Abstract
Bajc-Melfo ($\mathbf{BM}$) two-field ($S,\ensuremath{\phi}$) superpotentials define metastable F-term supersymmetry-breaking vacua suitable as hidden sectors for calculable and realistic family and grand unification models. The undetermined vacuum expectation value (VEV) $⟨{S}_{s}⟩$ of the Polonyi field that breaks supersymmetry can be fixed either by coupling to $N=1$ supergravity or by radiative corrections. $\mathbf{BM}$ hidden sectors extend to symmetric multiplets $(S,\ensuremath{\phi}{)}_{ab}$ of a gauged $O({N}_{g})$ family symmetry, broken at the GUT scale, so that the $O({N}_{g})$ charged component VEVs $⟨{\stackrel{^}{S}}_{ab}⟩$ are also undetermined before accounting for the $O({N}_{g})$ D-terms, which fix them by cancellation against D-term contributions from the visible sector. This facilitates Yukawon ultraminimal GUTs (YUMGUTs) proposed in [C. S. Aulakh and C. K. Khosa, Phys. Rev. D 90, 045008 (2014)] by relieving the visible sector from the need to give null D-terms for the family symmetry $O({N}_{g})$. We analyze symmetry breaking and spectra of the hidden-sector fields in the supergravity resolved case when ${N}_{g}=1,2,3$. Besides the Polonyi field ${S}_{s}$, most of the superfields ${\stackrel{^}{S}}_{ab}$ remain light, with fermions getting masses only from loop corrections. Such modes may yield novel dark matter lighter than 100 GeV. Possible Polonyi and moduli problems associated with the fields ${S}_{ab}$ call for detailed investigation of loop effects due to the Yukawa and gauge interactions in the hidden sector and of postinflationary field relaxation dynamics.
Highlights
Supersymmetry (SUSY) imposes remarkable restrictions on its own spontaneous violation and severely constrains models of physics beyond the standard model
[1,2,3,4,5] gravity mediation has been used to generate phenomenologically acceptable soft SUSYbreaking terms for globally supersymmetric GUTs. This requires supersymmetry breaking in a hidden sector with no superpotential couplings to the “visible” sector in which we live
The vacuum in the gravity mediated scenario is defined as the perturbation of a global SUSY-preserving minimum by a hidden sector with a global minimum which breaks supersymmetry spontaneously due to specialized superpotentials (Polonyi, O’Raifeartaigh [6,7], etc.) or due to strong dynamics
Summary
Supersymmetry (SUSY) imposes remarkable restrictions on its own spontaneous violation and severely constrains models of physics beyond the standard model. Minimal supersymmetric (MS) SOð10Þ GUTs [16,17,18,19,20,21,22,23] have been shown to be completely realistic and even to suppress d 1⁄4 5 proton decay [24,25] by a novel and generic mechanism based on the necessary emergence of a pair of light doublet Higgs in the effective MSSM Motivated by these two clues, we exploited the defining (i.e. 126) representation of MSGUTs (which gets large VEVs yet couples to matter fermions) to design a renormalizable Grand Unified Yukawon/ familion model [26] in which we generate hierarchical matter fermion Yukawas from flavor-bland parameters of the MSGUT extended by an OðNgÞ family symmetry. We will return to a study of cosmological constraints and alternative models elsewhere
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