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

Abstract

The $τ^\pm$, 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 $\longvec w_i=(w_1+w_2)/(1+w_1w_2) \widehat e_z$ can be used to construct the $T$ odd rotationally invariant product $(\longvec w_i\times\longvec p_μ)$. $\longvec w_μ$, where $w_1$ and $w_2$ are longitudinal polarization vectors of $e^-$ and $e^+$ respectively; $\longvec p_μ$ and $\longvec w_μ$ are the momentum and polarization of the muon in the decay $τ^-\rarrow μ^-+ \barν_μ+ν_τ$. T is violated by the existence of such a term. CP can be tested by comparing it with a similar term in $τ^+$ decay. If T violation in such a decay is milliweak or stronger, one can find it using the proposed polarized $τ$-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 $μ^\pm$ decay.