the Higgs boson in the SM, it is already evident from the consideration of CP-conservation in the electroweak bosonic sector that a $ZHH$ vertex cannot emerge as a part of the Lagrangian. Thus the SM cannot accommodate such kind of vector-scalar-scalar (VSS) interactions[^1]. Going beyond the SM, the appearance of interactions like Eq.  is quite common in models like the two-Higgs-doublet model (2HDM) and supersymmetric models, which may lead to the associated production of two scalar bosons [@Kanemura:2001hz; @Cao:2003tr] or Higgs-to-Higgs cascade decays [@Coleppa:2014hxa; @Coleppa:2014cca] as important collider signatures.

Besides the usual 2HDM and supersymmetric models which contain a linearly-realized scalar sector, VSS interactions have also been studied in the context of nonlinearly-realized scalar sectors. Nonlinearly-realized scalar sectors are frequently adopted when building a model in which the Higgs is realized as a pseudo-Goldstone boson of some global symmetry breaking [@Bellazzini:2014yua], which could be helpful in addressing the hierarchy problem. In principle the derivation of VSS vertices in such models is similar to the linearly-realized case: start from the gauge covariant kinetic terms of the scalar fields and then expand the interaction fields into vacuum expectation values and mass eigenstate fields after which the three-point VSS vertices could be extracted. 