Universal dual amplitudes and asymptotic expansions for ggrightarrow H and Hrightarrow gamma gamma in four dimensions

Félix Driencourt-Mangin,Germán Rodrigo,Germán F R Sborlini

doi:10.1140/epjc/s10052-018-5692-5

Abstract

Though the one-loop amplitudes of the Higgs boson to massless gauge bosons are finite because there is no direct interaction at tree level in the Standard Model, a well-defined regularization scheme is still required for their correct evaluation. We reanalyze these amplitudes in the framework of the four-dimensional unsubtraction and the loop-tree duality (FDU/LTD), and show how a local renormalization solves potential regularization ambiguities. The Higgs boson interactions are also used to illustrate new additional advantages of this formalism. We show that LTD naturally leads to very compact integrand expressions in four space-time dimensions of the one-loop amplitude with virtual electroweak gauge bosons. They exhibit the same functional form as the amplitudes with top quarks and charged scalars, thus opening further possibilities for simplifications in higher-order computations. Another outstanding application is the straightforward implementation of asymptotic expansions by using dual amplitudes. One of the main benefits of the LTD representation is that it is supported in a Euclidean space. This characteristic feature naturally leads to simpler asymptotic expansions.

Highlights

A well-defined renormalization scheme are still required for their correct evaluation
We have recently proposed a new approach to dealing with perturbative computations avoiding dimensional regularization (DREG)
The four-dimensional nature of the four-dimensional unsubtraction and the loop-tree duality (FDU/loop-tree duality theorem (LTD)) approach allows one to get an alternative insight into the structure of these scattering amplitudes, unveiling the origin of local UV singularities that vanish in the integrated amplitude but lead to finite contributions

Summary

Introduction

A well-defined renormalization scheme are still required for their correct evaluation. We show how to apply the LTD theorem to obtain compact expressions for the amplitude integrand that exhibit the same functional form for virtual charged scalars, fermions (top quarks) or W gauge bosons. [23] based on the assumption that if two physical processes correspond to a similar set of Feynman diagrams, their cross sections should be described by a common set of analytical functions Their calculation is reduced to determine the coefficients of a linear combination of those functions by solving a large set of linear equations arising from comparing the asymptotic expansions of a given ansatz and a one-dimensional integral representation of the amplitude. We will discuss how to implement a completely local renormalization to achieve integrability in four dimensions

Local renormalization and four-dimensional dual representation

Asymptotic expansions in the Euclidean space of the loop three-momentum

W m 2W

Conclusions