One-loop Feynman integral reduction by differential operators

For loop integrals the standard method is reduction. A well-known reduction method for one-loop integrals is the Passarino-Veltman (PV) reduction. Inspired by the recent paper [B. Feng, T. Li, and X. Li, J. High Energy Phys. 09 (2021) 081.] where the tadpole reduction coefficients have been solved, in this paper we show the same technique can be used to give a complete integral reduction for any one-loop integrals. The differential operator method is an alternative version of the PV-reduction method. Using this method, analytic expressions of all reduction coefficients of the master integrals can be given by algebraic recurrence relation easily. We demonstrate our method explicitly with several examples.

Automated summary

In this paper, we present a complete integral reduction method for one-loop integrals, inspired by previous research. The differential operator method can easily provide analytic expressions of all reduction coefficients of the master integrals.