Flavour invariants of the N Higgs doublet model

In this work, a systematic way of analyzing the N Higgs Doublet Models flavor sector will be developed. We introduce a complete set of mixing matrices describing the rotation between certain suitably defined bases, akin to the Cabibbo-Kobayashi-Maskawa matrix, which describes the relation between the up-quark and down-quark mass bases. We point out the crucial importance played by the charged Higgs basis. It is also introduced for the first time a complete set of weak basis transformation invariant traces of flavor matrices for the general N doublets case. This will be important for studies of the renormalization group evolution in terms of relevant physical parameters.