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In the Standard Model, custodial symmetry is violated by the hypercharge U(1)gauge interactions and the Yukawa couplings, while being preserved by the Higgsscalar potential. In the two-Higgs doublet model (2HDM), the generic scalarpotential introduces new sources of custodial symmetry breaking. We obtain abasis-independent expression for the constraints that impose custodial symmetryon the 2HDM scalar potential. These constraints impose CP-conservation on thescalar potential and vacuum, and in addition add one extra constraint on thescalar potential parameters. We clarify the mass degeneracies of the 2HDM thatarise as a consequence of the custodial symmetry. We also provide a computationof the "oblique" parameters (S, T, and U) for the most general CP-violating2HDM in the basis-independent formalism. We demonstrate that the 2HDMcontributions to T and U vanish in the custodial symmetry limit, as expected.Using the experimental bounds on S and T from precision electroweak data, weexamine the resulting constraints on the general 2HDM parameter space.

Basis-independent methods for the two-Higgs-doublet model III: The CP-conserving limit, custodial symmetry, and the oblique parameters S, T, U