Observing charge-parity ($CP$) or time-reversal ($T$) violations in the leptonic sector will give useful information to elucidate the nature of neutrinos. $CP$-violating couplings in charged leptonic currents carry out the weak phases necessary to break these symmetries. Here we study the interference of $W^{\pm }$ and $H^{\pm }$ boson mediated amplitudes as the origin of possible $CP$ and $T$ violation in semileptonic decays of $K^{\pm }$ mesons and ${\tau }^{\pm }$ leptons. We use the experimental bound on the $T$-odd transverse polarization asymmetry in $K_{\mu 3}^{+}$ decays to predict an upper limit on the $CP$ violating effects in $\tau \to K\pi \nu$ decays. In the framework of this model with scalar-mediated interactions, we find that current limits on the former process indicate that the $CP$ violating effects in the latter are much smaller than the limits reported so far.

• Received 24 August 2009

DOI:https://doi.org/10.1103/PhysRevD.80.096004