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

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 a 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 also present a numerical example for the RGE flow of Yukawa coupling parameters and masses of quarks. Detailed investigation, through RGE's, of connection between the low energy and the high energy structure of these 2HDM's would give us some additional insights into the viability of such frameworks, i.e., it would tell us for which choices of phenomenologically acceptable values of low energy parameters such frameworks can be regarded as reasonably natural (without excessive changes in the parameter structure as energy of probes increases over a wide range). Furthermore, such analyses could provide us with possible signals of new physics at high energies.