Stability and symmetry breaking in the general $n$-Higgs-doublet model

For potentials with $n$-Higgs-boson doublets stability, electroweak-symmetry breaking and the stationarity equations are discussed in detail. This is done within the bilinear formalism which simplifies the investigation, in particular since irrelevant gauge degrees of freedom are systematically avoided. For the case that the potential leads to the physically relevant electroweak symmetry breaking, the mass matrices of the physical Higgs bosons are given explicitly.

Figure 1

Numbering scheme for the generalized Gell-Mann matrices ${\lambda }_{\alpha }$ ($\alpha =0,\dots ,n^2-1$).