Is the lepton flavour changing observable in $Z\to {\mu }^{\pm }+{\tau }^{\mp }$ decay?

Abstract

Neutrino oscillations as suggested by the recent Super-Kamiokande result imply that lepton numbers could be violated, and Z$\to {\mu }^{\mp }+{\tau }^{\pm }$ is a typical manifestation. We point out that for this mode, the GIM cancelation is much milder with only a logarithmic behavior $\log (m_3/m_2)$ where $m_j$ is the neutrino mass. The ratio $\Gamma$(Z $\to {\mu }^{\mp }+{\tau }^{\pm })/\Gamma ($Z $\to {\mu }^{-}+{\mu }^{+})$ could be about $10^{-5}-10^{-6}$, in sharp contrast with the vanishingly small rate ${\tau }^{\pm }\to {\mu }^{\pm }+\gamma$ strongly suppressed by a quadratic power $(m_3^2-m_2^2)/M_{\mathrm{W}}^2$. Being complementary to neutrino oscillation experiments, measurements of Z$\to {\mu }^{\mp }+{\tau }^{\pm }$ -- which are at hand with the present colliders -- would give one more constraint to the lepton mixing angle $\sin 2{\theta }_{jk}$ and the neutrino mass ratio $m_j/m_k$.

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