Stage-two spin-correlation functions: Tests for non-CKM-type leptonic CP violation in τ→ρν decay

There are two tests for leptonic CP violation in τ→ρν decay by inclusion of ρ polarimetry observables in the energy correlation function for Z0 or γ*→τ-τ+→(ρ-ν)(ρ+bar ν). By CP invariance the moduli ratio of, and phase difference between, the two helicity amplitudes for τ-→ρ-ντ decay should equal those for τ+→ρ+bar ντ decay. The full angular distribution for the above process, including the πminus-plus momentum direction versus that of the ρminus-plus momentum, can be used to test for such a non-CKM-type leptonic CP violation in τ→ρν 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 τ→ρν decay are calculated for possible application at the Z0, at a B factory, or at the τ-charm threshold. S2SC functions should be useful for testing for possible non-CKM-type CP violation in top quark and in W boson decay processes