Ward Identities for η Decay in Perturbation Theory
Abstract
The process η>3π is known to violate a simple prediction of partial conservation of axialvector current. In many models, η>3π proceeds through a fermion loop with electromagnetic corrections. The first radiative corrections to fermion loops give rise to divergent doubleloop integrals with forms like d^{4}rd^{4}k[r^{2}m^{2}]^{2}[(r k)^{2}m^{2}]^{2}. As with single linearly divergent integrals, when a meaning is ascribed to them it may not always be possible to shift the origin of integration without changing the value of these integrals. Such integrals appear when one tries to check, in perturbation theory, Ward identities and lowenergy theorems which follow from the formal manipulation of the equations of motions. They can cause anomalies similar to the one in the axialvectorcurrent twophoton vertex. We study some applications to the ηπσ vertex, to the process η>3π, and to the corrections of order α^{2} to π^{0}>2γ. No anomalies which can be related to η decay are discovered.
 Publication:

Physical Review D
 Pub Date:
 January 1971
 DOI:
 10.1103/PhysRevD.3.485
 Bibcode:
 1971PhRvD...3..485A