Light sterile neutrinos, dark matter, and new resonances in a $U(1)$ extension of the MSSM

We present $psi$MSSM, a model based on a $U(1)_{psi}$ extension of the minimal supersymmetric standard model. The gauge symmetry $U(1)_{psi}$, also known as $U(1)_N$, is a linear combination of the $U(1)_chi$ and $U(1)_psi$ subgroups of $E_6$. The model predicts the existence of three sterile neutrinos with masses $lesssim 0.1~{rm eV}$, if the $U(1)_{psi}$ breaking scale is of order 10 TeV. Their contribution to the effective number of neutrinos at nucleosynthesis is $Delta N_{ u}simeq 0.29$. The model can provide a variety of possible cold dark matter candidates including the lightest sterile sneutrino. If the $U(1)_{psi}$ breaking scale is increased to $10^3~{rm TeV}$, the sterile neutrinos, which are stable on account of a $Z_2$ symmetry, become viable warm dark matter candidates. The observed value of the standard model Higgs boson mass can be obtained with relatively light stop quarks thanks to the D-term contribution from $U(1)_{psi}$. The model predicts diquark and diphoton resonances which may be found at an updated LHC. The well-known $mu$ problem is resolved and the observed baryon asymmetry of the universe can be generated via leptogenesis. The breaking of $U(1)_{psi}$ produces superconducting strings that may be present in our galaxy. A $U(1)$ R symmetry plays a key role in keeping the proton stable and providing the light sterile neutrinos.