order to illustrate propagator mixing between three physical scalar fields. If ${\mathcal{CP}}$ were assumed to be conserved in the MSSM, the ${\mathcal{CP}}$-violating self-energies would vanish, ${\hat{\Sigma}}_{hA}={\hat{\Sigma}}_{HA}=0$, so that only the two ${\mathcal{CP}}$-even states $h$ and $H$ would mix with each other. Our treatment corresponds to the case where non-zero phases from complex parameters are taken into account. Hence all renormalised self-energies ${\hat{\Sigma}_{ij}}{(p^{2})}$ of the Higgs bosons $i,j = h,H,A$ are in general non-vanishing, so that the matrix ${\textbf{M}}$ of mass squares consists of the tree-level masses $m_i^{2}$ on the diagonal and renormalised self-energies on the diagonal and off-diagonal entries. Expressed in terms of the lowest-order mass eigenstates $h, H, A$, which are also ${\mathcal{CP}}$ eigenstates, the matrix takes the form $${\textbf{M}}({p^{2}}) = {\begin{pmatrix}}m_h^{2}-\hat{\Sigma}_{hh}({p^{2}}) & -\hat{\Sigma}_{hH}({p^{2}}) &-\hat{\Sigma}_{hA}({p^{2}})\\
  -\hat{\Sigma}_{Hh}({p^{2}}) & m_H^{2}-\hat{\Sigma}_{HH}({p^{2}}) &-\hat{\Sigma}_{HA}({p^{2}})\\
  -\hat{\Sigma}_{Ah}({p^{2}}) & -\hat{\Sigma}_{AH}({p^{2}}) &m_A^{2}-\hat{\Sigma}_{AA}({p^{2}})
{\end{pmatrix}}. \label{eq:HiggsMassMatrix}$$ The renormalised irreducible 2-point vertex functions $$\hat{\Gamma}_{ij}{(p^{2})}= i\left[({p^{2}}-m_i^{2})\delta_{ij}+{\hat{\Sigma}}_{ij}{(p^{2})}\right] \label{eq:IrepVert}$$ can be collected in the $3\times3$ matrix ${\hat{\boldsymbol{\Gamma}}}_{hHA}$ in terms of ${\textbf{M}}$ as $${\hat{\boldsymbol{\Gamma}}}_{hHA}({p^{2}}) = i\left[{p^{2}}\textbf{1} -{\textbf{M}}({p^{2}}) \right] \label{eq:Gamma}.$$ Finally, the propagator matrix ${\boldsymbol{\Delta}}_{hHA}$ equals, up to the sign, the inverse of ${\hat{\boldsymbol{\Gamma}}}_{hHA}$, $${\boldsymbol{\Delta}}_{hHA}({p^{2}}) = - \left[{\hat{\boldsymbol{\Gamma}}}_{hHA}({p^{2}}) \right]^{-1}. \label{eq:DeltaGamInv}$$ Accordingly, the matrix inversion yields the individual propagators $\Delta_{ij}{(p^{2})}$ as the the $(ij)$ elements of the 