Would QFT allow for an interaction mediated by different massive gauge bosons that differ only in their masses?
If I’m not mistaken no known interactions fit such a description, as while the weak interaction is mediated by massive bosons of different masses the W and Z bosons are also different in the sense that the W boson is electrically charged while the Z boson is electrically neutral. I know that while there don’t seem to be any gauge bosons that only differ in mass there are particles that seem to differ only in mass. For instance the only difference between electrons and muons is their mass and what follows from differences in their mass, and similarly the only difference between the up quark and the charm quark is that the charm quark has a greater rest mass than the up quark.
So I was wondering if QFT would allow for an interaction mediated by different gauge bosons that differ only in their rest masses that differ by multiple orders of magnitude even if there are no known interactions to fit such a description.