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SUSY QCD and SUSY Electroweak Loop Corrections to $b, t$ and $τ$ Masses Including the Effects of CP Phases

We compute supersymmetric QCD and supersymmetric electroweak corrections to the b and t quark masses and to the $τ$ lepton mass in the presence of CP phases valid for all $\tanβ$. The analysis includes one loop diagrams arising from the exchange of gluinos, charginos and neutralinos. We find that the CP effects can change both the magnitude as well as the sign of the supersymmetric loop correction. In the region of parameter space studied we found that the numerical size of the correction to the b quark mass can be as large as 30 percent and to the $τ$ lepton mass as much as 5 percent. For the top quark mass the correction is typically less than a percent. These corrections are of importance in unified models since $b-τ$ and $b-t-τ$ unification is strongly affected by the size of these corrections. More generally these results will be of importance in analyses of quark-lepton textures with the inclusion of CP phases. Further, the analysis presented here is relevant in a variety of low energy phenomena where supersymmetric QCD and supersymmetric electroweak corrections on b mass enter prominently in B physics, e.g., in processes such as $B^0_{s,d}\to l^+ł^-$.