Supersymmetric type-III seesaw mechanism: Lepton flavor violation and LHC phenomenology

We study a supersymmetric version of the type-III seesaw mechanism considering two variants of the model: a minimal version for explaining neutrino data with only two copies of $\mathbf{24}$ superfields and a model with three generations of $\mathbf{24}$-plets. The latter predicts, in general, rates for $\mu \to e\gamma$ inconsistent with experimental data. However, this bound can be evaded if certain special conditions within the neutrino sector are fulfilled. In the case of two $\mathbf{24}$-plets, lepton flavor violation constraints can be satisfied much more easily. After specifying the corresponding regions in the minimal supergravity parameter space, we show that under favorable conditions one can test the corresponding flavor structures in the leptonic sector at the LHC. For this we perform Monte Carlo studies for the signals, also taking into account the supersymmetry background. We find that it is only of minor importance for the scenarios studied here.

Figure 1

$\mathrm{BR}(\mu \to e\gamma )$ versus the seesaw scale for the two (dashed) and the three (solid) $\mathbf{24}$-plet scenarios. The mSUGRA parameters of Eq. (23) have been used, neutrino data was fixed to the current experimental values, including ${sin}^2{\theta }_{13}=0.026$.

Figure 2

$\mathrm{BR}(\mu \to e\gamma )$ (blue/black line), $\mathrm{BR}(\tau \to e\gamma )$ (red/dark gray line) and $\mathrm{BR}(\tau \to \mu \gamma )$ (yellow/light gray line) over the reactor angle ${\theta }_{13}$ for real parameters with Dirac phases $\delta =0$ (upper left), $\delta =\pi$ (upper right) and $\delta =3\pi /4$ (lower panel). We set $M_W={10}^{14}·{\mathbb{1}}_3$ and the SUSY parameters as in Eq. (23). The dashed line indicates the current best-fit value for ${\theta }_{13}$.

Figure 3

$\mathrm{BR}(\mu \to e\gamma )$ (blue/black line), $\mathrm{BR}(\tau \to e\gamma )$ (red/dark gray line) and $\mathrm{BR}(\tau \to \mu \gamma )$ (yellow/light gray line) as functions of ${\widehat{M}}_3$ with ${\theta }_{13}$ at the current best-fit value. We have taken $\delta =\pi$, ${\widehat{M}}_1={\widehat{M}}_2={10}^{14}\mathrm{GeV}$ and the other parameters as in Eq. (23).

Figure 4

$\mathrm{BR}(\mu \to e\gamma )$ (blue/black line), $\mathrm{BR}(\tau \to e\gamma )$ (red/dark gray line) and $\mathrm{BR}(\tau \to \mu \gamma )$ (yellow/light gray line) as functions of ${sin}^2{\theta }_{13}$ in the two-generation model for $\delta =\pi$, ${\widehat{M}}_1={\widehat{M}}_2={10}^{14}\mathrm{GeV}$ (solid lines) and ${\widehat{M}}_1=2\times {10}^{14}\mathrm{GeV}$, ${\widehat{M}}_2={10}^{14}\mathrm{GeV}$ (dashed lines). The other parameters are as in Eq. (23).

Figure 5

$\mathrm{BR}(\mu \to e\gamma )$ (blue/black line), $\mathrm{BR}(\tau \to e\gamma )$ (red/dark gray line) and $\mathrm{BR}(\tau \to \mu \gamma )$ (yellow/light gray line) as functions of $\sin \varphi$ for two $\mathbf{24}$-plets with masses ${\widehat{M}}_1=5\times {10}^{14}\mathrm{GeV}$ and ${\widehat{M}}_2=5\times {10}^{13}\mathrm{GeV}$ on the left panel (right panel—vice versa, ${\widehat{M}}_1>{\widehat{M}}_2$), $\delta =0$ and the SUSY parameters as in Eq. (23).

Figure 6

Comparison of the two-body decays $l_i\to l_j\gamma$ (left panel) and the three-body decays $l_i\to 3l_j$ (right panel) for variation of $\sin ({\varphi }_1)$ at normal neutrino mass hierarchy, Dirac phase $\delta =0$ and a $\mathbf{24}$-plet hierarchy: ${\widehat{M}}_1={10}^{15}\mathrm{GeV}$, ${\widehat{M}}_2={10}^{14}\mathrm{GeV}$ and ${\widehat{M}}_3={10}^{13}\mathrm{GeV}$; $l_i$, $l_j=\mu$, $e$ (blue/black line); $\tau$, $e$ (red/dark gray line); $\tau$, $\mu$ (yellow/light gray line).

Figure 7

$\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0{l}_i{l}_j)$ and selected masses as a function of $M_{1/2}$ for $m_0=250\mathrm{GeV}$, $A_0=0$, $\tan \beta =10$ and $\mu >0$. Left plot: $\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\mu e)$ (blue/black line), $\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau e)$ (red/dark gray line) and $\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau \mu )$ (yellow/light gray line); right plot: ${\tilde{\chi }}_2^0$ (orange/upper gray line), ${\tilde{\chi }}_1^0$ (red/lower gray line), ${\tilde{l}}_{1,2,3}$ (blue/gray dotted line) and ${\tilde{l}}_{4,5,6}$ (green/light gray dotted line). The neutrino parameters are at tribimaximal values, normal neutrino mass hierarchy and $R=\mathbb{1}$; $M_W$ is varied to fit $\mathrm{BR}(\mu \to e\gamma )$ close to the experimental bound.

Figure 8

$\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\mu e)$ (blue/black line), $\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau e)$ (red/dark gray line) and $\mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau \mu )$ (yellow/light gray line) in the two-generation model as functions of $A_0$ for $m_0=250\mathrm{GeV}$, $M_{1/2}=1800\mathrm{GeV}$, $\tan \beta =10$ and $\mu >0$. The seesaw parameters are fixed as explained in the text.

Figure 9

Grid calculation of $\sigma ({\tilde{\chi }}_2^0)\times \mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\mu e)$ (blue/black line), $\sigma ({\tilde{\chi }}_2^0)\times \mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau e)$ (red/dark gray line) and $\sigma ({\tilde{\chi }}_2^0)\times \mathrm{BR}({\tilde{\chi }}_2^0\to {\tilde{\chi }}_1^0\tau \mu )$ (yellow/light gray line) in femtobarn over $M_{1/2}$ for different values of $m_0$; $A_0=0$, $\tan \beta =10$ and $\mu >0$. The seesaw parameters are fixed as explained in the text.

Figure 10

Invariant mass distributions for the signal and SUSY background for final states containing $\mu$, $e$ (left plot) or $\tau$, $\mu$ (right plot), missing transverse energy and at least two jets in the final state for a luminosity of $300{\mathrm{fb}}^{-1}$, $m_0=50\mathrm{GeV}$, $M_{1/2}=1484\mathrm{GeV}$, $A_0=0$, $\tan \beta =10$ and $\mu >0$.