TEST OF T AND CP VIOLATION IN LEPTONIC DECAY OF tau^+-

Abstract

The ${\tau }^{\pm }$, highly polarized in the direction of the incident beam, can be obtained from the $e^{\pm }$ collider with the polarized incident $e^{-}$ (and preferably also the $e^{+}$) beam. This polarization vector $\text{longvec}{w}_i=(w_1+w_2)/(1+w_1{w}_2){\hat{e}}_z$ can be used to construct the $T$ odd rotationally invariant product $(\text{longvec}{w}_i\times \text{longvec}{p}_{\mu })$. $\text{longvec}{w}_{\mu }$, where $w_1$ and $w_2$ are longitudinal polarization vectors of $e^{-}$ and $e^{+}$ respectively; $\text{longvec}{p}_{\mu }$ and $\text{longvec}{w}_{\mu }$ are the momentum and polarization of the muon in the decay ${\tau }^{-}\text{rarrow}{\mu }^{-}+{\bar{\nu }}_{\mu }+{\nu }_{\tau }$. T is violated by the existence of such a term. CP can be tested by comparing it with a similar term in ${\tau }^{+}$ decay. If T violation in such a decay is milliweak or stronger, one can find it using the proposed polarized $\tau$-charm factory with luminosity of $1\sim 3\times 10^{33}/{\text{cm}}^2/\sec$. One can test whether T (and CP) violation is due to the charged Higgs boson exchange by doing a similar experiment for the ${\mu }^{\pm }$ decay.

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