CP violation in τ→3π ν τ
We consider CP-violating effects in the decays \ensuremath{\tau}\ensuremath{\rightarrow}(3\ensuremath{\pi})${\ensuremath{\nu}}_{\mathrm{\ensuremath{\tau}}}$ where both the ${\mathrm{J}}^{\mathrm{P}}$=${1}^{+}$ resonance ${\mathrm{\ensuremath{\alpha}}}_{1}$,and ${\mathrm{J}}^{\mathrm{P}}$=${0}^{\mathrm{\ensuremath{-}}}$ resonance \ensuremath{\pi}\ensuremath{'} can contribute. The interference between the ${\mathrm{\ensuremath{\alpha}}}_{1}$ and \ensuremath{\pi}\ensuremath{'} resonances can lead to enhanced CP-violating asymmetries whose magnitudes depend crucially on the \ensuremath{\pi}\ensuremath{'} decay constant ${\mathrm{f}}_{\mathrm{\ensuremath{\pi}}\ensuremath{'}}$. We make an estimate of ${\mathrm{f}}_{\mathrm{\ensuremath{\pi}}\ensuremath{'}}$ 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 \ensuremath{\tau} can be reconstructed for three-prong decays. We find that, while CP-violating effects in the scalar-leptoquark models may require more than ${10}^{10}$ \ensuremath{\tau} leptons, CP-violating effects from the multi-Higgs-doublet model can be seen at the 2\ensuremath{\sigma} level with about ${10}^{7}$ \ensuremath{\tau} leptons for the maximal value of the CP-violation parameter allowed by present experiments and for the chiral Lagrangian estimate of ${\mathrm{f}}_{\mathrm{\ensuremath{\pi}}\ensuremath{'}}$=(1\char21{}5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ GeV.