Implications of Abelian Extended Gauge Structures From String Models

TL;DR

This work analyzes a class of string vacua with an extra non-anomalous $U(1)'$, focusing on how radiative $U(1)'$ breaking occurs in the observable sector and the resulting phenomenology of the $Z'$ boson and associated exotics. It shows that breaking is driven by large Yukawa couplings to exotic states and yields either $M_{Z'}$ near the electroweak scale or at an intermediate scale, with the former offering potential collider tests. A key contribution is the identification of scenarios where an EW-scale $Z'$ mass is achieved with modest tuning, and where the same framework generates a natural, radiatively induced effective $oldsymbol{q}$ term via a SM-singlet VEV. The results underscore how string-derived Abelian extensions can yield concrete, testable predictions for new gauge bosons and exotic matter while addressing the $q$-problem in the MSSM context.

Abstract

Within a class of superstring vacua which have an additional non-anomalous $U(1)'$ 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 $μ$ 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 one, which occurs for $Z_2\times Z_2$ fermionic orbifold constructions at symmetric points of moduli space. The $Z'$ mass is either of ${\cal O}(M_Z)$, when the symmetry breaking is due to a single standard model singlet, or is of a scale intermediate between the string and electro-weak scales, determined by the radiative corrections (or by competing non-renormalizable operators), when the breaking is due to two or more mirror-like singlets. In the former case, the $M_{Z'}/M_Z$ hierarchy achievable without excessive fine tuning is within future experimental reach.