Electroweak Symmetry Breaking and Bottom-Top Yukawa Unification

TL;DR

The paper investigates the feasibility of unifying the third-generation Yukawa couplings ($Y_t=Y_b=Y_τ$) within the MSSM under universal soft-breaking boundary conditions and radiative electroweak symmetry breaking, focusing on the large $tanβ$ regime. It demonstrates strong correlations among high-scale parameters, especially between $μ_0$, $M_{1/2}$, and $δ=B_0-(6r/7)A_0$, which shape a predictive sparticle spectrum with a bino LSP and relatively light Higgs states. A central result is that large SUSY-induced corrections to the running bottom mass ($Δm_b$) significantly affect the predicted top-quark mass and $tanβ$, lowering them compared to prior estimates. The analysis also shows that $b\rightarrow sγ$ constraints impose a nontrivial lower bound on $M_{1/2}$, making the framework highly testable with upcoming collider and flavor data.

Abstract

The condition of unification of gauge couplings in the minimal supersymmetric standard model provides successful predictions for the weak mixing angle as a function of the strong gauge coupling and the supersymmetric threshold scale. In addition, in some scenarios, e.g.\ in the minimal SO(10) model, the tau lepton and the bottom and top quark Yukawa couplings unify at the grand unification scale. The condition of Yukawa unification leads naturally to large values of $\tanβ$, implying a proper top quark--bottom quark mass hierarchy. In this work, we investigate the feasibility of unification of the Yukawa couplings, in the framework of the minimal supersymmetric standard model with (assumed) universal mass parameters at the unification scale and with radiative breaking of the electroweak symmetry. We show that strong correlations between the parameters $μ_0$ and $M_{1/2}$ appear within this scheme. These correlations have relevant implications for the sparticle spectrum, which presents several characteristic features. In addition, we show that due to large corrections to the running bottom quark mass induced through the supersymmetry breaking sector of the theory, the predicted top quark mass and $\tanβ$ values are significantly lower than those previously estimated in the literature.