e.g.  Refs. [@Williams:2007dc; @Fowler:2009ay; @Williams:2011bu; @Bharucha:2012nx], and therefore need to be included in order to obtain a complete one-loop result for processes of this kind. For contributions to the propagator matrix with an incoming and outgoing Higgs boson the mixing contributions with $G$ and $Z$ enter from the order of $({\hat{\Sigma}}_{i,G/Z})^{2}$ onwards, which is of subleading two-loop order. For our numerical analysis below, see Sect.\[sect:NumBWfull\], we will use use the program `FeynHiggs`[@Heinemeyer:1998np; @Heinemeyer:1998yj; @Degrassi:2002fi; @Heinemeyer:2007aq], where dominant two-loop corrections and leading higher-order contributions are incorporated in the irreducible self-energies. Since sub-leading two-loop contributions that are of the same order as the mixing contributions with $G$ and $Z$[@Frank:2006yh] are neglected in this analysis, we include no further corrections beyond the $(3 \times 3)$ propagator matrix of the physical Higgs fields in this case.

In this section we introduce the relevant quantities and fix our notation for the propagator matrix and the wave function normalisation factors, see Refs.[@Dabelstein:1994hb; @Dabelstein:1995js; @Heinemeyer:2000fa; @Heinemeyer:2001iy; @Hahn:2002gm; @Frank:2006yh; @Hahn:2006np; @Williams:2007dc; @Fowler:2010eba; @Williams:2011bu]. In Sect.\[sect:poles\] we will analyse the pole structure of propagator matrices of unstable particles.

Propagator matrix and the effective self-energy
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As explained above, we use the case of the MSSM with complex parameters in 