Implications of Abelian extended gauge structures from string models

Within a class of superstring vacua which have an additional nonanomalous U(1)′ gauge factor, we address the scale of the U(1)′ symmetry breaking and constraints on the exotic particle content and their masses. We also show that an extra gauge U(1)′ provides a new mechanism for generating a naturally small effective $\mu$ term. In general, existing models are not consistent with all phenomenological constraints; however, they do provide a testing ground to address the above issues, yielding a set of concrete scenarios. Under the assumptions that the spontaneous U(1)′ breaking takes place in the observable sector and that the supersymmetry-breaking scalar mass square terms are positive at the string scale, the breaking of U(1)′ symmetry is radiative. It can take place when the appropriate Yukawa couplings of exotic particles are of order 1, which occurs for $Z_2\times Z_2$ fermionic orbifold constructions at symmetric points of moduli space. The $Z^{\prime }$ mass is either of $O\left(M_Z\right)$, when the symmetry breaking is due to a single standard model singlet, or of a scale intermediate between the string and electroweak scales, determined by the radiative corrections (or by competing nonrenormalizable operators), when the breaking is due to two or more mirrorlike singlets. In the former case, the $\frac{M_{Z^{\prime }}}{M_Z}$ hierarchy achievable without excessive fine-tuning is within future experimental reach.