Lower bounds on lepton flavor violating branching ratios in a radiative seesaw model

We study the lepton flavor violating decays such as $\mu \to e\gamma$, $\tau \to e\gamma$, $\tau \to \mu \gamma$ in the three-loop radiative seesaw model proposed by Krauss, Nasri, and Trodden. In this model, the relevant coupling constants are larger for the heavier scalars that run inside loop diagrams to generate the appropriate magnitude of neutrino masses. Imposing a criterion that all the coupling constants must be small enough to be treated perturbatively, we find an upper bound on the mass of one of the scalars. By combining it with neutrino mass parameters, we derive lower bounds on the branching ratios of the lepton flavor violating processes. In a case with the inverted mass ordering and best-fit neutrino oscillation parameters, one of the lower bounds is $\mathrm{Br}(\mu \to e\gamma )>1.1\times {10}^{-13}$, which is within the reach of the MEG II experiment.

Figure 1

The diagram relevant to the neutrino mass matrix in the KNT model.

Figure 2

Contour plot of $f(x,y)$. It has maximal value 1.044 when $x/y={10}^{1.47}$, $y\gg 1$.

Figure 3

Loop function $f(x,y)$ with $x/y={10}^{1.47}$. The horizontal line shows the upper bound 1.05. The loop function becomes constant for large $y$ [see Eq. (13)].

Figure 4

Contour plots of the lower bounds on $\mathrm{Br}(\mu \to e\gamma )$ in the inverted mass ordering cases. $n_{\mathrm{eff}}$ ($\le n_N-1$) is the number of right-handed neutrinos that contribute to $M_{\tau \tau }$. In cases (a) and (b), the other neutrino oscillation parameters are fixed to the best-fit values [19]. In cases (c) and (d), they are chosen to realize minimal $\mathrm{Br}(\mu \to e\gamma )$ within two standard deviations. The blue regions are already excluded by MEG [27]. The green regions can be excluded by MEG II [17]. The solid- and dashed-vertical lines indicate the best-fit value and $2\sigma$ ranges of $\delta$. (a) $n_{\mathrm{eff}}=1$, best-fit. (b) $n_{\mathrm{eff}}=2$, best-fit. (c) $n_{\mathrm{eff}}=1$, minimal. (d) $n_{\mathrm{eff}}=2$, minimal.

Figure 5

Contour plots of the lower bound on $\mathrm{Br}(\mu \to e\gamma )$ in the IO case. Notation is same as Fig. 4. The Majorana phase $\eta$ is converted to $|M_{ee}|$ by Eq. (64). (a) $n_{\mathrm{eff}}=1$, best-fit. (b) $n_{\mathrm{eff}}=2$, best-fit. (c) $n_{\mathrm{eff}}=1$, minimal. (d) $n_{\mathrm{eff}}=2$, minimal.

Figure 6

Contour of the minimal value of $\mathrm{Br}(\tau \to \mu \gamma )$ (red lines). The light-red region is already excluded by the BABAR experiment [28]. The dark gray region shows where the charged particle $S_2$ is stable. The lines labeled “0.75” and “3” indicate $\sigma v/(\sum |g_{1i}^{*}{g}_{1j}{|}^2({10}^{-26}{\mathrm{cm}}^3/\mathrm{s}))$, and the light-gray region upper of the dot-dashed curve, either $|g_{12}|>1$ or $|g_{13}|>1$ is required to satisfy ${\mathrm{\Omega }}_{N_1}{h}^2\simeq 0.1$. The cyan region is excluded by the direct search of the right-handed slepton at the LHC [33, 34].