In this paper we illustrate the simplifications produced by FDR in NNLO
computations. We show with an explicit example that - due to its
four-dimensionality - FDR does not require an order-by-order renormalization
and that, unlike the one-loop case, FDR and dimensional regularization (DR)
generate intermediate two-loop results which are no longer linked by a simple
subtraction of the ultraviolet (UV) poles in epsilon. Our case study is the
two-loop amplitude for H -> gamma gamma, mediated by an infinitely heavy top
loop, in the presence of gluonic corrections. We use this to elucidate how
gauge invariance is preserved with no need of introducing counterterms in the
Lagrangian. In addition, we discuss a possible four-dimensional approach to the
infrared (IR) problem compatible with the FDR treatment of the UV infinities.Comment: 34 pages, 8 figures, version enlarged to be published in EPJ
