$\tau \to \mu\mu\mu$ at a rate of one out of $10^{14}$ tau decays?
| Autor: | Blackstone, Patrick, Fael, Matteo, Passemar, Emilie |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1140/epjc/s10052-020-8059-7 |
| Popis: | We present in a full analytic form the partial widths for the lepton flavour violating decays $\mu^\pm \to e^\pm e^+ e^-$ and $\tau^\pm \to \ell^\pm \ell'^{+} \ell'^{-}$, with $\ell,\ell'=\mu,e$, mediated by neutrino oscillations in the one-loop diagrams. Compared to the first result by Petcov in [1], obtained in the zero momentum limit $\mathcal{P}\ll m_{\nu} \ll M_W$, we retain full dependence on $\mathcal{P}$, the momenta and masses of external particles, and we determine the branching ratios in the physical limit $m_\nu \ll \mathcal{P} \ll M_W$. We show that the claim presented in [2] that the $\tau \to \ell \ell' \ell'$ branching ratios could be as large as $10^{-14}$, as a consequence of keeping the $\mathcal{P}$ dependence, is flawed. We find rates of order $10^{-55}$, even smaller than those obtained in the zero momentum limit, as the latter prediction contains an unphysical logarithmic enhancement. Comment: 6 pages, 2 figures, 1 table. v2 version published in EPJC, minor changes |
| Databáze: | arXiv |
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