CP Violation in $\tau \to 3\pi {\nu }_{\tau }$

Abstract

We consider CP violating effects in the decays $\tau \to (3\pi ){\nu }_{\tau }$ where both the ${\mathrm{J}}^{\mathrm{P}}=1^{+}$ resonance, $a_1$, and ${\mathrm{J}}^{\mathrm{P}}=0^{-}$ resonance, ${\pi }^{\prime }$, can contribute. The interference between the $a_1$ and ${\pi }^{\prime }$ resonances can lead to enhanced CP-violating asymmetries whose magnitudes depend crucially on the ${\pi }^{\prime }$ decay constant, $f_{{\pi }^{\prime }}$. We make an estimate of $f_{{\pi }^{\prime }}$ with a simplified chiral Lagrangian coupled to a massive pseudoscalar field, and we compare the estimates from the non-relativistic 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. We find that, while CP-violating effects in the scalar-leptoquark models may require more than $10^{10}$ $\tau$ leptons, CP-violating effects from the multi-Higgs-doublet model can be seen at the $2\sigma$ level with about $10^7$ $\tau$ leptons using the chiral Lagrangian estimate of $f_{{\pi }^{\prime }}=(1\sim 5)\times 10^{-3}$ GeV.

Comments: Latex, 30 pages, 2 figures (not included). Three compressed postscript files of the paper available at ftp://ftp.kek.jp/kek/preprints/TH/TH-419/kekth419.ps.gz, Tau1.ps.gz, Tau2.ps.gz