Lower Limits on $\mu \to e\gamma$ from new Measurements on $U_{e3}$

Abstract

New data on the lepton mixing angle ${\theta }_{13}$ imply that the $e\mu$ element of the matrix $m_{\nu }{m}_{\nu }^{†}$, where $m_{\nu }$ is the neutrino Majorana mass matrix, cannot vanish. This implies a lower limit on lepton flavor violating processes in the $e\mu$ sector in a variety of frameworks, including Higgs triplet models or the concept of minimal flavor violation in the lepton sector. We illustrate this for the branching ratio of $\mu \to e\gamma$ in the type II seesaw mechanism, in which a Higgs triplet is responsible for neutrino mass and also mediates lepton flavor violation. We also discuss processes like $\mu \to e\bar{e}e$ and $\mu \to e$ conversion in nuclei. Since these processes have sensitivity on the individual entries of $m_{\nu }$, their rates can still be vanishingly small.

9 pages, 4 .eps figures; Discussions, 2 new figures and references added, Abstract and text modified, matches with the published version in Physical Review D

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