Two-Higgs doublet models confront the naturalness problem

The conjecture that some unknown symmetry is responsible for keeping the Higgs boson light at 125 GeV does not hold for the Standard Model, where the coefficient of the quadratic divergence of Higgs boson self-energy is far from zero. We show that such a cancellation can be achieved in two-Higgs doublet models, by virtue of which all the scalars remain at the electroweak scale and the naturalness problem is avoided. We explore the consequences of such cancellations in different two-Higgs doublet models with no flavour-changing neutral current, and show that the parameter space becomes tightly constrained; in particular, the ratio of two vacuum expectation values, $\tan\beta$, no longer remains a free parameter but turns out to be a function of the quartic couplings.