PV-Reduction of Sunset Topology with Auxiliary Vector

TL;DR

This paper introduces an improved PV-reduction method using an auxiliary vector, enabling efficient reduction of two-loop sunset integrals with high-rank tensors through algebraic recursion relations.

Contribution

The paper presents a novel PV-reduction technique with an auxiliary vector for two-loop integrals, extending applicability to high-rank tensor structures.

Findings

Efficient reduction of sunset topology integrals up to tensor rank four.

Development of algebraic recursion relations for reduction coefficients.

Applicability to integrals with arbitrary high-rank tensors.

Abstract

Passarino-Veltman (PV) reduction method has been proved to be very useful for the computation of general one-loop integrals. However, not much progress has been made when applying to higher loops. Recently, we have improved the PV-reduction method by introducing an auxiliary vector. In this paper, we apply our new method to the simplest two-loop integrals, i.e., the sunset topology. We show how to use differential operators to establish algebraic recursion relations for reduction coefficients. Our algorithm can be easily applied to the reduction of integrals with arbitrary high-rank tensor structures. We demonstrate the efficiency of our algorithm by computing the reduction with the total tensor rank up to four.