Is the lepton flavour changing observable in $Z \to μ^\pm + τ^\mp$ decay?

Abstract

Neutrino oscillations as suggested by the recent Super-Kamiokande result imply that lepton numbers could be violated, and Z$\to μ^{\mp} +τ^{\pm}$ 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 $Γ$(Z $\to μ^{\mp} + τ^{\pm})/Γ($Z $ \to μ^{-} + μ^{+})$ could be about $10^{-5}-10^{-6}$, in sharp contrast with the vanishingly small rate $τ^{\pm}\to μ^{\pm} + γ$ strongly suppressed by a quadratic power $(m_3^2-m_2^2)/ M_{\rm W}^2$. Being complementary to neutrino oscillation experiments, measurements of Z$\to μ^{\mp} +τ^{\pm}$ -- which are at hand with the present colliders -- would give one more constraint to the lepton mixing angle $\sin 2θ_{jk}$ and the neutrino mass ratio $m_j/m_k$.