LHC and dark matter implications of t-b-τ Yukawa unification in split SUSY GUTs

TL;DR

The paper investigates a GUT-inspired MSSM with a left-right 4-2-2 gauge group and $t$-$b$-$\tau$ Yukawa unification under split soft SUSY breaking, testing compatibility with LHC and dark matter constraints. Using SARAH/SPheno/MicrOMEGAs, it scans a constrained parameter space (including $M_1=(3/5)M_2+(2/5)M_3$ and $\mu$, $M_2<0$) to find regions with successful Yukawa unification, correct Higgs mass, and viable DM relic density. The results show viable regions with $m_{12}/m_3\lesssim 0.5$ and $|M_2|$ around a few hundred GeV, realized via bino–wino or slepton coannihilation, and compatible with $B$-physics observables; Yukawa unification prefers $\tan\beta$ in the high range, $43\lesssim\tan\beta\lesssim52$, and $R_{tb\tau}\approx1.1$. Direct-detection limits constrain parts of the parameter space, but substantial, experimentally testable regions remain accessible to current and upcoming collider and DM experiments. This work demonstrates that minimalist GUT-inspired SUSY scenarios can accommodate Yukawa unification while remaining consistent with contemporary experimental data.

Abstract

We investigate a grand unification (GUT) inspired version of the minimal supersymmetric standard model (MSSM) based on a left-right symmetric $4$-$2$-$2$ gauge group, incorporating Yukawa coupling unification and current phenomenological constraints. Utilizing a split soft supersymmetry-breaking (SSB) parameter space motivated by flavor symmetries, we analyze the implications of recent results from ATLAS, CMS, LHCb, and dark matter direct detection experiments. Our numerical scans, conducted with SARAH and SPheno, identify viable low-energy regions consistent with third-generation Yukawa unification, the observed Higgs boson mass, dark matter relic density, and flavor observables such as $B \to X_s γ$, $B_s \to μ^+ μ^-$ and $B_u \to τν_τ$ . Our findings suggest that while current bounds severely constrain much of the MSSM-like parameter space, substantial regions remain experimentally viable and testable in the ongoing LHC run and next-generation dark matter experiments.

Figures (17)

• Figure 1: The $\left(m_{12}/m_3, M_2\right)$ plane. The constraints are shown in different colors and applied successively in the order: data consistent with neutralino LSP (grey), B Physics constraints (yellow), mass bounds from ATLAS and CMS (blue), cosmological abundance of dark matter (orchid) and points satisfying $\Delta a_\mu$ bounds within the $2 \sigma$ range (red). We emphasize that the constraints are applied successively, so that red points satisfy all constraints considered while orchid points satisfy all constraints other than the bounds coming from $\Delta a_\mu$.
• Figure 2: The $\left(A_{0}/m_3, \tan\beta\right)$ plane. Color coding is the same as in Fig. \ref{['m12Overm3-M2']}. Further we show the contour (in black) corresponding to $R_{tb\tau}\simeq 1.1.$
• Figure 3: The $(\Omega h^{2}, R_{tb\tau})$ plane. The blue points satisfy B Physics constraints and mass bounds as in the previous figures. The pink (green) points form that subset of blue points that are predominantly wino (bino) in their constitution and have $\Omega h^2\lesssim 0.12$. The horizontal lines correspond to $R_{tb\tau}=1.05,\, 1.10.$
• Figure 4: The $\left( m_{H_d}/m_{H_u}, M_{1}\right)$ plane. Color coding is the same as in Fig. \ref{['m12Overm3-M2']}.
• Figure 5: The $\left( m_{\tilde{\mu}_{1}}, m_{\tilde{\chi}^{o}_{1}} \right)$ plane. Color coding is the same as in Fig. \ref{['m12Overm3-M2']}.