Dispersive approach to the axial anomaly and nonrenormalization theorem

Abstract

Anomalous triangle graphs for the divergence of the axial-vector current are studied using the dispersive approach generalized for the case of higher orders of perturbation theory. The validity of this procedure is proved up to two-loop level. By direct calculation in the framework of dispersive approach we have obtained that the two-loop AVV amplitude is equal to zero. According to the Vainshtein's theorem the transversal part of the anomalous triangle is not renormalized in the chiral limit. We generalize this theorem for tha case of finite fermion mass in the triangle loop.

12 pages, version to appear in Physical Review D

References in corpus (6)

• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Perturbative and nonperturbative renormalization of anomalous quark triangles
• New nonrenormalization theorems for anomalous three point functions
• Adler function and hadronic contribution to the muon g-2 in a nonlocal chiral quark model
• VA\tilde V correlator within the instanton vacuum model
• Singlet VA \tilde V correlator within the instanton vacuum model

Cited by in corpus (10)

• Explicit Results for the Anomalous Three Point Function and Non-Renormalization Theorems
• Axial anomaly as a collective effect of meson spectrum
• Pion elastic and $({\pi }^0,\eta ,{\eta }^{\prime })\to \gamma {\gamma }^{\ast }$ transition form factors in a broad range of momentum transfers
• The puzzle of the π-> γγ* transition form factor
• Dispersion relations for the hadronic VVA correlator
• On the ${\gamma }^{\ast }\gamma \to \pi (\eta ,{\eta }^{\prime })$ transition form factors
• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c$ transition form factor
• Matching lightcone- and anomaly-sum-rule predictions for the pion-photon transition form factor
• On the QCD corrections to Vainshtein's theorem for VVA correlator
• Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball