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 $\Delta N_{\nu}\simeq 0.29$. 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.
