On the QCD corrections to Vainshtein's theorem for VVA correlator

Abstract

We point out that, contrary to existing claims of the opposite, Vainshtein's theorem on the non-renormalization of the correlator of an axial and two vector currents, is only valid in the chiral limit. When quarks, that contribute to the correlator, are massive, the QCD corrections do not vanish and the transversal and longitudinal functions are renormalized differently. We compute those corrections and study their implications for QCD effects in electroweak corrections to the muon anomalous magnetic moment.

arXiv comment6 pages, 4 figures

References in corpus (12)

• Measurement of the Negative Muon Anomalous Magnetic Moment to 0.7 ppm
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Precise Measurement of the Positive Muon Anomalous Magnetic Moment
• The renormalization of the axial anomaly in dimensional regularization
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.7 ppm
• Electroweak Hadronic Contributions to the muon g-2
• Calculation of Feynman Diagrams from their Small Momentum Expansion
• Perturbative and nonperturbative renormalization of anomalous quark triangles
• Results and Techniques of Multi-Loop Calculations
• Improved Measurement of the Positive Muon Anomalous Magnetic Moment
• New nonrenormalization theorems for anomalous three point functions
• Dispersive approach to the axial anomaly and nonrenormalization theorem

Cited by in corpus (8)

• Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2{)}_{\mu }$ with large-$N_c$ Regge models
• The anomalous magnetic moment of the muon in the Standard Model: an update
• Axial anomaly as a collective effect of meson spectrum
• Anomalous $A{V}^{\ast }V$ vertex function in the soft-wall holographic model of QCD
• Dispersion relations for the hadronic VVA correlator
• Improved evaluation of the electroweak contribution to muon $g-2$
• On Anomaly Matching and Holography
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$