The fact that neutrinos are massive suggests that the minimal supersymmetric standard model (MSSM) might be extended in order to include three gauge-singlet neutrino superfields with Yukawa couplings of the type H 2 L ν c . We propose to use these superfields to solve the µ problem of the MSSM without having to introduce an extra singlet superfield as in the case of the next-to-MSSM (NMSSM). In particular, terms of the type ν c H 1 H 2 in the superpotential may carry out this task spontaneously through sneutrino vacuum expectation values. In addition, terms of the type (ν c ) 3 avoid the presence of axions and generate effective Majorana masses for neutrinos at the electroweak scale. On the other hand, these terms break lepton number and R-parity explicitly implying that the phenomenology of this model is very different from the one of the MSSM or NMSSM. For example, the usual neutralinos are now mixed with the neutrinos. For Dirac masses of the latter of order 10 −4 GeV, eigenvalues reproducing the correct scale of neutrino masses are obtained.

Abstract:The µνSSM is a supersymmetric standard model that solves the µ problem of the MSSM using the R-parity breaking couplings between the right-handed neutrino superfields and the Higgses in the superpotential, λ iν c iĤ dĤu . The µ term is generated spontaneously through sneutrino vacuum expectation values, µ = λ i ν c i , once the electroweak symmetry is broken. In addition, the couplings κ ijkν c iν c jν c k forbid a global U(1) symmetry avoiding the existence of a Goldstone boson, and also contribute to spontaneously generate Majorana masses for neutrinos at the electroweak scale. Following this proposal, we have analysed in detail the parameter space of the µνSSM. In particular, we have studied viable regions avoiding false minima and tachyons, as well as fulfilling the Landau pole constraint. We have also computed the associated spectrum, paying special attention to the mass of the lightest Higgs. The presence of right and left-handed sneutrino vacuum expectation values leads to a peculiar structure for the mass matrices. The most important consequence is that neutralinos are mixed with neutrinos, and neutral Higgses with sneutrinos.

We analyse the direct detection of neutralino dark matter in the framework of the Next-to-Minimal Supersymmetric Standard Model. After performing a detailed analysis of the parameter space, taking into account all the available constraints from LEPII, we compute the neutralino-nucleon cross section, and compare the results with the sensitivity of detectors. We find that sizable values for the detection cross section, within the reach of dark matter detectors, are attainable in this framework. For example, neutralino-proton cross sections compatible with the sensitivity of present experiments can be obtained due to the exchange of very light Higgses with m h 0 1 < ∼ 70 GeV. Such Higgses have a significant singlet composition, thus escaping detection and being in agreement with accelerator data. The lightest neutralino in these cases exhibits a large singlino-Higgsino composition, and a mass in the range 50 < ∼ mχ0 1 < ∼ 100 GeV. PACS: 12.60.Jv, 95.35.+d

The µνSSM provides a solution to the µ-problem of the MSSM and explains the origin of neutrino masses by simply using right-handed neutrino superfields. Given that R-parity is broken in this model, the gravitino is a natural candidate for dark matter since its lifetime becomes much longer than the age of the Universe. We consider the implications of gravitino dark matter in the µνSSM, analyzing in particular the prospects for detecting gamma rays from decaying gravitinos. If the gravitino explains the whole dark matter component, a gravitino mass larger than 20 GeV is disfavored by the isotropic diffuse photon background measurements. On the other hand, a gravitino with a mass range between 0.1 − 20 GeV gives rise to a signal that might be observed by the FERMI satellite. In this way important regions of the parameter space of the µνSSM can be checked.

We analyze relevant signals expected at the LHC for a left sneutrino as the lightest supersymmetric particle (LSP). The discussion is carried out in the 'µ from ν' supersymmetric standard model (µνSSM), where the presence of R-parity breaking couplings involving right-handed neutrinos solves the µ problem and reproduces neutrino data. The sneutrinos are pair produced via a virtual W , Z or γ in the s channel. From the prompt decay of a pair of left sneutrinos LSPs of any family, a significant diphoton signal plus missing transverse energy (MET) from neutrinos can be present in the mass range 118-132 GeV, with 13 TeV center-of-mass energy and an integrated luminosity of 100 fb −1 . In addition, in the case of a pair of tau left sneutrinos LSPs, given the large value of the tau Yukawa coupling diphoton plus leptons and/or multileptons can appear. We find that the number of expected events for the multilepton signal, together with properly adopted search strategies, is sufficient to give a significant evidence for a sneutrino of mass in the range 130-310 GeV, even with the integrated luminosity of 20 fb −1 . In the case of the signal producing diphoton plus leptons, an integrated luminosity of 100 fb −1 is needed to give a significant evidence in the mass range 95-145 GeV. Finally, we discuss briefly the presence of displaced vertices and the associated range of masses.