No Anomaly and New Renormalization Scheme

Takehisa Fujita, Naohiro Kanda

Department of Physics, Faculty of Science and Technology, Nihon University, Tokyo, Japan.

DOI: 10.4236/jmp.2012.38091                

Abstract

We review the physics of chiral anomaly and show that the anomaly equation of δ_μJ^μ₅ =e²16π²ε_μνρδ F^μνF^ρδis not connected to any physical observables. This is based on the fact that the reaction process of π⁰→2γ has no diver- gence at all, and the triangle diagrams with the vertex of γ^μγ₅ describing the Z⁰→2γ decay do not have any di- vergences either. The recent calculated branching ratio of the Z⁰→2γ decay rate is found to be Г_Z⁰→2γ/Г□2.4×10^-8. Further, we discuss the anomaly equation in the Schwinger model which is known as δ_μJ^μ₅=e2πε_μνF^μν , and prove that this anomaly equation disagrees with the exact value of the chiral charge δ₅=±1 in the Schwinger vacuum. Therefore, the chiral anomaly is a spurious effect induced by the regularization. In connection with the anomaly prob- lem, we clarify the physical meaning why the self-energy of photon should not be included in the renormalization scheme. Also, we present the renormalization scheme in weak interactions without Higgs particles, and this is achieved with a new propagator of massive vector bosons, which does not give rise to any logarithmic divergences in the vertex corrections. Therefore, there is no necessity of the renormalization procedure of the vertex corrections arising from the weak vector boson propagation.

Keywords

Anomaly; Renormalization Scheme

Conflicts of Interest

The authors declare no conflicts of interest.

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