MSSM with Yukawa quasiunification

We consider the constrained minimal supersymmetric standard model which emerges from one theory with a small deviation from Yukawa unification which is adequate for $\mu>0$. We show that this model possesses a wide and natural range of parameters which is consistent with the data on $b\to s\gamma$, the muon anomalous magnetic moment, the cold dark matter abundance in the universe, and the Higgs boson masses.