Higgs mechanism with non-parallel vacuum and physical field

Spontaneous symmmetry breaking of scalar potentials provide degenerate vacuum configurations of fields. We investigate the Higgs mechanism in gauge theories with a non-alligned physical field with the vacuum. We calculate the effective potential with corrections to first order in the coupling constant of a renormalizable fourth-power scalar potential, including a derived third-power contribution. We find that these non- alligned configurations are possible for potentials with non- zero second-power term. We discuss applications of this mechanism in standard-model extensions that provide CP- violating phase generation, and restrictions on the mass of the Higgs particle.