# Universal dual amplitudes and asymptotic expansions for $gg\to H$ and $H\to \gamma\gamma$ in four dimensions

## TL;DR

This paper reanalyzes Higgs to gauge boson amplitudes using four-dimensional unsubtraction and loop-tree duality, revealing compact integrand forms and facilitating asymptotic expansions in a Euclidean space.

## Contribution

It introduces a local renormalization scheme within FDU/LTD to resolve regularization ambiguities and demonstrates the advantages of LTD for simplifying one-loop amplitude computations.

## Key findings

- LTD yields compact integrand expressions in four dimensions.
- Amplitudes with electroweak gauge bosons resemble those with top quarks and scalars.
- LTD supports straightforward asymptotic expansions in Euclidean space.

## 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.