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

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 $\longvec w_i=(w_1+w_2)/(1+w_1w_2) \widehat e_z$canbeusedtoconstructthe$T$ odd rotationally invariant product $(\text{longvec}{w}_i\times \text{longvec}{p}_{\mu })$. $\longvec w_\mu$,where$w_1$and$w_2$arelongitudinalpolarizationvectorsof$e^-$and$e^+$respectively;$\longvec p_\mu$and$\longvec w_\mu$ are the momentum and polarization of the muon in the decay $\tau^-\rarrow \mu^-+ \bar\nu_\mu+\nu_\tau$. 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 $1 \sim 3 \times 10^{33}/\cm^2/\sec$. 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.