Stage-two spin-correlation functions: Tests for non-CKM-type leptonic [ital CP] violation in [tau][r arrow][rho][nu] decay

There are two tests for leptonic [ital CP] violation in [tau][r arrow][rho][nu] decay by inclusion of [rho] polarimetry observables in the energy correlation function for [ital Z][sup 0] or [gamma][sup *][r arrow][tau][sup [minus]][tau][sup +][r arrow]([rho][sup [minus]][nu])([rho][sup +][bar [nu]]). By [ital CP] invariance the moduli ratio of, and phase difference between, the two helicity amplitudes for [tau][sup [minus]][r arrow][rho][sup [minus]][nu][sub [tau]] decay should equal those for [tau][sup +][r arrow][rho][sup +][bar [nu]][sub [tau]] decay. The full angular distribution for the above process, including the [pi][sup [minus plus]] momentum direction versus that of the [rho][sup [minus plus]] momentum, can be used to test for such a non-CKM-type leptonic [ital CP] violation in [tau][r arrow][rho][nu] decay. Since this adds on spin-correlation information from the next stage of decays in the decay sequence, we call such an energy-angular distribution a stage-two spin-correlation (S2SC) function. Ideal statistical errors for [tau][r arrow][rho][nu] decay are calculated for possible application at the [ital Z][sup 0], at a [ital B] factory, or at the [tau]-charm threshold. S2SC functions should be useful for testing for possible non-CKM-type [ital CP] violation in top quark and in [ital W] boson decay processes.