Polarization amplitudes in $\tau^{-} \rightarrow \nu_{\tau} VP$ decay beyond the Standard Model

Abstract.

We study the amplitudes of the $\tau^{-} \rightarrow \nu_{\tau} VP$ decay for the different polarizations of the vector meson V, using a formalism where the mapping from the quark degrees of freedom to the meson ones is done with the ³P₀ model. We extend the formalism to a case, with the operator $\gamma^{\mu} -\alpha\gamma^{\mu} \gamma_{5}$, that can account for different models beyond the Standard Model and study in detail the $\tau^{-} \rightarrow \nu_{\tau} K^{\ast 0} K^{-}$ reaction for the different polarizations of the $K^{\ast 0}$. The results are shown in terms of the $\alpha$ parameter that differs for each model. We find that $\frac{\mathrm{d} \Gamma}{\mathrm{d} M_{inv}^{(K^{\ast 0} K^{-})}}$ is very different for each of the third components of the vector spin, $M=\pm 1, 0$, and in particular the magnitude $\frac{\mathrm{d} \Gamma}{\mathrm{d} M_{inv}^{(K^{\ast 0} K^{-})}}\vert _{M=+1} -$$\frac{\mathrm{d} \Gamma}{\mathrm{d} M_{inv}^{(K^{\ast 0} K^{-})}}\vert _{M=-1}$ is very sensitive to the $\alpha$ parameter, which makes the investigation of this magnitude very useful to test different models beyond the Standard Model.