One-loop renormalization group equations of the general framework with two Higgs doublet

Using a finite energy cutoff method, we derive one-loop renormalization group equations (RGE's) for Yukawa coupling parameters of quarks and for the vacuum expectation values of the Higgs doublets in the general framework of the Standard Model with two Higgs doublets (2HDM "type III"). In the model, the neutral-Higgs-mediated flavor-changing neutral currents are allowed but are assumed to be reasonably suppressed at low energies. The popular "type II" and "type I" models are just special cases of this framework. We then compare our RGE results with those of other authors who derived them for general (semi)simple gauge groups. We find out that our one-loop results disagree with those of Vaughn and Machacek, and agree with those of Jack and Osborn. We identify the mistakes of the former authors. We subsequently present a numerical example for the RGE flow of Yukawa coupling parameters and masses of quarks. The example shows a remarkable persistence of the suppression of the neutral-Higgs-mediated FCNC's as the energy of probes increases, in contrast to the usual expectations and reservations about this model.