Alignment, reverse alignment, and wrong sign Yukawa couplings in two Higgs doublet models

Understand

We consider two Higgs doublet models with a softly broken U(1) symmetry, for various limiting values of the scalar mixing angles $\alpha$ and $\beta$.

• These correspond to the Standard Model Higgs particle being the lighter CP-even scalar (alignment) or the heavier CP-even scalar (reverse alignment), and also the limit in which some of the Yukawa couplings of this particle are of the opposite sign from the vector boson couplings (wrong sign).
• In these limits we impose a criterion for naturalness by demanding that quadratic divergences cancel at one loop.
• We plot the allowed masses of the remaining physical scalars based on naturalness, stability, perturbative unitarity and constraints coming from the $\rho$ parameter.