2020 Impact factor 4.590
Particles and Fields
Eur. Phys. J. C 8, 513-516
DOI 10.1007/s100529901088

Lepton flavor changing in neutrinoless $\tau$ decays

Xuan-Yem Pham

Laboratoire de Physique Théorique et Hautes Energies, Paris CNRS, Université P. et M. Curie, Université D. Diderot

Received: 29 October 1998 / Published online: 11 March 1999

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 mj, 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 mj/mk, and therefore is complementary to neutrino oscillation experiments.

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