Right sneutrino with $\mathrm{\Delta }L=2$ masses as nonthermal dark matter

We consider the minimal supersymmetric standard model (MSSM) with right-chiral neutrino superfields with Majorana masses, where the lightest right-handed sneutrino dominated scalars constitutes nonthermal dark matter (DM). The $\mathrm{\Delta }L=2$ masses are subject to severe constraints coming from freeze-in relic density of such DM candidates as well as from sterile neutrino freeze-in. In addition, big bang nucleosynthesis and freeze-out of the next-to-lightest superparticle shrink the viable parameter space of such a scenario. We examine various $\mathrm{\Delta }L=2$ mass terms for families other than that corresponding to the LSP sneutrino. $\mathrm{\Delta }L=2$ masses are difficult to reconcile with a right-sneutrino DM, unless there is either (a) a hierarchy of about 3 orders of magnitudes among various supersymmetry-breaking mass parameters, or, (b) strong cancellation between the Higgsino mass and the trilinear supersymmetry breaking mass parameter for sneutrinos.

Figure 1

For $m_{\text{susy}}=1\mathrm{TeV}$ the dependence of freeze-in relic density with $\mu$ [subfigure 1], $(m_N{)}_{11}$ [subfigure 1] and $M_N$ [subfigure 1] have been shown. All the Majorana masses have been taken in the keV scale, $A_{\nu }$ is varied in the EW scale and $\tan \beta =10.5$ has been taken. The allowed region in the $\mu -A_{\nu }$ plane for $M_N=10\mathrm{keV}$ is shown in the subfigure 1. This plot also embodies how the allowed region of $\mu -A_{\nu }$ plane shrinks as $M_N$ is increased.

Figure 2

Subfigure 2 shows how the exact cancellation between supersymmetry conserving term $\mu \cot \beta$ and supersymmetry breaking term $A_{\nu }$ leads to correct freeze-in relic density for sneutrino with MeV-GeV scale Majorana masses. Subfigures 2 and 2 show the variation of freeze-in relic density with $(m_N{)}_{11}$ and $M_N$ respectively. For each of the different values of $\mu$, $A_{\nu }$ has been chosen such that Eq. (15) is satisfied and one obtains the maximum possible values of $(m_N{)}_{11}(M_N)$ for that choice of $|A_{\nu }-\mu \cot \beta |$. If one chooses $A_{\nu }$ and $\mu \cot \beta$ to cancel more finely, one will get a larger value of $(m_N{)}_{11}(M_N)$, but the order of magnitude will not change. Subfigure 2 shows the allowed ${\tilde{\tau }}_R$ soft masses $m_{{\tilde{\tau }}_R}$ of ${\tilde{\tau }}_1$ NLSP such that its lifetime is $\le 100\sec$. All the parameters $(A_{\tau },\mu ,\tan \beta ,{\theta }_{\tilde{\nu }}\approx {\mathrm{\Theta }}_{\tilde{\nu }13})$ that contributes to ${\tilde{\tau }}_1$ lifetime, are quoted in the figure. We have assumed $\tan \beta =10.5$ in all the cases.

Figure 3

Subfigure 3 show the variation of relic density a with increase in $m_{\text{susy}}$ for $A_{\nu }$,$\mu$,$(m_N{)}_{11}$, and $M_N^H$ around the electroweak scale. In order to generate correct SM like Higgs mass and satisfy all the constraints of EWSB $\tan \beta =3.5$ have been taken. Subfigure 3 depicts how the allowed region of $\mu -A_{\nu }$ plane have been extended due to such increase in SUSY-breaking masses i.e., $m_{\text{susy}}$. The subfigure 3 and 3 plots of the lower panel show the variation of freeze-in relic density with $(m_N{)}_{11}$ and $M_N^H$ respectively.