Reduction of one-loop integrals with higher poles by unitarity cut method

TL;DR

This paper extends the unitarity cut method to efficiently reduce one-loop integrals with higher powers of propagators by differentiating over masses, enabling calculations of scalar bubble, triangle, box, and pentagon integrals.

Contribution

It generalizes the unitarity cut method to handle integrals with higher propagator powers using mass differentiation tricks.

Findings

Successfully reduces scalar integrals with higher powers of propagators.

Provides explicit reduction formulas for bubble, triangle, box, and pentagon integrals.

Enhances the applicability of unitarity methods in loop integral calculations.

Abstract

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We show how to use the trick of differentiation over masses to translate the problem to the integrals where all powers are just one. Then by using the unitarity cut method, we can find the wanted reduction coefficients of all basis except the tadpole. Using this method, we calculate the reduction of scalar bubble, scalar triangle, scalar box and scalar pentagon with general power of propagators.