Abstract
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 consider two strategies that minimize the dependence on the gauge-fixing parameter and field-renormalization of one-loop order in the definition of the mass and decay observables, both in degenerate and non-degenerate scenarios. 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.
Highlights
Using the global SU (2)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 higherorder terms may lead to numerically large spurious effects
One may directly use the LSZ reduction formula in order to define the Higgs mixing in terms of the loop corrections applying on an external Higgs leg in a physical amplitude: this has been described in e.g. Refs. [17,18,19]
The associated masses are obtained at the strict one-loop order from the Two-Higgs-Doublet Model (THDM) self-energies projecting onto the tree-level Higgs-field directions of the THDM: they are displayed in dashed orange/brown and show a variation of ∼ 0.5 GeV for μmap ∈ [MW, mSUSY]
Summary
The loop-induced mixing in the Higgs sector is defined at the level of the Higgs self-energies. The latter are not gauge-invariant objects, in general, highlighting the artificiality of the loop-corrected mixing matrix. We detail how gauge invariance is ensured at the one-loop order in observable quantities such as the Higgs masses and decays, or how one could attempt to remedy its violation by terms of higher order
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