Abstract
We show that the lack of the (global or local) chiral symmetry at the quantum level produces (1) a linearly divergent quark mass for massless QCD or (2) a quadratically divergent gauge boson mass for a chiral gauge theory by using lattice and Pauli-Villars regularizations, contrary to the usual claim that both are absent because of the chiral symmetry. We point out that the dimensional regularization, which is used to get the usual claim, fails to reproduce such dimensionful divergences, though the gauge invariance of the gauge boson propagator is broken by the dimensionless finite term. We conclude that dimensional regularization should not be used to discuss the divergent structure of some theory.
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