Evaluation of the chiral anomaly in gauge theories with γ5 couplings

A straightforward application of various regularization schemes in perturbation theory generally leads to physically unacceptable results in the evaluation of the chiral anomaly if the gauge theory contains γ5 couplings. In gauge theory the anomaly-free properties should be imposed on all the gauge vertices, regardless of whether they are vector or axial-vector, and thus the (nongauge) vector vertex of a triangle diagram could contain an anomaly if the gauge couplings involve γ5. This is illustrated by the fermion number (vector) current in the Weinberg-Salam theory. It is then shown that the path-integral formalism naturally resolves those complications and gives rise to a unique gauge-invariant result. The Hermiticity of eigenvalue equations in Euclidean gauge theory plays an important role in the path-integral formalism. A path-integral treatment of gauge theory with S and P Higgs couplings is also described