Massless vector bosons have only two independent degrees of freedom, while massive ones have three. In spontaneous symmetry breaking, the massless vector belonging to the broken group becomes massive and absorbs the Goldstone boson degree of freedom as its third independent (longitudinal) component.
Breaking a symmetry explicitly does not supply an additional field that can serve as third degree of freedom. From this I gather two possibilities:
- Vector bosons that belong to explicitly broken symmetries remain massless or
- there is some mechanism that I'm not aware of that can supply the required degree of freedom.
Which option is it? Or is there a third option that I'm not considering?