The fate of the axial anomaly in a finite field theory

Abstract

The conservation of the vector current and the axial anomaly responsible for the ${\pi }_0\to \gamma \gamma$ decay amplitude are obtained in leading order within the Taylor-Lagrange formulation of fields considered as operator-valued distributions. As for gauge theories, where this formulation eliminates all divergences and preserves gauge-symmetry, it is shown that the different contributions can be evaluated directly in $4$-dimensional space-time, with no restrictions whatsoever on the four-momentum of the internal loop, and without the need to introduce any additional non physical degrees of freedom like Pauli-Villars fields. We comment on the similar contributions responsible for the decay of the Higgs boson into two photons.

arXiv comment15 pages, one figure

References in corpus (7)

• Improved Epstein-Glaser Renormalization II. Lorentz invariant framework
• Taylor-Lagrange renormalization scheme. Application to light-front dynamics
• UV and IR behaviour in QFT and LCQFT with fields as Operator Valued Distributions:Epstein and Glaser revisited
• Taylor-Lagrange renormalization scheme, Pauli-Villars subtraction, and light-front dynamics
• Aspects of fine-tuning of the Higgs mass within finite field theories
• Once more on the Higgs decay into two photons
• The renormalization group equations revisited

Cited by in corpus (2)

• The fate of the trace anomaly in a finite formulation of field theory
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