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Abstract
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.
Highlights
Computing radiative corrections has become of uppermost importance in particle phenomenology [1]
In this paper we investigate the possibility of further simplifying NNLO computations by abandoning dimensional regularization [29]
We have presented the first two-loop calculation ever performed in FDR
Summary
Computing radiative corrections has become of uppermost importance in particle phenomenology [1]. Loop functions used at a given perturbative level must be further expanded in —when appearing at higher orders—to include terms generating O( 0) contributions when multiplied by the new poles Such complications arise in DR because constants needed to preserve the symmetries of the Lagrangian are often produced by terms, which are kept under control by the iterative renormalization. This has driven us to study the performances of FDR [30] as a simpler four-dimensional approach beyond one loop.. The two-loop FDR calculation of H → γ γ is presented in Sect. 3 and the technical details are collected in the final appendices
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