  The matter spectrum of the MSSM, including three right-handed neutrino
supermultiplets and one pair of Higgs-Higgs conjugate superfields, can be
obtained by compactifying the E_{8} x E_{8} heterotic string and M-theory on
Calabi-Yau manifolds with specific SU(4) vector bundles. These theories have
the standard model gauge group augmented by an additional gauged U(1)_{B-L}.
Their minimal content requires that the B-L gauge symmetry be spontaneously
broken by a vacuum expectation value of at least one right-handed sneutrino. In
previous papers, we presented the results of a quasi-analytic renormalization
group analysis showing that B-L gauge symmetry is indeed radiatively broken
with an appropriate B-L/electroweak hierarchy. In this paper, we extend these
results by 1) enlarging the initial parameter space and 2) explicitly
calculating all renormalization group equations numerically, without
approximation. The regions of the initial parameter space leading to realistic
vacua are presented and the B-L/electroweak hierarchy computed over these
regimes. At representative points, the mass spectrum for all sparticles and
Higgs fields is calculated and shown to be consistent with present experimental
bounds. Some fundamental phenomenological signatures of a non-zero right-handed
sneutrino expectation value are discussed, particularly the cosmology and
proton lifetime arising from induced lepton and baryon number violating
interactions.
