Higgs sector is taken into account, non-vanishing mixing contributions can occur between all neutral Higgs bosons of the model. Examples are general two-Higgs-doublet models, the Higgs sector of the minimal supersymmetric extension of the SM (MSSM), as well as the Higgs sectors of non-minimal supersymmetric models. Similarly, propagator mixing between vector resonances can occur for instance for the Kaluza–Klein excitations of the $Z$-boson and the photon ($Z'$ and $A'$, respectively), which can have similar masses and have a large mixing with each other[@Cacciapaglia:2009ic]. New, possibly nearly degenerate vector bosons can also arise in extended gauge symmetries and theories with a strongly coupled sector, e.g. composite Higgs models. For the case of the mixing of two $Z'$-like vectors, see e.g. Ref.[@deBlas:2012qp]. An example involving mixing with a new fermion is the mixing between the top quark $t$ and a top partner $t'$[@Pilaftsis:1997dr].

In order to properly treat external particles in physical processes, the correct on-shell properties of in- and outgoing particles have to be ensured. While the S-matrix theory is formulated only for stable in- and outgoing states [@Eden:AnaSmatrix], in practical applications one often needs to deal with the case of unstable external particles. The proper normalisation of external particles requires 