Decay of the Higgs boson $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ for a non-Hermitian Yukawa interaction

Abstract

The differential rate of the decay of the Higgs boson ($h$) to a pair of $\tau$ leptons with their subsequent decay in the ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{+}\to {\pi }^{+}{\bar{\nu }}_{\tau }$ channels is studied. The Yukawa interaction between the Higgs boson and the $\tau$ leptons is assumed to include scalar ($S$) and pseudoscalar ($PS$) couplings. Angular distributions of the pions in the $h\to {\tau }^{-}{\tau }^{+}\to {\pi }^{-}{\nu }_{\tau }{\pi }^{+}{\bar{\nu }}_{\tau }$ decay are considered. For real values of the $S$ and $PS$ couplings, this decay is known to be a source of information on $\mathcal{C}\mathcal{P}$ violation in the $h\tau \tau$ interaction. In the present paper, the main attention is paid to a possible non-Hermiticity of this interaction. Influence of non-Hermiticity on the distribution of the angle between planes of the ${\tau }^{-}\to {\pi }^{-}{\nu }_{\tau }$ and ${\tau }^{+}\to {\pi }^{+}{\bar{\nu }}_{\tau }$ decays, and distribution of the polar angle of one of the pions are analyzed. Asymmetries sensitive to parameters of $\mathcal{C}\mathcal{P}$ violation and non-Hermiticity of $h\tau \tau$ interaction are proposed.

Comments: 12 pages, 4 figures, appolb style; v2: published version