Symmetries of the 2HDM: an invariant formulation and consequences

A bstract Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to whole Lagrangian, i.e. CP-symmetries CP1, CP2, CP3 and Higgs-family symmetries Z 2 , U(1) SO(3) are discussed. Sufficient necessary conditions in terms constraints on masses physical couplings for respect each these found. Each symmetry realized through several alternative cases, case being a set relations among parameters. We will show some those invariant under renormalization group, but others not. The cases corresponding group illustrated by analyzing interplay between vacuum expectation values.