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

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.

💡 Research Summary

In this work the authors explore a Grand‑Unified‑Theory (GUT) motivated version of the Minimal Supersymmetric Standard Model (MSSM) built on the left‑right symmetric gauge group SU(4)_c × SU(2)_L × SU(2)_R (often called the “4‑2‑2” model). The central aim is to investigate whether the third‑generation Yukawa couplings of the top quark, bottom quark and τ lepton can be unified (t‑b‑τ Yukawa unification) while simultaneously satisfying the most recent experimental constraints from the Large Hadron Collider (ATLAS, CMS, LHCb), flavor physics, the observed Higgs boson mass, and dark‑matter (DM) searches.

A distinctive feature of the study is the adoption of a “split‑SUSY” soft‑supersymmetry‑breaking (SSB) pattern motivated by flavor symmetries: the first two sfermion families share a common soft mass m₁₂, whereas the third family receives an independent mass m₃. This hierarchy allows the third‑generation squarks to be heavy enough (∼ TeV) to generate the required radiative corrections to the Higgs mass, while keeping the first‑two families relatively light, thereby preserving some LHC‑accessible superpartner spectrum. The gaugino masses at the GUT scale are not universal; they obey the relation M₁ = (3/5) M₂ + (2/5) M₃, a consequence of the 4‑2‑2 embedding. Moreover, the sign choice μ < 0 and M₂ < 0 is made to favor Yukawa unification (sgn(μ) = −1) and to keep the supersymmetric contribution to the muon anomalous magnetic moment proportional to μ M₂ under control.

The authors perform a comprehensive numerical scan of the parameter space using the SARAH package to generate model files, SPheno for spectrum calculation, and MicrOMEGAs for dark‑matter observables. The scanned ranges are:

• m₁₂ ∈