AxialVector Vertex in Spinor Electrodynamics
Abstract
Working within the framework of perturbation theory, we show that the axialvector vertex in spinor electrodynamics has anomalous properties which disagree with those found by the formal manipulation of field equations. Specifically, because of the presence of closedloop "triangle diagrams," the divergence of axialvector current is not the usual expression calculated from the field equations, and the axialvector current does not satisfy the usual Ward identity. One consequence is that, even after the externalline wavefunction renormalizations are made, the axialvector vertex is still divergent in fourth (and higher) order perturbation theory. A corollary is that the radiative corrections to ν_{l}l elastic scattering in the local currentcurrent theory diverge in fourth (and higher) order. A second consequence is that, in massless electrodynamics, despite the fact that the theory is invariant under γ_{5} tranformations, the axialvector current is not conserved. In an Appendix we demonstrate the uniqueness of the triangle diagrams, and discuss a possible connection between our results and the π^{0}>2γ and η>2γ decays. In particular, we argue that as a result of triangle diagrams, the equations expressing partial conservation of axialvector current (PCAC) for the neutral members of the axialvectorcurrent octet must be modified in a welldefined manner, which completely alters the PCAC predictions for the π^{0} and the η twophoton decays.
 Publication:

Physical Review
 Pub Date:
 January 1969
 DOI:
 10.1103/PhysRev.177.2426
 Bibcode:
 1969PhRv..177.2426A