Searching singlet extensions of the supersymmetric standard model in Z 6−II orbifold compactification of heterotic string

Abstract

We search for supersymmetric standard model realizations with extra singlets and extra U (1) using the heterotic string compactification on the Z6−II orbifold with two Wilson lines. The effective superpotential produced through the vacuum restabilization mechanism is examined for three representative Pati-Salam string models obtained in the literature. An automated selection of semirealistic vacua along flat directions in the non-Abelian singlet modes field space is performed by requiring the presence of massless pairs of electroweak Higgs bosons having trilinear superpotential couplings with massless singlet modes and the decoupling of color triplet exotic modes needed to suppress B and L number violating processes. PACS numbers: 12.60.-i,12.60.Jv I. INTRODUCTIONModel building with the heterotic string [1-9] has received a vigorous stimulus thanks to the recent focus [10-26] on anisotropic compactifications on the orbifold Z 6−II . Recent reviews are given in [27,28]. Satisfactory representative vacuum solutions are also reported for the Z 12−I orbifold [29][30][31][32][33]. The exploration of the vast moduli space of the Z 6−II orbifold with two authorized Wilson lines [17,20] was found to give access to a fertile mini-landscape of vacua for minimal supersymmetric standard models descending from 5-d or 6-d grand unified theories. Sampling the still wider space of solutions with three Wilson lines [34] leads to equally hopeful conclusions.One characteristic feature of these top-down constructions is the profusion of U (1) gauge factors which remain after the first gauge symmetry breaking from the orbifold gauge twist and the presence of Wilson lines. One of them is anomalous, creating a one-loop Fayet-Iliopoulos D-term a bit below the string scale that needs to be cancelled. This step usually leaves a lot of freedom due to the large vacuum degeneracy. In the vacuum restabilisation process, the U (1) gauge symmetries will get broken and most of the extra modes beyond the MSSM (minimal supersymmetric standard model) matter content, but hopefully not all of them, will decouple with large masses. Except for searches of extensions including right-handed neutrino supermultiplets [35,36], most studies have restricted to solutions in which the whole set of Standard Model singlet modes acquire large masses and decouple from the low energy field theory. It is natural, however, to ask whether the large moduli space of these compactifications does not include regions where extra singlets and extra U (1) symmetries might realize the NMSSM (next-to-minimal supersymmetric standard model) or one of the related versions proposed in the literature [37][38][39][40][41][42] and analyzed over the years in phenomenological [43][44][45][46][47][48] and formal [49][50][51][52][53] studies. (After completion of the present work, there appeared a study of NMSSM realizations complying with the severe selection criteria of [17,20] which reports that solutions exist only in the case with three Wilson lines [54].)Filling this gap is the purp...