Evaluation of Feynman integrals with arbitrary complex masses via series expansions

TL;DR

This paper introduces a Mathematica package that evaluates multiloop Feynman integrals with complex masses using series expansions and analytical continuation, improving accuracy for high-order quantum corrections.

Contribution

It presents a novel algorithm and implementation for evaluating Feynman integrals with complex masses via differential equations and series expansions, with analytical continuation in the complex plane.

Findings

Successfully evaluated Master Integrals for NNLO QCD-EW corrections.

Implemented in Mathematica package SeaSyde.

Demonstrated improved handling of complex masses in Feynman integrals.

Abstract

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package \textsc{SeaSyde}. The implementation solves by series expansions the system of differential equations satisfied by the Master Integrals. At variance with respect to other existing codes, the analytical continuation of the solution is performed in the complex plane associated to each kinematical invariant. We present the results of the evaluation of the Master Integrals relevant for the NNLO QCD-EW corrections to the neutral-current Drell-Yan processes.