We study the processes ${\nu }_{\tau }n\to {\mathrm{\Lambda }}_c{\tau }^{-}({\pi }^{-}{\nu }_{\tau })$ and ${\overline{\nu }}_{\tau }p\to \mathrm{\Lambda }{\tau }^{+}({\pi }^{+}{\overline{\nu }}_{\tau })$, with particular emphasis on the pion energy and angular distributions, as a possible signal for lepton flavor universality violation, and in general of physics beyond the Standard Model (SM), as well as a sensitive probe of the $\tau$ polarization vector. We work within an effective low-energy extension of the SM with all dimension-six four-fermion operators. In this framework, complex Wilson coefficients which encode new physics can generate $CP$-violating contributions. We propose an observable that provides a genuine $CP$-odd signal due to its sensitivity to particular transverse components of the $\tau$ polarization vector. Namely, we show that the asymmetry in the azimuthal-angle distribution of the pion in the decay ${\tau }^{\pm }\to {\pi }^{\pm }{\nu }_{\tau }$ constitutes a smoking-gun prediction of such a beyond the SM scenario. We estimate the strength of this effect extrapolating nucleon-hyperon form factors recently obtained from lattice QCD calculations.

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• Electroweak interaction
• Neutrino interactions