effectively absorbed into the vertices of neutral Higgs bosons. If ${\hat{\textbf{Z}}}$-factors are applied to supplement the Born result, only non-Higgs propagator type corrections (such as mixing with the Goldstone and $Z$-bosons) as well as vertex, box and real corrections need to be calculated individually.

As it is the case for the usual (UV-divergent) on-shell field renormalisation constants, the finite wave function normalisation factors are in general gauge-dependent quantities. While the gauge-parameter dependence drops out at a fixed order in perturbation theory, the inclusion of higher-order contributions into the ${\hat{\textbf{Z}}}$-factors described above can give rise to a residual gauge-parameter dependence, which is formally of sub-leading higher order. This is caused by the fact that the ${\hat{\textbf{Z}}}$-factors contain not only gauge-parameter independent leading higher-order contributions but also sub-leading higher-order contributions that are in general gauge-parameter dependent. Those sub-leading higher-order contributions would cancel with corresponding sub-leading higher-order contributions from other Green functions such as vertex and box contributions.

Effective couplings {#sect:Ueff}
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Since the ${\hat{\textbf{Z}}}$-matrix is not unitary, it does not represent a unitary transformation between the $\{h,H,A\}$ and the $\{h_1,h_2,h_3\}$ basis. However, it is not necessary to diagonalise the mass matrix for the determination of the poles of the propagators. Hence there 