$h,H,A$[@Williams:2007dc; @Fuchs:2015jwa]. For $2\times 2$ mixing, of course only the two indices involved in the mixing can be permuted.

All choices allowed by the mixing structure are generally possible because of the pole structure of each propagator. However, they might not be equally numerically stable. If the loop-corrected mass eigenstate $h_a$ contains only a small admixture of the lowest-order state $i$, the propagator still has a pole at ${\mathcal{M}^{2}}_a$, but the contribution of $i$ to $h_a$ is suppressed at ${p^{2}}\neq {\mathcal{M}^{2}}_a$.

In order to be definite, it is in any case necessary to define at which pole to evaluate which normalisation and mixing ${\hat{Z}}$-factor. This choice corresponds to fixing an assignment between the indices $i,j,k$ of the lowest-order states and the indices $a,b,c$ of the higher-order mixed states and then using it consistently. The assignment $(i,a), (j,b), (k,c)$, which we label as scheme $I$, prescribes to evaluate ${\hat{Z}}_i$, ${\hat{Z}}_{ij}$ and ${\hat{Z}}_{ik}$ at ${\mathcal{M}^{2}}_a$. Once the indices have been assigned we can clear up the notation by writing $${\hat{Z}}_a\big\rvert_I := {\hat{Z}}_{i}^{a},~~ {\hat{Z}}_{aj}\big\rvert_I := {\hat{Z}}_{ij}^{a},~~ {\hat{Z}}_{bi}\big\rvert_I := {\hat{Z}}_{ji}^{b}\,,\label{eq:Zidentification}$$ and accordingly for the other indices such that the first index always refers to a loop-corrected mass eigenstate ($a,b,c\in\{1,2,3\}$)[^2] and the second index to 