Probing New Physics and CP Violation in $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ and $\bar\nu_\tau p \to \Lambda \tau^+ (\pi^+ \bar\nu_\tau)$

Abstract

We study the processes $\nu_\tau n \to \Lambda_c \tau^- (\pi^- \nu_\tau)$ and $\bar\nu_\tau p \to \Lambda \tau^+ (\pi^+ \bar\nu_\tau)$, 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.