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Prospects for New Physics from gauge Left-Right-Colour-Family Grand Unification hypothesis

Given the tremendous phenomenological success of the Standard Model (SM) framework, it becomes increasingly important to understand to what extent its specific structure dynamically emerges from unification principles. In this study, we present a novel anomaly-free supersymmetric (SUSY) Grand Unification model based upon gauge trinification $[\mathrm{SU}(3)]^3$ symmetry and a local $\mathrm{SU}(2)_{\mathrm{F}} \times \mathrm{U}(1)_{\mathrm{F}}$ family symmetry, with particle spectra and gauge symmetries inspired by a possible reduction pattern $\mathrm{E}_8 \to \mathrm{E}_6\times \mathrm{SU}(2)_{\mathrm{F}} \times \mathrm{U}(1)_{\mathrm{F}}$, with subsequent $\mathrm{E}_6\to [\mathrm{SU}(3)]^3$ symmetry breaking step. In this framework, higher-dimensional operators of $\mathrm{E}_6$ induce the threshold corrections in the gauge and Yukawa interactions leading, in particular, to only two distinct Yukawa couplings in the fundamental sector of the resulting $[\mathrm{SU}(3)]^3\times \mathrm{SU}(2)_{\mathrm{F}} \times \mathrm{U}(1)_{\mathrm{F}}$ Lagrangian. Among the appealing features emergent in this framework are the Higgs-matter unification and a unique minimal three Higgs doublet scalar sector at the electroweak scale as well as tree-level hierarchies in the light fermion spectra consistent with those observed in nature. In addition, our framework reveals a variety of prospects for New Physics searches at the LHC and future colliders such as vector-like fermions, as well as rich scalar, gauge and neutrino sectors.