Lepton flavor violation in the supersymmetric seesaw model after the LHC 8 TeV run

We study the lepton flavor violation in the supersymmetric seesaw model, taking into account recent experimental improvements, especially for the Higgs boson mass measurement, direct searches of superpartners, and the rare decay of $B_s\to {\mu }^{+}{\mu }^{-}$ at the LHC; the neutrino mixing angle of ${\theta }_{13}$ in the neutrino experiments; and the search of $\mu \to e\gamma$ in the MEG experiment. We obtain the latest constraints on the parameters in the supersymmetry-breaking terms and study the effect on the lepton-flavor-violating decays of $\tau \to \mu \gamma$ and $\mu \to e\gamma$. In particular, we consider two kinds of assumption on the structures in the Majorana mass matrix and the neutrino Yukawa matrix. In the case of the Majorana mass matrix proportional to the unit matrix, allowing nonvanishing $CP$-violating parameters in the neutrino Yukawa matrix, we find that the branching ratio of $\tau \to \mu \gamma$ can be larger than ${10}^{-9}$ within the improved experimental limit of $\mu \to e\gamma$. We also consider the neutrino Yukawa matrix that includes the mixing only in the second and third generations, and we find that a larger branching ratio of $\tau \to \mu \gamma$ than ${10}^{-9}$ is possible while satisfying the recent constraints.

Figure 1

Excluded region plots for $(M_0,M_{1/2})$ with fixed parameters of $[\text{sign}(\mu ),A_0,\tan \beta ]$ in the degenerate case with the normal hierarchical neutrino masses. The parameters in the neutrino sector are assumed as ${\tilde{M}}_N=7\times {10}^{12}\mathrm{GeV}$ and $O_N=\mathbf{1}$. Each colored region is excluded by the observable as exhibited in the legend. The dotted, dashed, and solid lines show the contours of $m_h$, $\mathcal{B}(\tau \to \mu \gamma )$, and $\mathcal{B}(\mu \to e\gamma )$, respectively.

Figure 2

Excluded region plots in the nondegenerate case with the normal hierarchical neutrino masses. The parameters in $Y_N$ are assumed as $y_1=0.05$, $y_2=y_3=1.5$, and $\theta =\pi /4$. The notation is the same as in Fig. 1.

Figure 3

(a) Correlation between $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$ in the degenerate case with $O_N=\mathbf{1}$. The SUSY parameters $(M_{1/2},M_0,A_0)$ are randomly generated, and we take $\tan \beta =30$ and $\mu >0$. The upper-right group of dots along each line corresponds to ${\tilde{M}}_N=5\times {10}^{14}\mathrm{GeV}$, and the lower-left one corresponds to ${\tilde{M}}_N=7\times {10}^{12}\mathrm{GeV}$. The results of NH and IH within ${\sin }^2{\theta }_{13}=0.022–0.026$ and with ${\sin }^2{\theta }_{13}=0$ are shown as indicated. The vertical and horizontal solid lines show the present upper bounds of $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$, respectively. The dotted lines indicate expected sensitivities at SuperKEKB/Belle II and MEG II. (b) The ratio $R_{\tau /\mu }=\mathcal{B}(\tau \to \mu \gamma )/\mathcal{B}(\mu \to e\gamma )$ for IH as a function of ${\sin }^2{\theta }_{13}$. The gray region is the present experimental value of ${\sin }^2{\theta }_{13}$.

Figure 4

Contour plots of $R_{\tau /\mu }$ on the planes of $(c,{\delta }_{\nu })$ and $(a,{\delta }_{\nu })$ for (a) normal and (b) inverted hierarchical cases. The black (gray) region corresponds to $R_{\tau /\mu }>1800$ (100). The regions of $R_{\tau /\mu }>1800$ (100) with the Majorana $CP$-violating phases being fixed as ${\beta }_{\nu }=0$, ${\alpha }_{\nu }=0$, $\pm \pi$, and $\pm 2\pi$ are also shown with darker (lighter) color.

Figure 5

Correlation between $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$ in the nondegenerate case. The parameters $(y_1,y_2,y_3,\theta )$ in the $Y_N$ are randomly generated within the designated range, and the SUSY parameters are fixed as $M_{1/2}=1.5\mathrm{TeV}$, $M_0=2.0\mathrm{TeV}$, $A_0=-2$, $\tan \beta =30$, and $\mu >0$. The solid lines show the present upper bounds of $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$. The dotted lines indicate expected sensitivities at SuperKEKB/Belle II and MEG II.

Figure 6

Contour plots of $\mathcal{B}(\tau \to \mu \gamma )$ on planes of parameters in the neutrino Yukawa matrix in the nondegenerate case with the normal hierarchy and $\theta =\pi /4$. The red (orange) lines are $\mathcal{B}(\tau \to \mu \gamma )={10}^{-9}$ (${10}^{-10}$). The gray region is excluded by the present bound of $\mathcal{B}(\mu \to e\gamma )$. The dotted line shows the expected sensitivity of MEG II, $\mathcal{B}(\mu \to e\gamma )=5\times {10}^{-14}$.

Figure 7

Correlation between $\mathcal{B}(\mu \to e\gamma )$ and $\mathcal{B}(\tau \to \mu \gamma )$ in the nondegenerate case for three different choices of SUSY parameters. The parameters $(y_1,y_2,y_3,\theta )$ are randomly generated within the designated range.