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

TL;DR

This paper investigates the gauge dependence issues in defining Higgs masses and decay widths in extended Higgs models like the (N)MSSM, proposing strategies to preserve gauge invariance and analyzing the impact of higher-order corrections.

Contribution

It provides a detailed analysis of gauge dependence in Higgs mixing and decay calculations, and suggests methods to maintain gauge invariance in the (N)MSSM.

Findings

Gauge-violating effects can significantly affect Higgs decay calculations.

Higher-order corrections may introduce large spurious effects if not properly handled.

Strategies are proposed to preserve or restore gauge invariance in Higgs sector computations.

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 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.