Tensor Reduction of Sunset by Generating Function

Abstract

Recently, the generating function has been proposed as an alternative reduction method. This method has been tested at the one-loop level, including the tensor reduction and propagators with higher powers. In this work, we initiate the study of the method for higher loops by focusing on the sunset diagram, which is the simplest nontrivial two-loop integral. By employing PV reduction equations together with syzygy equations, we construct a complete system of differential equations. Through series expansion, we derive a complete set of recurrence relations, which can efficiently reduce any high-rank tensor structure.