Numerical Evaluation of Two-Loop Integrals in FDR

TL;DR

This paper introduces a numerical method for evaluating two-loop integrals in FDR, using subtraction terms to handle logarithmic mass dependence, and applies it to QCD corrections in Higgs decay and the rho parameter.

Contribution

The paper presents a novel numerical approach for two-loop integrals in FDR that efficiently isolates logarithmic mass dependence using analytically integrable subtraction terms.

Findings

Successfully computed QCD corrections to Higgs decay rates.

Calculated contributions to the rho parameter.

Demonstrated the method's effectiveness for infrared-finite integrals.

Abstract

We present a method to numerically evaluate infrared-finite one- and two-loop integrals within the Four-Dimensional Regularization/Renormalization approach, in which a small mass serves as regulator. Typical integrals exhibit a logarithmic dependence on this mass, which we extract with the aid of suitable subtraction terms that can easily be integrated analytically until the logarithmic structure is revealed. As first physical applications to test the method, we calculate QCD corrections to the decay rates of scalar and pseudoscalar Higgs bosons into two photons in the limit of an infinite top-quark mass as well as to the $\rho$ parameter.