CPviolation in τ→3πντ

We consider CP-violating effects in the decays τ→(3π)${\nu }_{\mathrm{\tau }}$ where both the ${\mathrm{J}}^{\mathrm{P}}$=$1^{+}$ resonance ${\mathrm{\alpha }}_1$,and ${\mathrm{J}}^{\mathrm{P}}$=$0^{\mathrm{-}}$ resonance π′ can contribute. The interference between the ${\mathrm{\alpha }}_1$ and π′ resonances can lead to enhanced CP-violating asymmetries whose magnitudes depend crucially on the π′ decay constant ${\mathrm{f}}_{\mathrm{\pi }\prime }$. We make an estimate of ${\mathrm{f}}_{\mathrm{\pi }\prime }$ with a simplified chiral Lagrangian coupled to a massive pseudoscalar field, and we compare the estimates from the nonrelativistic quark model and from the QCD sum rule with the estimate from the “mock” meson model. We then estimate quantitatively the size of CP-violating effects in a multi-Higgs-doublet model and scalar-leptoquark models, by assuming that the rest frame of the τ can be reconstructed for three-prong decays. We find that, while CP-violating effects in the scalar-leptoquark models may require more than ${10}^{10}$ τ leptons, CP-violating effects from the multi-Higgs-doublet model can be seen at the 2σ level with about ${10}^7$ τ leptons for the maximal value of the CP-violation parameter allowed by present experiments and for the chiral Lagrangian estimate of ${\mathrm{f}}_{\mathrm{\pi }\prime }$=(1–5)×${10}^{\mathrm{-}3}$ GeV.