Numerical evaluation of two-loop integrals in FDR

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 ρ parameter.

Collider Physics at the Precision Frontier

“…Among four-dimensional methods where two-loop applications already have been achieved is also the Four-Dimensional Regularisation/Renormalisation (FDR) approach [819][820][821][822][823][824], which subtracts UV divergences at integrand level and regulates IR singularities by a dimensionful scale in the propagators.…”

Regularization-scheme dependence of QCD amplitudes in the massive case

“…The fdh scheme has been adapted to the so-called fdf scheme (four-dimensional formulation) for using unitary-based methods to compute NLO amplitudes [21,22]. There are also proposals to abandon dimensional regularization altogether and perform computations completely in four dimensions in the context of implicit regularization [23][24][25][26], fdr (four-dimensional regularization/renormalization) [27][28][29], and using loop-tree duality to deal with IR singularities at the integrand level [30][31][32].…”