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We consider a class of unified models based on the gauge group$\mathsf{SO(10)}$ which with appropriate choice of Higgs representationsgenerate in a natural way a pair of light Higgs doublets needed to accomplishelectroweak symmetry breaking. In this class of models higher dimensionaloperators of the form matter-matter-Higgs-Higgs in the superpotential afterspontaneous breaking of the GUT symmetry generate contributions to Yukawacouplings which are comparable to the ones from cubic interactions.Specifically we consider an $\mathsf{SO(10)}$ model with a sector consisting of$\mathsf{126+\overline{126} + 210}$ of heavy Higgs which breaks the GUTsymmetry down to the standard model gauge group and a sector consisting of$2\times \mathsf{10+120}$ of light Higgs fields. In this model we compute thecorrections from the quartic interactions to the Yukawa couplings for the topand the bottom quarks and for the tau lepton. It is then shown that inclusionof these corrections to the GUT scale Yukawas allows for consistency of thetop, bottom and tau masses with experiment for low $\tan\beta$ with a value aslow as $\tan\beta$ of 5$-$10. We compute the sparticle spectrum for a set ofbenchmarks and find that satisfaction of the relic density is achieved via acompressed spectrum and coannihilation and three sets of coannihilationsappear: chargino-neutralino, stop-neutralino and stau-neutralino. Weinvestigate the chargino-neutralino coannihilation in detail for thepossibility of observation of the light chargino at the high luminosity LHC(HL-LHC) and at the high energy LHC (HE-LHC) which is a possible future 27 TeVhadron collider. It is shown that all benchmark models but one can bediscovered at HL-LHC and all would be discoverable at HE-LHC. The onesdiscoverable at both machines require a much shorter time scale and a lowerintegrated luminosity at HE-LHC.

Corrections to Yukawa couplings from higher dimensional operators in a natural SUSY $\mathsf{SO(10)}$ and HL-LHC implications