PV-reduction of sunset topology with auxiliary vector

The Passarino-Veltman (PV) reduction method has proven to be very useful for the computation of general one-loop integrals. However, not much progress has been made when it is applied 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.

Automated summary

The Passarino-Veltman (PV) reduction method is useful for computing one-loop integrals, but little progress has been made for higher loops. Recently, an improved PV-reduction method using an auxiliary vector was introduced. In this paper, the new method is applied to compute the simplest two-loop integrals, and the efficiency of the algorithm is demonstrated by computing reductions with up to four tensor rank.