Numerical approach to multi-loop integrals

TL;DR

The paper introduces the Direct Computation Method (DCM), a new numerical approach for calculating complex multi-loop Feynman integrals, capable of handling arbitrary parameters and aiding higher order radiative correction calculations.

Contribution

It presents a novel numerical method, DCM, combining integration and series extrapolation, applicable to diverse multi-loop diagrams with automatic divergence separation.

Findings

Successfully computed two-loop box diagrams numerically.

Demonstrated DCM's ability to handle arbitrary masses and momenta.

Discussed optimal parameter choices for DCM.

Abstract

For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle diagrams of arbitrary internal masses and external momenta, and can calculate integrals with general numerator function. As an example of the performance of DCM, a numerical computation of two-loop box diagrams is presented. Further discussion is given on the choice of control parameters in DCM. This method will be an indispensable tool for the higher order radiative correction when it is tested for a wider class of physical parameters and the separation of divergence is done automatically.