Efficiency improvements for the numerical computation of NLO corrections

TL;DR

This paper presents various techniques to significantly enhance the efficiency of Monte Carlo integration in numerical NLO QCD corrections, focusing on subtraction methods and contour deformation.

Contribution

It introduces novel optimization strategies for Monte Carlo integration, including contour optimization and improved subtraction terms, specifically for one-loop QCD amplitude calculations.

Findings

Significant efficiency gains in Monte Carlo integration for NLO corrections

Effective contour deformation and importance sampling techniques

Enhanced ultraviolet subtraction terms improve convergence

Abstract

In this paper we discuss techniques, which lead to a significant improvement of the efficiency of the Monte Carlo integration, when one-loop QCD amplitudes are calculated numerically with the help of the subtraction method and contour deformation. The techniques discussed are: holomorphic and non-holomorphic division into sub-channels, optimisation of the integration contour, improvement of the ultraviolet subtraction terms, importance sampling and antithetic variates in loop momentum space, recurrence relations.