# A Pati-Salam SUSY GUT with Yukawa Unification

## TL;DR

This paper refines a Pati-Salam SUSY GUT model with Yukawa unification, improving low-energy observable fits and analyzing collider constraints, suggesting the model remains viable with potential for discovering SUSY particles soon.

## Contribution

The study modifies the Yukawa sector of a Pati-Salam SUSY GUT, achieving better low-energy fits and updating collider bounds, demonstrating the model's continued viability.

## Key findings

- Improved fit to low-energy observables, especially $ aneta$ and quark masses.
- Gluino mass bound of approximately 1.9 TeV consistent with current LHC data.
- Model remains viable with potential for discovering SUSY particles in future experiments.

## Abstract

Previous studies of a three family Yukawa unified supersymmetric grand unified theory (SUSY GUT) with SO(10) or Pati-Salam (PS) gauge symmetry proposed by Raby and students show that this model is able to fit low energy and inflation observables. However, the fit to low energy observables is not great especially for $\sin2\beta$, and up and down quark masses. In this paper, we show that by choosing PS as the gauge group and modifying the Yukawa sector, the low energy fit improves significantly while other qualities of the model are maintained. In particular, the lightest SUSY particle is the neutralino with mass of order 300 - 500 GeV, the lightest stop and sbottom have mass of order 3 - 5 TeV and the CP odd Higgs mass is of order 5 - 6 TeV, so we are in the decoupling limit for the light Higgs. In addition, we reinterpret gluino simplified model analyses by the ATLAS and CMS collaborations and find that the most stringent gluino mass bound for our model is $M_{\tilde{g}}\sim1.9\,\text{TeV}$. The current best fit point, consistent with this bound, with gluino mass $M_{\tilde{g}}=1.9\,\text{TeV}$ has $\chi^2/\text{dof}\approx1.12$, compared to the best fit point of the previous model with $\chi^2/\text{dof}=1.90$. We find that predictions for the electric dipole moment of the electron, the branching ratio $BR(\mu \rightarrow e \gamma)$ and the CP violating angle in the lepton sector, $\sin\delta$, are affected significantly as compared to previous results. In summary, we are unable to rule out this model or place an upper bound on gluino mass accessible by this run of the LHC because the $\chi^2/\text{dof}$ of this model is well below $2\sigma$ even for a gluino mass as high as 2.7 TeV. On the bright side, this means that this model is still viable and we might find low energy SUSY particles in the near future.