CP violation in two meson tau decays

Abstract

CP violation in $τ\to K_S πν_τ$ decays has attracted a lot of attention recently, due to the BaBar anomaly in the corresponding rate asymmetry. Within an effective field theory formalism, only extreme fine-tuning would allow to understand such measurement, which is currently being scrutinized at Belle(-II), as will be in the future super-charm-tau factory. Here we summarize the results of applying the same formalism to the other two-meson tau decay channels, which can help solve this conundrum. Our main conclusion is that current and future experiments would be sensitive to the maximum allowed CP rate asymmetry in the related $K^\pm K_S$ modes with a measurement having 5$\%$ precision, that will either support or cast further doubts on the BaBar anomaly.

Figures (5)

• Figure 1: Pion tensor form factor modulus as a function of the $\pi\pi$ invariant mass. The solid curve corresponds to the central value, and the dashed ones covers one standard deviation uncertainties, assuming $|\delta_+(s)-\delta_T(s)|=2\delta_+^{inel}(s)$.
• Figure 2: Pion vector form factor phase as a function of the $\pi\pi$ invariant mass. The solid curve represents the central value, and the dashed lines cover the one sigma uncertainties Gonzalez-Solis:2019iod.
• Figure 3: Pion tensor form factor phase as a function of the $\pi\pi$ invariant mass. The solid curve corresponds to the inelastic contributions, and the black dashed ones depict one standard deviation uncertainties, assuming $|\delta_+(s)-\delta_T(s)|=2\delta_+^{inel}(s)$. The central value of $\delta_+(s)$, according to Ref. Gonzalez-Solis:2019iod (see fig. \ref{['Fig_deltaF+']}), is shown by a black dot-dashed line for reference.
• Figure 4: Maximal $A^{\tau\rightarrow K_SK\nu_{\tau}}_{FB}(s)$ (black solid line), corresponding to the Wilson coefficients values $\Re e[\epsilon_S^d]=-3.1\times10^{-2}$ , $\Im m[\epsilon_S^d]=-2.7\times 10^{-4}$, $\Re e[\epsilon_T^d]=-7.9\times 10^{-2}$ and $\Im m[\epsilon_T^d]=8 \times 10^{-5}$, compared to the SM case (black dashed line).
• Figure 5: 3D density plot for the FOM described in eq. (\ref{['eq_FOM']}) on the parameter space, fixing $|\Im m[\hat{\epsilon}_T^d]| = 8\times 10^{-5}$, for the $KK_S$ decay channel.