CP asymmetry in the angular distribution of τ → KS πν τ decays

Abstract

Abstract In this work, we study the C P asymmetry in the angular distribution of τ → K S πν τ decays, taking into account the known C P violation in K 0 − K ¯ 0 $$ {K}^0-{\overline{K}}^0 $$ mixing. It is pointed out for the first time that, once the well-measured C P violation in the neutral kaon system is invoked, a non-zero C P asymmetry would appear in the angular observable of the decays considered, even within the Standard Model. By employing the reciprocal basis, which is most convenient when a K S(L) is involved in the final state, the C P -violating angular observable is derived to be two times the product of the time-dependent C P asymmetry in K → π + π − and the mean value of the angular distribution in τ ± → K 0 K ¯ 0 π ± ν ¯ τ ν τ $$ {\tau}^{\pm}\to {K}^0\left({\overline{K}}^0\right){\pi}^{\pm }{\overline{\nu}}_{\tau}\left({\nu}_{\tau}\right) $$ decays. Compared with the Belle results measured in four different bins of the K π invariant mass, our predictions lie within the margins of these measurements, except for a 1.7 σ deviation for the lowest mass bin. While being below the current Belle detection sensitivity that is of O $$ \mathcal{O} $$ (10 −3), our predictions are expected to be detectable at the Belle II experiment, where 70 $$ \sqrt{70} $$ times more sensitive results will be obtained with a 50 ab −1 data sample.

Keywords

• Chiral Lagrangians
• CP violation