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

Abstract

In this paper, we present analytical results for one-loop contributing to the decay processes $H\to Z{\nu }_l{\bar{\nu }}_l$ (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 $H\to Z{\nu }_l{\bar{\nu }}_l$ via the production processes $e^{-}{e}^{+}\to Z{H}^{\ast }\to Z(H^{\ast }\to Z{\nu }_l{\bar{\nu }}_l)$ including the initial beam polarizations at future lepton collider. The Standard Model background such as the processes $e^{-}{e}^{+}\to {\nu }_l{\bar{\nu }}_{l}ZZ$ 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 $H\to Z{\nu }_l{\bar{\nu }}_l$ 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.

arXiv comment28 pages, references are added

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