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

We consider MSSM with right-chiral neutrino superfields with Majorana masses, where the lightest right-handed sneutrino dominated scalars constitutes non-thermal 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 $\mathit{\text{freeze-in}}$. In addition, big-bang Nucleosynthesis and $\mathit{\text{freeze-out}}$ 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 $\mathrm{\Delta }L=2$ 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.