# $b-\tau$ Yukawa Unification in SUSY SU(5) with Mirage Mediation: LHC and Dark Matter Implications

## TL;DR

This paper explores $b- au$ Yukawa unification in SUSY SU(5) models with mirage mediation, analyzing implications for LHC searches and dark matter detection, identifying two distinct viable parameter regions with different dark matter properties.

## Contribution

It introduces a SUSY SU(5) GUT model with combined gravity and mirage mediation, detailing the resulting gaugino mass spectrum and dark matter scenarios, including Higgsino-like and bino-wino mixed neutralinos.

## Key findings

- Gluino mass bounded below 4 TeV, with two distinct parameter regions.
- First region features low $mbda$-term, nearly degenerate stop and neutralino, and Higgsino-like dark matter.
- Second region has light gluino (~1 TeV), bino-wino dark matter, and coannihilation effects reducing relic abundance.

## Abstract

We consider a class of $b-\tau$ Yukawa unified Supersymmetric (SUSY) $SU(5)$ GUTs, in which the asymptotic gaugino $M_{1,2,3}$ masses are generated through a combination of gravity and mirage mediated supersymmetry breaking. Due to the contributions from mirage mediation, $M_{3}$ is always lighter than M_{1} and M_{2}, and consequently for the range of asymptotic masses considered, the gluino mass at low scale is bounded from above at about 4 TeV. We realize two different regions, one in which the MSSM $\mu-$term is less than about 3 TeV. This region yields a stop mass up to 5 TeV, and the stop mass is nearly degenerate with the LSP neutralino for mass around 0.8 to 1.7 TeV. A stau mass can be realized up to about 5 TeV, and the stau mass is approximately degenerate with the LSP neutralino for mass around 2 to 3 TeV. In addition, an A-funnel solution $m_{A}$ with mass $\sim 1.4-1.8$ TeV is realized. A second region, on the other hand, arises for gluino around 1.1 TeV. The $\mu-$term is rather large than 20 TeV, and the LSP neutralino is a bino-wino mixture. The gluino mass ($\sim 0.8-1.2$ TeV) is nearly degenerate with the LSP neutralino mass and hence, the gluino-neutralino coannihilation processes play a role in reducing the relic abundance of LSP neutralino down to ranges allowed by the current WMAP measurements. The two regions above can be distinguished through the direct detection experiments. The first region with relatively low $\mu$ values yields Higgsino-like DM, whose scattering on the nucleus typically has a large cross-section. We find that such solutions are still allowed by the current results from the LUX experiment, and they will be severely tested by the LUX-Zeplin experiment. The second region contains bino-wino DM whose scattering cross-section is relatively low. These solutions are harder to rule out in the foreseeable future.