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In previous work, we presented a statistical scan over the soft supersymmetrybreaking parameters of the minimal SUSY $B-L$ model. For specificity ofcalculation, unification of the gauge parameters was enforced by allowing thetwo ${\mathbb Z}_{3}\times {\mathbb Z}_{3}$ Wilson lines to have mass scalesseparated by approximately an order of magnitude. This introduced an additional"left-right" sector below the unification scale. In this paper, for threeimportant reasons, we modify our previous analysis by demanding that the massscales of the two Wilson lines be simultaneous and equal to an "averageunification" mass $\left<M_{U}\right>$. The present analysis is 1) more"natural" than the previous calculations, which were only valid in a veryspecific region of the Calabi-Yau moduli space, 2) the theory is conceptuallysimpler in that the left-right sector has been removed and 3) in the presentanalysis the lack of gauge unification is due to thresholdeffects--particularly heavy string thresholds, which we calculate statisticallyin detail. As in our previous work, the theory is renormalization group evolvedfrom $\left<M_{U}\right>$ to the electroweak scale--being subjected,sequentially, to the requirement of radiative $B-L$ and electroweak symmetrybreaking, the present experimental lower bounds on the $B-L$ vector boson andsparticle masses, as well as the lightest neutral Higgs mass of $\sim$125 GeV.The subspace of soft supersymmetry breaking masses that satisfies all suchconstraints is presented and shown to be substantial.

The Minimal SUSY $B-L$ Model: Simultaneous Wilson Lines and String Thresholds