$D$-term spectroscopy in realistic heterotic-string models

The recent emergence of free fermionic heterotic string models with solely the MSSM charged spectrum below the string scale reinforces the motivation to investigate the pheneomelogical characteristics of this class of string models, which possess an underlying $Z_2\times Z_2$ orbifold structure. An important property of the $Z_2\times Z_2$ orbifold is the cyclic permutation symmetry between the three twisted sectors. If preserved in the three-generation models the cyclic permutation symmetry results in a family universal anomalous $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_A,$ which is instrumental in explaining squark degeneracy, provided that the dominant component of supersymmetry breaking arises from the $\mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_A$ D term. Interestingly, the contribution of the family-universal $D_A$ term to the squark masses may be intrafamily nonuniversal, and may differ from the usual (universal) boundary conditions assumed in the MSSM. We contemplate how $D_A$-term spectroscopy may be instrumental in studying superstring models irrespective of our ignorance of the details of supersymmetry breaking. We examine the possible effect of the intrafamily nonuniversality on the resulting SUSY spectrum and the values of the strong coupling, effective weak mixing angle, and W-gauge boson mass, up to a two-loop accuracy, in the two models (universal and nonuniversal). We find that nonuniversality relaxes the constraint of color and charge breaking minima which appears in the universal case. In addition, it predicts a 3% smaller value of ${\alpha }_s$ due to different threshold masses obtained in the latter scenario. Finally, we present the experimentally allowed predictions of the two models in an $M_0$ and $M_{1/2}$ parameter space.