No Anomaly and New Renormalization Scheme

Abstract

We review the physics of chiral anomaly and show that the anomaly equation of δ μ J μ 5 =e 2 16π 2 ε μνρδ F μν F ρδ is not connected to any physical observables. This is based on the fact that the reaction process of π 0 →2γ has no diver- gence at all, and the triangle diagrams with the vertex of γ μ γ 5 describing the Z 0 →2γ decay do not have any di- vergences either. The recent calculated branching ratio of the Z 0 →2γ decay rate is found to be Г Z 0 →2γ /Г□2.4×10 -8 . Further, we discuss the anomaly equation in the Schwinger model which is known as δ μ J μ 5 =e2πε μν F μν , and prove that this anomaly equation disagrees with the exact value of the chiral charge δ 5 =±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.