that it is possible to evaluate integrals with singularities involving unrationalizable roots in terms of conventional multiple polylogarithms, by either parametric integration or matching the symbol. As our main application, we evaluate the two-loop master integrals relevant to the $\ensuremath{\alpha}{\ensuremath{\alpha}}_{s}$ corrections to Drell-Yan lepton pair production at hadron colliders. We optimize our functional basis to allow for fast and stable numerical evaluations in the physical region of phase space.
Highlights
The Drell-Yan process [1] is one of the most important and basic processes measured at the Large Hadron Collider at CERN
In fixed-order perturbation theory, the pure quantum chromodynamic (QCD) corrections to the cross section are known through to next-to-nextto-leading order [2,3,4,5], the pure quantum electrodynamics (QED) corrections to neutral gauge boson production and decay are known at next-to-next-to-leading order [6,7], whereas the exact electroweak (EW) corrections are known only at next-to-leading order [8,9,10]
The two-loop master integrals relevant to the virtual part of the mixed EW-QCD corrections to the Drell-Yan process were studied in [14,15] and all of them admit ε-decoupled and, subsequently, ε d ln differential equations [16]
Summary
The Drell-Yan process [1] is one of the most important and basic processes measured at the Large Hadron Collider at CERN. We show for the first time that it is possible to integrate Feynman integrals of current phenomenological interest with unrationalizable roots in their symbol letters in terms of multiple polylogarithms, focusing primarily on the most complicated two-loop mixed EWQCD Drell-Yan master integrals. In Appendix B we give an example for the construction of algebraic letters in the presence of multiple root-valued leading singularities
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