RENORMALIZATION INVARIANTS AND QUARK FLAVOR MIXINGS

Abstract

A set of renormalization invariants is constructed using approximate, two-flavor, analytic solutions to RGE's. These invariants exhibit explicitly the correlation between quark flavor mixings and mass ratios from electroweak scale to GUT scale in the context of the SM, DHM and MSSM models. The well-known empirical relations θ23 ∝ ms/mb, θ13 ∝ md/mb at electroweak scale can thus be understood as the result of renormalization evolution toward the infrared point. The validity of this approximation is evaluated by comparing the numerical solutions with the analytical approach. It is found that the scale dependence of these quantities for general three-flavor mixing follows closely these invariants up to the GUT scale.