Physics implications of flat directions in free fermionic superstring models. II. Renormalization group analysis

We continue the investigation of the physics implications of a class of flat directions for a prototype quasi-realistic free fermionic string model (CHL5), building upon the results of a previous paper in which the complete mass spectrum and effective trilinear couplings of the observable sector were calculated to all orders in the superpotential. We introduce soft supersymmetry breaking mass parameters into the model, and investigate the gauge symmetry breaking patterns and the renormalization group analysis for two representative flat directions, which leave an additional ${U\left(1\right)\mathrm{}}^{\prime }$ as well as the SM gauge group unbroken at the string scale. We study symmetry breaking patterns that lead to a phenomenologically acceptable $Z-Z^{\prime }$ hierarchy, $M_{Z^{\prime }}\sim \mathcal{O}\left(1\mathrm{}\hspace{0.5em}\mathrm{TeV}\right)$ and ${10}^{12}\hspace{0.5em}\mathrm{GeV}$ for electroweak and intermediate scale ${U\left(1\right)\mathrm{}}^{\prime }$ symmetry breaking, respectively, and the associated mass spectra after electroweak symmetry breaking. The fermion mass spectrum exhibits unrealistic features, including massless exotic fermions, but has an interesting d-quark hierarchy and associated CKM matrix in one case. There are (some) non-canonical effective $\mu$ terms, which lead to a non-minimal Higgs sector with more than two Higgs doublets involved in the symmetry breaking, and a rich structure of Higgs particles, charginos, and neutralinos, some of which, however, are massless or ultralight. In the electroweak scale cases the scale of supersymmetry breaking is set by the $Z^{\prime }$ mass, with the sparticle masses in the several TeV range.