The W Z have only mass from the Higgs and nothing else for example.
But to answer your point completely here is an answer which is in the two following links making the point for the Dirac fields
https://physics.stackexchange.com/questions/607435/what-part...
https://cds.cern.ch/record/292286/files/B00008237.pdf at page 46
Or have I misunderstood your point?