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The issue of Hermiticity of the Higgs boson interaction with fermions isaddressed. A model for non-Hermitian Yukawa interaction is proposed andapproximation of one fermion generation is considered. Symmetry properties ofthe corresponding $h f \bar{f}$ Lagrangian with respect to the discrete P, Cand T transformations are analyzed, and the modified Dirac equation for thefree fermion is studied. Longitudinal polarization of the fermions in the decay$h \to f \bar{f}$, which arises due to non-Hermiticity of the $h f \bar{f}$interaction, is discussed. It is suggested to study effects of thisnon-Hermiticity in the decay $h \to \tau^- \tau^+ \to \mu^- {\bar \nu}_\mu\nu_\tau \, \mu^+ \nu_\mu {\bar \nu}_\tau$, for which observables (asymmetries)are constructed which take nonzero values for a non-Hermitian $h \tau^- \tau^+$interaction. These asymmetries are analyzed for various configurations of themuon energies.

Decay of the Higgs boson to $\tau^- \tau^+$ and non-Hermiticity of the Yukawa interaction