One-loop formulas for $H\rightarrow Z \nu_l\bar{\nu}_l$ for $l = e,\mu, \tau$ in 't Hooft-Veltman gauge

TL;DR

This paper provides analytical one-loop calculations for the decay process $H\rightarrow Z \nu_l\bar{\nu}_l$ within the Standard Model, evaluates decay rates numerically, and analyzes potential signals at future lepton colliders.

Contribution

It presents the first detailed one-loop form factors for $H\rightarrow Z \nu_l\bar{\nu}_l$ in 't Hooft-Veltman gauge, including numerical decay rate evaluations and collider signal analysis.

Findings

One-loop corrections contribute about 10% to decay rates.

Signals are detectable at $\sqrt{s}=250$ GeV but challenging at higher energies.

The study emphasizes the importance of including one-loop effects in future collider analyses.

Abstract

In this paper, we present analytical results for one-loop contributing to the decay processes $H\rightarrow Z \nu_l\bar{\nu}_l$ (for $l = e, \mu, \tau$). The calculations are performed within the Standard Model framework in 't Hooft-Veltman gauge. One-loop form factors are then written in terms of scalar one-loop functions in the standard notations of {\tt LoopTools}. As a result, one-loop decay rates for the decay channels can be evaluated numerically by using the package. Furthermore, we analyse the signals of $H\rightarrow Z \nu_l\bar{\nu}_l$ via the production processes $e^-e^+ \rightarrow ZH^* \rightarrow Z (H^* \rightarrow Z \nu_l\bar{\nu}_l)$ including the initial beam polarizations at future lepton collider. The Standard Model background such as the processes $e^-e^+ \rightarrow \nu_l\bar{\nu}_l ZZ$ are also examined in this study. In numerical results, we find that one-loop corrections are about $10\%$ contributions to the decay rates. They are sizeable contributions and should be taken into account at future colliders. We show that the signals $H\rightarrow Z\nu_l\bar{\nu}_l$ are clearly visible at center-of-mass energy $\sqrt{s}=250$ GeV and it is hard to probe at higher-energy regions due to the dominant of the background.