I would like to clarify my understanding on why mass terms in Lagrangians of gauge theories are forbidden.
It's often repeated that particle masses are forbidden by electroweak symmetry because it is a chiral theory. I want to make a distinction between fermionic masses and gauge boson masses.
Looking through the transformations of gauge boson mass terms, it seems that these are in fact always forbidden by their respective gauge symmetry. Is this correct? (So if there was no SU(2) symmetry, the photon and gluon would still need to be massless?)
In which case, the electroweak symmetry is actually responsible for forbidding all other mass terms (i.e. weak boson masses and fermion masses) due to the usual chiral arguments. Is this correct?