Has the general two-Higgs-doublet model unnatural FCNC suppression? An RGE analysis

There is a widespread belief that the general two-Higgs-doublet model (G2HDM) behaves unnaturally with respect to evolution of the flavor-changing neutral Yukawa coupling parameters (FCNYCP's) -- i.e., that the latter, although being suppressed at low energies of probes, in general increase by a large factor as the energy of probes increases. We investigate this, by evolving Yukawa parameters by one-loop renormalization group equations (RGE's) and neglecting contributions of the first quark generation. For patterns of FCNYCP suppression at low energies suggested by the existing quark mass hierarchies, FCNYCP's remain remarkably stable (suppressed) up to energies very close to the Landau pole. This indicates that G2HDM preserves FCNYCP suppression, for reasonably chosen patterns of that suppression at low energies.