The three Higgs-family symmetries Z_2, U(1), SO(3) and the three CP-symmetries CP1, CP2, CP3 all constrain the general 2HDM if imposed upon the potential. These symmetries are usually formulated in terms of the vanishing, or constraints among certain parameters of the potential that are satisfied in a certain basis (the symmetry basis). These symmetries are still present, but they may become hidden if we rotate into another basis. An equivalent formulation of these symmetries exist, formulated in terms of the vanishing, or constraints among the masses and couplings of the model. These (physical) constraints will remain the same even if we rotate into another basis. All six symmetries are presented in terms of constraints on masses and couplings, followed by a discussion for each symmetry.
With support from FCT through project UIDB/00777/2020