what what what? my dear colleague! What is this talking about symmetry? We have not the slightest idea of the nether dimensions of the neutral Higgs field. I have not heard of such models existing yet. If you do, however, I would be most fascinated, and so will >>1.
Also, I have the impression that 'neutral' may be a misnomer as I have evidence of quantum excitations, given exceptionally large bose condensates. I will repeat again, my colleague. Don't forget the pressure!