$CP$ asymmetry in the angular distribution of $\tau \to K_S\pi {\nu }_{\tau }$ decays

Abstract

In this work, we study the $CP$ asymmetry in the angular distribution of $\tau \to K_S\pi {\nu }_{\tau }$ decays, taking into account the known $CP$ violation in $K^0-{\bar{K}}^0$ mixing. It is pointed out for the first time that, once the well-measured $CP$ violation in the neutral kaon system is invoked, a non-zero $CP$ 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 $CP$-violating angular observable is derived to be two times the product of the time-dependent $CP$ asymmetry in $K\to {\pi }^{+}{\pi }^{-}$ and the mean value of the angular distribution in ${\tau }^{\pm }\to K^0({\bar{K}}^0){\pi }^{\pm }{\bar{\nu }}_{\tau }({\nu }_{\tau })$ decays. Compared with the Belle results measured in four different bins of the $K\pi$ invariant mass, our predictions lie within the margins of these measurements, except for a $1.7\sigma$ deviation for the lowest mass bin. While being below the current Belle detection sensitivity that is of $\mathcal{O}(10^{-3})$, our predictions are expected to be detectable at the Belle II experiment, where $\sqrt{70}$ times more sensitive results will be obtained with a $50{\text{ab}}^{-1}$ data sample.

arXiv comment23 pages, 3 figures, and 2 tables; minor corrections, final version published in the journal

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Cited by in corpus (10)

• STCF Conceptual Design Report: Volume 1 -- Physics & Detector
• $CP$ asymmetry in the angular distributions of $\tau \to K_S\pi {\nu }_{\tau }$ decays -- II: general effective field theory analysis
• Flavor Physics at the CEPC: a General Perspective
• Feasibility study of $CP$ Violation in ${\tau }^{-}\to K_S{\pi }^{-}{\nu }_{\tau }$ decays at Super Tau Charm Facility
• Tension between $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ and ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ data and non-standard interactions
• CP violation in two-meson Tau decays induced by heavy new physics
• Study of CP Violation in $D^{\pm }\to K^{\ast }(892{)}^0{\pi }^{\pm }+{\bar{K}}^{\ast }(892{)}^0{\pi }^{\pm }\to K_{S,L}^0{\pi }^0{\pi }^{\pm }$ Decays
• CP Asymmetry in $\tau \to K\pi {\nu }_{\tau }$ within Non-Minimal $SU(5)$
• Effect of $K^0-{\bar{K}}^0$ Mixing on CP and CPT Violations in $B_c^{\pm }\to B^{\pm }{K}_{S,L}^0$ Decays
• Electromagnetic corrections in hadronic tau decays