Infrared quasi-fixed point structure of the fermion masses in the standard model: The two-loop analysis

In the standard model, the renormalization group equation for the Yukawa couplings has the infrared quasi-fixed point which determines the upper bound for the masses of fermions present in the theory. We analyse this effect within the two loop approximation and report the 15% increase of the quark bound compared to the one loop results. We notice and investigate the strong dependence of the bound on the precise value of the Weinberg angle. The detailed study of the Yukawa coupling evolution is also included.