The New Minimal Supersymmetric GUT : Spectra, RG analysis and Fermion Fits

arXiv:0807.0917v3 [hep-ph] 3 Jan 2012 The New Minimal Supersymmetric GUT : Spectra, RG analysis and Fermion Fits Charanjit S. Aulakha and Sumit K. Gargb a Dept. of Physics, Panjab University, Chandigarh, India bCenter for High Energy Physics, IISc, Bangalore, India The supersymmetric SO(10) GUT based on the 210 ⊕10 ⊕120 ⊕126 ⊕126 Higgs system provides a minimal framework for the emergence of the R-parity exact MSSM at low energies and a viable supersymmetric seesaw explanation for the observed neu- trino masses and mixing angles. We present formulae for MSSM decomposition of the superpotential invariants, tree level light charged fermion effective Yukawa cou- plings, Weinberg neutrino mass generation operator, and the d = 5, ∆B = ∆L ̸= 0 effective superpotential in terms of GUT parameters. We use them to determine fits of the 18 available fermion mass-mixing data in terms of the superpotential pa- rameters of the NMSGUT and SUGRY(NUHM) type soft supersymmetry breaking parameters ({m ˜f, m1/2, A0, M2 H, ¯ H}) specified at the MSSM one loop unification scale M0 X = 1016.33 GeV. Our fits are compatible with electroweak symmetry breaking and Unification constraints and yield right-handed neutrino masses in the leptogenesis rel- evant range : 108 −1013 GeV. Matching the SM data requires lowering the strange and down quark Yukawas in the MSSM via large tan β driven threshold corrections and characteristic soft Susy breaking spectra. The Susy spectra have light pure Bino LSP, heavy exotic Higgs(inos) and large µ, A0, MH, ¯ H parameters ∼100 TeV. Typi- cally third generation sfermions are much heavier than the first two generations. The smuon is often the lightest charged sfermion thus offering a Bino-CDM co-annihilation channel. The parameter sets obtained are used to calculate B violation rates which are found to be generically much faster(∼10−28 yr−1) than the current experimental limits. Improvements which may allow acceptable B violation rates are identified. 1. Introduction The discovery of neutrino mass was both preceded by [1] and itself provoked [2–4, 6–8] inten- sive investigation of unifying models that naturally incorporate supersymmetry and the seesaw mechanisms [9] : in particular models with the left-right gauge group as a part of the gauge symmetry and B −L broken at a high scale and R/M-parity preserved to low energies [1]. The close contiguity of the seesaw scale and the Grand Unified scale pushed SO(10) GUTs, which are the natural GUT home of both Type I and Type II seesaw mechanisms, but were long rele- gated as baroque cousins of the -seemingly- more elegant minimal SU(5) GUT, into centre stage. The understanding that the Susy SO(10) GUT based on the 210 ⊕10 ⊕126 ⊕126 Higgs sys- tem proposed [10,11] long ago was an optimal candidate for the Minimal Supersymmetric GUT (MSGUT) crystallized after the demonstration of its minimality on parameter counting grounds and an elegant reduction of its spontaneous symmetry breaking problem to a single cubic equation with just one unknown parameter [12]. Careful computations of the symmetry breaking [10–12] and mass spectra [3,4,6,7] became available for the MSGUT. These theories naturally maintain a structural distinction between Higgs and matter fields and therefore naturally preserve R-parity down to low energies [1,2,13]. The initial euphoria [8] that the version utilizing only 10, 126 Higgs representations might prove sufficient [14] to fit all low energy fermion data in an elegant and predictive way ran aground when the successful generic fits of fermion mass data were shown to be unrealizable [15–17] in the context of the actual seesaw mechanisms(both Type I and Type II) available in the MSGUT. Both types of seesaw yielded neutrino masses that were too small and Type I was shown to generically dominate Type II. Faced with this impasse it is natural to have recourse to the third allowed type of Fermion Mass (FM) Higgs, i.e the 120-plet of SO(10). The 120-plet had previously played a relatively minor role in fitting the fermion mass data [18,19]. In view of our no-go result in the MSGUT, however, we proposed [16] a re-allocation of roles among the three types of FM Higgs representation by suppressing the 126 Yukawa couplings relative to those of 10, 120. Since the Type I seesaw neutrino masses are inversely proportional to the 126 Yukawa coupling this would enhance the Type I seesaw masses to viable levels(Type II contributions get further suppressed) while perhaps still allowing sufficient freedom to fit all the fermion mass and mixing data. This also has the interesting consequence that right-handed neutrino masses would be significantly lowered into a range (108 −1013) GeV compatible with leptogenesis. Related subsequent work [20–22] gave mixed signals regarding the viability of our proposal to use 10 + 120 Higgs to fit charged fermion masses while small 126 Yukawa couplings to raise Type I neutrino masses by lowering 126 vev generated right-handed neutrino masses. Howe

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