Dynamical relaxation in 2HDM models

The dynamical relaxation provides an interesting solution to the hierarchy problem in face of the missing signatures of any new physics in recent experiments. Through a dynamical process taking place in the inflationary phase of the universe it manages to achieve a small electroweak scale without introducing new states observable in current experiments. Appropriate approximation makes it possible to derive an explicit formula for the final vevs in the double-scanning scenario extended to the two Higgs doublet models (2HDM). Analysis of the relaxation in 2HDM indicates, that in a general case it is impossible to keep vevs of both scalars small, unless fine-tuning is present or additional symmetries are cast upon the Lagrangian. Within the slightly constrained variant of 2HDM, where odd powers of the fields' expectation values are not present (which can be easily enforced by requiring that the doublets have different gauge transformations or by imposing a global symmetry) it is shown that the the difference between the vevs of two scalars tends to be proportional to the cutoff. The analysis of the relaxation in 2HDM indicates, that in a~general case the relaxation would be stopped by the first doublet that gains a vev, with the other one remaining vevless with a mass of the order of the cutoff. This happens to conform with the inert doublet model.