Anatomy of Higgs decays into $\gamma \gamma$ and $\gamma Z$ within the EChL in the $R_{\xi }$ gauges

Abstract

In this work we study the Higgs boson decays into two photons and into one photon and one $Z$ gauge boson within the context of the non-linear Effective Field Theory called the Electroweak Chiral Lagrangian. We present a detailed computation of the corresponding amplitudes to one-loop level in the covariant $R_{\xi }$ gauges. We assume that the fermionic loop contributions are as in the Standard Model and focus here just in the computation of the bosonic loop contributions. Our renormalization program and the anatomy of the various contributions participating in the $R_{\xi }$ gauges are fully explored. With this present computation we demonstrate the gauge invariance of the EChL result, not only for the case of on-shell Higgs boson, but also for the most general and interesting case of off-shell Higgs boson. We finally analyse and conclude on the special relevance of the Goldstone boson loops, in good agreement with the expected chiral loops behaviour in Chiral Lagrangians. We perform a systematic comparison with the corresponding computation of the Standard Model in the $R_{\xi }$ gauges and with the previous EChL results in the unitary gauge. This work represents the first computation within the EChL of these Higgs observables to one-loop in the most general $R_{\xi }$ gauges and with a full renormalization program description, not yet fully explored in the previous literature and which is different to the most frequently used in the linear Effective Field Theory (SMEFT).

44 pages, 10 figures. Minor corrections to typos detected and added new references respect to the version 1

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Cited by in corpus (7)

• One-loop renormalization of VBS with the electroweak chiral Lagrangian in covariant gauges
• Introducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT
• Double Higgs production at TeV $e^{+}{e}^{-}$ colliders with Effective Field Theories: sensitivity to BSM Higgs couplings
• Exploring correlations between HEFT Higgs couplings ${\kappa }_V$ and ${\kappa }_{2V}$ via HH production at $e^{+}{e}^{-}$ colliders
• Diphoton decay of the higgs from the Epstein--Glaser viewpoint
• Rare Higgs Decay into a Photon and a Z Boson in Radiatively-Driven Natural Supersymmetry
• Tests of BSM Higgs interactions by the combination $({\kappa }_V^2-{\kappa }_{2V})$ in HHjj production at LHC