Can the observed $CP$ asymmetry in $\tau \to K\pi {\nu }_{\tau }$ be due to nonstandard tensor interactions?

An intriguing opposite sign of the $CP$-violating asymmetry from that expected within the Standard Model was recently measured in the tau decay modes ${\tau }^{\pm }\to K_s{\pi }^{\pm }{\stackrel{(-)}{\nu }}_{\tau }$ by the BABAR collaboration. If this result is confirmed with higher precision, the observed decay rate asymmetry $A_{CP}$ can only arise from some nonstandard interactions occurring possibly in both the hadronic as well as in the leptonic sectors. We illustrate that, while a simple charged scalar interaction cannot yield this rate asymmetry, it will be possible to generate this in the presence of a tensor interaction. Parametrizing the strength and weak phase of this nonstandard interaction contribution, the observed branching ratio and the decay-rate $CP$ asymmetry for the particular mode ${\tau }^{\pm }\to K_s{\pi }^{\pm }{\stackrel{(-)}{\nu }}_{\tau }$ are used to determine the $CP$-violating weak phase and the coupling of a tensorial interaction that can give a consistent sign and magnitude of the asymmetry.

Figure 1

The Feynman diagram for the Standard Model decay mode via W exchange is shown in the left panel, and that for the New physics exchange diagram via some exotic particle X is shown in the right panel.

Figure 2

The figures on the left and the right show the $\sqrt{Q^2}$ dependence of $|F_V|$ and $|F_S|$, respectively, where the parameters appearing in the combination of the Briet–Wigner forms for the resonances, $K^{*}(892)$, $K^{*}(1410)$, and $K^{*}(800)$, were used from the Belle fits for case I.

Figure 3

The figure shows the $\sqrt{Q^2}$ dependence of ${\delta }_v$ as extracted from the complex form with contributions from the combination of the two vector resonances, $K^{*}(892)$ and $K^{*}(1410)$, with parameters from Belle fits for case I.

Figure 4

The figure on the left shows the $\sqrt{Q^2}$ dependence of $|F_V|$, and that on the right shows the $\sqrt{Q^2}$ dependence of $|F_S|$, when these form factors include the Briet–Wigner contributions from the vector resonance $K^{*}(892)$ and the scalars, $K^{*}(1430)$ and $K^{*}(800)$, as used in the Belle fits for case II.

Figure 5

The figure shows the $\sqrt{Q^2}$ dependence of ${\delta }_v$ corresponding to the vector form factor for the Belle fits of case II.