A quark-lepton unified Pati-Salam model with Z2 symmetry realizes a leptoquark gauge boson as light as 4.3 TeV, compatible with LHC and flavor constraints, and predicts testable lepton flavor violation plus new vector-like quarks.
SO(10) a la Pati-Salam
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abstract
We present rules for rewriting SO(10) tensor and spinor invariants in terms of invariants of its ``Pati-Salam'' maximal subgroup (SU(4)$\times \rm{SU(2)}_L\times \rm{SU(2)}_R)$ supplemented by the discrete symmetry called D parity. Explicit decompositions of quadratic and cubic invariants relevant to GUT model building are presented and the role of D parity in organizing the terms explained. Our rules provide a complete and explicit method for obtaining the "Clebsch-Gordon" Coefficients for $SO(10)\leftrightarrow G_{PS}$ in a notation appropriate for field theory models. We illustrate the usefulness our methods by calculating previously unavailable mass matrices and couplings of the $SU(2)_L$ doublets and $SU(3)_c $ triplets in the minimal Susy SO(10) GUT which are essential to specify the phenomenology of this model. We also present the bare effective potential for Baryon number violation in this model and show that it recives novel contributions from exchange of triplet Higgsinos contained the in ``neutrino mass'' Higgs submultiplets ${\bf{\bar{\Sigma}}}_{126}(10,1,3)$. This further tightens the emerging connection between neutrino mass and proton decay.
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Corrected reality conditions on the 10 and 120 Higgs representations in minimal SO(10) allow the Yukawa sector to fit all fermion masses and mixings while predicting a hierarchical right-handed neutrino spectrum and proton decay modes testable in upcoming experiments.
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TeV Scale Quark-Lepton Unification
A quark-lepton unified Pati-Salam model with Z2 symmetry realizes a leptoquark gauge boson as light as 4.3 TeV, compatible with LHC and flavor constraints, and predicts testable lepton flavor violation plus new vector-like quarks.
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Reality-constrained Minimal Yukawa Structure in SO(10) GUT
Corrected reality conditions on the 10 and 120 Higgs representations in minimal SO(10) allow the Yukawa sector to fit all fermion masses and mixings while predicting a hierarchical right-handed neutrino spectrum and proton decay modes testable in upcoming experiments.