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 \((m_j^2-m_k^2)/ M_{\rm W}^2\). 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.
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Received: 29 October 1998 / Published online: 11 March 1999
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Pham, XY. Lepton flavor changing in neutrinoless \(\tau\) decays. Eur. Phys. J. C 8, 513–516 (1999). https://doi.org/10.1007/s100529901088
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DOI: https://doi.org/10.1007/s100529901088