Lepton flavor changing in neutrinoless $\tau$ decays

Abstract

Neutrino oscillations, as recently reported by the Super-Kamiokande collaboration, imply that lepton numbers could be violated, and ${\tau }^{\pm }\to {\mu }^{\pm }+{\ell }^{+}+{\ell }^{-},{\tau }^{\pm }\to {\mu }^{\pm }+{\rho }^0$ are some typical examples. We point out that in these neutrinoless modes, the GIM cancelation is much milder with only a logarithmic behavior $\log (m_j/m_k)$ where $m_{j,k}$ are the neutrino masses. This is in sharp contrast with the vanishingly small amplitude ${\tau }^{\pm }\to {\mu }^{\pm }+\gamma$ strongly suppressed by the quadratic power $(m_j^2-m_k^2)/M_{\mathrm{W}}^2$. In comparison with the hopelessly small branching ratio B$({\tau }^{\pm }\to {\mu }^{\pm }+\gamma )\approx 10^{-40}$, the B$({\tau }^{\pm }\to {\mu }^{\pm }+{\ell }^{+}+{\ell }^{-})$ could be larger than $10^{-14}$. The latter mode, if measurable, could give one more constraint to the lepton mixing angle $\sin 2{\theta }_{jk}$ and the neutrino mass ratio $m_j/m_k$, and therefore is complementary to neutrino oscillation experiments.

Latex (7 pages) + 3 postscript figures

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