Test of T and CP violation in leptonic decay of τ±

The τ±, highly polarized in the direction of the incident beam, can be obtained from the e± collider with the polarized incident e- (and preferably also the e+) beam. This polarization vector rvec ωi = (ω1 + ω2)/(1 + ω1ω2)ez can be used to construct the T odd rotationally invariant product (rvec ωi x rvec pμ). rvec ωμ, where ω1 and ω2 are longitudinal polarization vectors of e- and e+ respectively; rvec pμ and rvec ωμ are the momentum and polarization of the muon in the decay τ- → μ- + bar νμ + ντ. 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 ∼ 3 x 1033/cm2/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± decay