is a priori no need to introduce a unitary transformation. Though, if a unitary matrix ${\textbf{U}}$ is desired for the definition of effective couplings, an approximation of the momentum dependence of ${\hat{\textbf{Z}}}$ is required. There is no unique prescription of how to achieve a unitary mixing matrix as an approximation of the ${\hat{\textbf{Z}}}$-matrix, but a possible choice is the ${p^{2}}=0$ approximation[@Frank:2006yh; @Hahn:2007fq]. As in the effective potential approach, the external momentum ${p^{2}}$ is set to zero in the renormalised self-energies ${\hat{\Sigma}_{ij}}({p^{2}})\rightarrow {\hat{\Sigma}_{ij}}(0)$ so that they become real. Then ${\textbf{U}}$ diagonalises the real matrix ${\textbf{M}}(0)$. ${\textbf{U}}$ can be chosen real and it transforms the ${\mathcal{CP}}$-eigenstates into the mass eigenstates, $$\begin{aligned}
 {\begin{pmatrix}}h_1\\ h_2\\ h_3 {\end{pmatrix}}= {\textbf{U}}{\begin{pmatrix}}h\\ H\\ A {\end{pmatrix}},~~~~
 {\textbf{U}}= {\begin{pmatrix}}{\textbf{U}}_{1h}& {\textbf{U}}_{1H}& {\textbf{U}}_{1A}\\
        {\textbf{U}}_{2h}& {\textbf{U}}_{2H}& {\textbf{U}}_{2A}\\
        {\textbf{U}}_{3h}& {\textbf{U}}_{3H}& {\textbf{U}}_{3A}
    {\end{pmatrix}}\label{eq:Urotate},\end{aligned}$$ so that $U_{aA}^{2}$ quantifies the admixture of a ${\mathcal{CP}}$-odd component inside $h_a$[@Frank:2006yh]. The elements of ${\textbf{U}}$ can then be used to introduce effective couplings of the loop-corrected states $h_a$ to any other particles $X$ in terms of the couplings of the unmixed states $i$ by the relation $$C_{h_a X}^{U} = \sum_{i=h,H,A} {\textbf{U}}_{ai} C_{i X} \label{eq:EffCoup}.$$ absorbing some higher-order corrections, but neglecting imaginary parts and the full momentum dependence of the self-energies. Hence, 