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

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.

11 pages, no figures. Minor modifications, discussion improved. Final version published in EPJC

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• Mathematical properties of nested residues and their application to multi-loop scattering amplitudes
• Geometrical approach to causality in multi-loop amplitudes
• Integrands of loop amplitudes within loop-tree duality
• Causal representation of multi-loop Feynman integrands within the loop-tree duality
• Loop-tree duality from vertices and edges
• Quantum algorithm for Feynman loop integrals
• Universal opening of four-loop scattering amplitudes to trees
• On the vanishing of certain cuts or residues of loop integrals with higher powers of the propagators
• Asymptotic expansions through the loop-tree duality
• Rewording Theoretical Predictions at Colliders with Vacuum Amplitudes
• Loop Feynman integration on a quantum computer
• Once more on the Higgs decay into two photons