Physics implications of flat directions in free fermionic superstring models. I. Mass spectrum and couplings

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 proved 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 ${U(1)}^{\ensuremath{'}}$ 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 analyze for two representative flat directions: for the fermion texture, baryon- and lepton-number violating couplings, R-parity breaking, non-canonical $\ensuremath{\mu}$ terms, and the possibility of electroweak and intermediate scale symmetry breaking scenarios for ${U(1)}^{\ensuremath{'}}.$ The gauge coupling predictions are obtained in the electroweak scale case. Fermion masses possess $t\ensuremath{-}b$ and $\ensuremath{\tau}\ensuremath{-}\ensuremath{\mu}$ 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, $N\ensuremath{-}\overline{N}$ oscillations, leptoquark interactions and R-parity violation, leading to the absence of a stable LSP.