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Dark matter and neutrino masses in the R-parity violating NMSSM

The R-Parity symmetry Violating (RPV) version of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) is attractive simultaneously with regard to the so-called mu-problem and the accommodation of three-flavor neutrino data at tree level. In this context, we show here that if the Lightest Supersymmetric Particle (LSP) is the gravitino, it possesses a lifetime larger than the age of the universe since its RPV induced decay channels are suppressed by the weak gravitational strength. This conclusion holds if one considers gravitino masses ~ 10^2 GeV like in supergravity scenarios, and is robust if the lightest pseudoscalar Higgs field is as light as ~ 10 GeV [as may occur in the NMSSM]. For these models predicting in particular an RPV neutrino-photino mixing, the gravitino lifetime exceeds the age of the universe by two orders of magnitude. However, we find that the gravitino cannot constitute a viable dark matter candidate since its too large RPV decay widths would then conflict with the flux data of last indirect detection experiments. The cases of a sneutrino LSP or a neutralino LSP as well as the more promising gauge-mediated supersymmetry breaking scenario are also discussed. Both the one-flavor simplification hypothesis and the realistic scenario of three neutrino flavors are analyzed. We have modified the NMHDECAY program to extend the neutralino mass matrix to the present framework.