Right-handed sneutrino and gravitino multicomponent dark matter in light of neutrino detectors

We investigate the possibility that right-handed (RH) sneutrinos and gravitinos can coexist and explain the dark matter (DM) problem. We compare extensions of the minimal supersymmetric standard model (MSSM) and the next-to-MSSM (NMSSM) adding RH neutrinos superfields, with special emphasis on the latter. If the gravitino is the lightest supersymmetric particle (LSP) and the RH sneutrino the next-to-LSP (NLSP), the heavier particle decays to the former plus left-handed (LH) neutrinos through the mixing between the scalar partners of the LH and RH neutrinos. However, the interaction is suppressed by the Planck mass, and if the LH-RH sneutrino mixing parameter is small, $\ll O(10^{-2})$, a long-lived RH sneutrino NLSP is possible even surpassing the age of the Universe. As a byproduct, the NLSP to LSP decay produces monochromatic neutrinos in the ballpark of current and planned neutrino telescopes like Super-Kamiokande, IceCube and Antares that we use to set constraints and show prospects of detection. In the NMSSM+RHN, assuming a gluino mass parameter $M_3 = 3$ TeV we found the following lower limits for the gravitino mass $m_{3/2} \gtrsim 1-600$ GeV and the reheating temperature $T_R \gtrsim 10^5 - 3 \times 10^7$ GeV, for $m_{\tilde{\nu}_R} \sim 10-800$ GeV. If we take $M_3=10$ TeV, then the limits on $T_R$ are relaxed by one order of magnitude.