Symmetry-breaking patterns in QCD with 27 scalars

We investigate the symmetry-breaking patterns of the SU(3)-invariant Higgs potential with the 27 scalar fields. We find that the absolute minima can be invariant under subgroups yielding one, two, and three singlets. Analyzing the corresponding Coleman-Weinberg potential it is shown that the vacuum, when released from the SU(3)×$Z_2$-symmetric phase, evolves and rolls down along the ${\mathrm{W}}_2$×${\mathrm{U}}_{\mathrm{m}}$(1)- and ${\mathrm{W}}_2$×U’(1)×U(1)-invariant directions. This analysis of the symmetry-breaking patterns can be extended to other more complicated examples.