Towards Higgs masses and decay widths satisfying the symmetries in the (N)MSSM

In models with an extended Higgs sector, such as the (N)MSSM, scalar states mix with one another. Yet, the concept of Higgs mixing is problematic at the radiative level, since it introduces both a scheme and a gauge dependence. In particular, the definition of Higgs masses and decay amplitudes can be impaired by the presence of gauge-violating pieces of higher order. We discuss in depth the origin and magnitude of such effects and suggest two strategies preserving or restoring gauge invariance. In addition, the intuitive concept of mixing and the simplicity of its definition in terms of two-point diagrams can make it tempting to include higher-order corrections on this side of the calculation, irrespectively of the order achieved in vertex diagrams. Using the global $SU(2)_{\mathrm{L}}$-symmetry in the decoupling limit, we show that no improvement can be expected from such an approach at the level of the Higgs decays, but that, on the contrary, the higher-order terms may lead to numerically large spurious effects.