Lower limits on $\mu \to e\gamma$ from new measurements on $U_{e3}$

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 $\mu \to e\overline{e}e$ 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.

Figure 1

Plots showing the effect of the Dirac $CP$-phase $\delta$ on various $x_{\alpha \beta }$ where $x\equiv |(m_{\nu }{m}_{\nu }^{†})|$. The remaining oscillation parameters are fixed at their best-fit values (see Table ).

Figure 2

Plots showing the variation of the lowest possible $\mathrm{Br}(\mu \to e\gamma )$ vs $M_{H^{\pm \pm }}$ with different values of $v_{\Delta }$ for the normal neutrino mass ordering. The left plots are considering the present constraints on different LFV processes and the right ones are with the future constraints. Plots in the upper row are with the lightest neutrino mass $m_1=0.003\mathrm{eV}$, the middle row is for $m_1=0.05\mathrm{eV}$, and the lower row is for $m_1=0.2\mathrm{eV}$. The solid (dotted) line corresponds to the $3\sigma$ ($1\sigma$) range of the oscillation parameters. The colored (dark) band corresponds to the exclusion region as suggested by present and future experimental bounds. All constraints are listed in Table . The corresponding plots for the inverted ordering look basically identical.

Figure 3

Plots showing the effects of the constraints on other LFV processes on the minimal branching ratio of $\mu \to e\gamma$. The colored (dark) band corresponds to the exclusion region as suggested by the present experimental bound.