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Bajc-Melfo Vacua enable YUMGUTs

Bajc-Melfo(\textbf{BM}) two field ($S,ϕ$) superpotentials define metastable F-term supersymmetry breaking vacua suitable as hidden sectors for calculable and realistic family and Grand Unification unification models. The undetermined vev $<S_s>$ of the Polonyi field that breaks Supersymmetry can be fixed either by coupling to N=1 Supergravity or by radiative corrections. \textbf{BM} hidden sectors extend to symmetric multiplets $(S,ϕ)_{ab}$ of a gauged $O(N_g)$ family symmetry, broken at the GUT scale, so that the $O(N_g)$ charged component vevs $<\hat S_{ab}>$ 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 Ultra Minimal 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 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 $\hat S_{ab}$ 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 the fields $S_{ab}$ call for detailed investigation of loop effects due to the Yukawa and gauge interactions in the hidden sector and of post-inflationary field relaxation dynamics.