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We present a locally supersymmetric extension of the minimal supersymmetricStandard Model (MSSM) based on the gauge group $SU(3)_C\times SU(2)_L\timesU(1)_Y\times U(1)^\prime$ where, except for the supersymmetry breaking scalewhich is fixed to be $\sim 10^{11}$ GeV, we require that all non-Standard-Modelparameters allowed by the {\it local} spacetime and gauge symmetries assumetheir natural values. The $U(1)^\prime$ symmetry, which is spontaneously brokenat the intermediate scale, serves to ({\it i}) explain the weak scalemagnitudes of $\mu$ and $b_\mu$ terms, ({\it ii}) ensure that dimension-3 anddimension-4 baryon-number-violating superpotential operators are forbidden,solving the proton-lifetime problem, ({\it iii}) predict {\it bilinear leptonnumber violation} in the superpotential at just the right level to accommodatethe observed mass and mixing pattern of active neutrinos (leading to a novelconnection between the SUSY breaking scale and neutrino masses), whilecorresponding trilinear operators are strongly supppressed. The phenomenologyis like that of the MSSM with bilinear R-parity violation, were the would-belightest supersymmetric particle decays leptonically with a lifetime of $\sim10^{-12}-10^{-8}$ s. Theoretical consistency of our model requires theexistence of multi-TeV, stable, colour-triplet, weak-isosinglet scalars orfermions, with either conventional or exotic electric charge which should bereadily detectable if they are within the kinematic reach of a hadron collider.Null results of searches for heavy exotic isotopes implies that the re-heatingtemperature of our Universe must have been below their mass scale which, inturn, suggests that sphalerons play a key role for baryogensis. Finally, thedark matter cannot be the weakly interacting neutralino.

Addressing \mu-b_\mu and proton lifetime problems and active neutrino masses in a U(1)^\prime-extended supergravity model