Big-bang nucleosynthesis and leptogenesis in the CMSSM

We have studied the constrained minimal supersymmetric standard model with three right-handed neutrinos, and investigated whether there still is a parameter region consistent with all experimental data/limits such as the baryon asymmetry of the Universe, the dark matter abundance and the lithium primordial abundance. Using Casas-Ibarra parametrization, we have found a very narrow parameter space of the complex orthogonal matrix elements where the lightest slepton can have a long lifetime, which is necessary for solving the lithium problem. We have studied three cases of the right-handed neutrino mass ratio (i) $M_2=2\times M_1$, (ii) $M_2=4\times M_1$, (iii) $M_2=10\times M_1$, while $M_3=40\times M_1$ is fixed. We have obtained the mass range of the lightest right-handed neutrino that lies between $10^9$ and $10^{11}\mathrm{GeV}$. The important result is that its upper limit is derived by solving the lithium problem and the lower limit comes from leptogenesis. Lepton flavor violating decays such as $\mu \to e\gamma$ in our scenario are in the reach of MEG-II and Mu3e.

Figure 1

Evolutions of $|Y_{B-L}|$ and each lepton asymmetry $|Y_{{\mathrm{\Delta }}_i}|$ for a typical parameter in this paper. Horizontal band (gray) corresponds to the observed baryon asymmetry. $|Y_{B-L}^{\text{non}\text{−}\mathrm{f}}|$ shows the lepton asymmetry in the absence of flavor effect.

Figure 2

The lightest slepton lifetime as a function of $x_{23}$. The blue and green band corresponds to the lifetime required to solve the ${}^7\mathrm{Li}$ problem only and both the ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ problems, respectively.

Figure 3

The slepton lifetime in terms of $x_{12}$, $x_{13}$, $x_{23}$ in case 2. In the left and right panel, $M_1$ is taken to $1.2\times {10}^{11}\mathrm{GeV}$ and $3.0\times {10}^{10}\mathrm{GeV}$, respectively.

Figure 4

$\mathrm{BR}(\mu \to e\gamma )$, $\mathrm{BR}(\mu \to 3e)$, $\mathrm{BR}(\tau \to \mu \gamma )$, and $\mathrm{BR}(\tau \to 3\mu )$ as a function of $M_1$ for $M_2=2\times M_1$, $4\times M_1$, and $10\times M_1$. The ${}^7\mathrm{Li}$ problem is solved with parameters in each line, while both the ${}^7\mathrm{Li}$ and ${}^6\mathrm{Li}$ problems are solved only for thick part. Gray region is excluded by MEG experiment, and the horizontal lines show future sensitivity.