Polarization amplitudes in $\tau^- \to \nu_{\tau} V P$ decay beyond the standard model

TL;DR

This paper develops a formalism to analyze polarization amplitudes in tau decays involving vector and pseudoscalar mesons, exploring beyond Standard Model effects through helicity amplitude differences sensitive to new physics parameters.

Contribution

It extends a recent formalism to include operators beyond the Standard Model, enabling detailed study of helicity-dependent decay amplitudes in tau decays.

Findings

Helicity amplitudes vary significantly with the model parameter lpha.

The difference in decay rates for helicities nd  is highly sensitive to new physics effects.

The formalism allows for testing beyond Standard Model scenarios through polarization observables.

Abstract

We use a recent formalism of the weak hadronic reactions $\tau^- \to \nu_{\tau} M_1 M_2$ to study the helicity amplitudes in $\tau^- \to \nu_{\tau} V P$ decay. This recent formalism maps the transition matrix elements at the quark level into hadronic matrix elements, and finally writes the weak matrix elements in terms of easy analytical formulas evaluated by means of an elaborate angular momentum algebra. The formalism provides directly the amplitudes for the different spin third components of the vector mesons involved. We extend the formalism to a general 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^- \to \nu_{\tau} K^{*0} K^{-} $ reaction for the different helicities of the $K^{*0}$. The results are shown in terms of the $\alpha$ parameter that differs for each model. We find that $\frac{d \Gamma}{d M_{\rm inv}^{(K^{*0} K^{-} )}}$ is very different for the different components $M=\pm 1, 0$ and in particular the magnitude $\frac{d \Gamma}{d M_{\rm inv}^{(K^{*0} K^{-} )}}|_{M=+1} -\frac{d \Gamma}{d M_{\rm inv}^{(K^{*0} K^{-} )}}|_{M=-1} $ is very sensitive to the $\alpha$ parameter, which makes the investigation of this magnitude a most welcome initiative to test different models beyond the standard model.