# Direct numerical computation and its application to the higher-order radiative corrections

## TL;DR

This paper advances a direct computation method for multi-loop amplitudes with general masses and momenta, demonstrating progress in scalar integrals and applications to 2-loop physical processes.

## Contribution

It introduces improvements to the direct computation method for multi-loop integrals, including handling of numerator functions and divergence control.

## Key findings

- Progress in calculating scalar multi-loop integrals.
- Application of DCM to 2-loop physical processes.
- Effective management of ultraviolet divergences.

## Abstract

The direct computation method(DCM) is developed to calculate the multi-loop amplitude for general masses and external momenta. The ultraviolet divergence is under control in dimensional regularization. In this paper we report on the progress of DCM to several scalar multi-loop integrals after the presentation in ACAT2016. Also the discussion is given on the application of DCM to physical 2-loop processes including numerator functions.