receive contributions from the mixing with the longitudinal components of the neutral gauge bosons $Z$ and $\gamma$. While the $Z$-boson propagator contributes to the diagonal elements of the Higgs propagator matrix at the two-loop level, the photon enters in those elements only at the four-loop level. Besides the mixing with the longitudinal component of the $Z$ boson, also the mixing with the unphysical (would-be) Goldstone boson $G$ needs to be taken into account. Instead of considering a $(6\times6)$ propagator matrix of the states $\left\lbrace h,H,A,G,Z,\gamma\right\rbrace$, we focus on the full mixing contributions of the physical Higgs fields, i.e. we treat the case of a $(3
\times 3)$ propagator matrix (which would generalise to $(n \times n)$ for the case of $n$ physical scalar fields). For the $(3 \times 3)$ propagator matrix of physical Higgs fields, higher-order effects from the inversion of the matrix of the irreducible 2-point vertex functions are taken into account. In contrast, we treat the mixing contributions with the gauge bosons and the (would-be) Goldstone boson in a strict perturbative expansion up to the desired order. It should be noted that Higgs–$G/Z$ mixing contributions already appear at the one-loop level in processes with external Higgs bosons, see 