Physics Implications of Flat Directions in Free Fermionic Superstring Models I: Mass Spectrum and Couplings

TL;DR

This work systematically analyzes D- and F-flat directions in a quasi-realistic CHL5 free-fermionic string model, focusing on directions built from non-Abelian singlets that leave an extra $U(1)'$ unbroken at the string scale. The authors classify flat directions, prove F-flatness to all orders for a subset, and compute the full mass spectrum and effective trilinear couplings in the observable sector, highlighting how string selection rules constrain couplings and often yield a large spectrum of exotics. Two representative flat directions, $P_1'P_2'P_3'$ and $P_2P_3|_F$, illustrate the emergence of MSSM-like fields alongside exotics, the appearance of lepton- and baryon-number violating couplings, a non-canonical $ ext{mu}$-term, and the possibility of $U(1)'$ breaking at either the electroweak or an intermediate scale, depending on the direction. The study provides a controlled top-down framework to assess $Z'$ phenomenology, fermion textures, and proton- and neutron-number violation within string-inspired models, while also noting challenges posed by light exotics and the lack of a canonical $ ext{mu}$-term; future work will address soft SUSY-breaking effects and more realistic symmetry-breaking patterns.

Abstract

From the "top-down" approach we investigate physics implications of the class of D- and F- flat directions formed from non-Abelian singlets which are proven flat to all orders in the nonrenormalizable superpotential, for a prototype quasi-realistic free fermionic string model with the standard model gauge group and three families (CHL5). These flat directions have at least an additional U(1)' unbroken at the string scale. For each flat direction, the complete set of effective mass terms and effective trilinear superpotential terms in the observable sector are computed to all orders in the VEV's of the fields in the flat direction. The "string selection-rules" disallow a large number of couplings allowed by gauge invariance, resulting in a massless spectrum with a large number of exotics, in most cases excluded by experiment, thus signifying a generic flaw of these models. Nevertheless, the resulting trilinear couplings of the massless spectrum possess a number of interesting features which we analyse for two representative flat directions: for the fermion texture; baryon- and lepton-number violating couplings; R-parity breaking; non-canonical mu terms; and the possibility of electroweak and intermediate scale symmetry breaking scenarios for U(1)'. The gauge coupling predictions are obtained in the electroweak scale case. Fermion masses possess t-b and tau-mu universality, with the string scale Yukawa couplings g and $g/\sqrt{2}$, respectively. Fermion textures are present for certain flat directions, but only in the down-quark sector. Baryon- and lepton- number violating couplings can trigger proton-decay, $N-{\bar N}$ oscillations, leptoquark interactions and R-parity violation, leading to the absence of a stable LSP.

Figures (1)

• Figure 3: Proton decay diagrams for (a) $\langle h_b^0 \rangle \ne 0$, (b) $\langle h_b^0 \rangle = 0$. $u_{b}^{'}$, $d_{c}$ are the conjugates of $u_{b}^{c'}$, $d_{c}^c$.