Gauge-covariant diagonalization of π-a₁ mixing and the resolution of a low energy theorem

2020/06/17 by Osipov, A. A., Khalifa, M. M., Hiller, B.
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph)

paper · doi:10.48550/arxiv.2006.09715

Abstract

Using a recently proposed gauge covariant diagonalization of πa₁-mixing we show that the low energy theorem F^π=e f_π² F^3π of current algebra, relating the anomalous form factor F_{γ→ π⁺π⁰π^-} = F^3π and the anomalous neutral pion form factor F_{π⁰ → γγ}=F^π, is fulfilled in the framework of the Nambu-Jona-Lasinio (NJL) model, solving a long standing problem encountered in the extension including vector and axial-vector mesons. At the heart of the solution is the presence of a γπ q q vertex which is absent in the conventional treatment of diagonalization and leads to a deviation from the vector meson dominance (VMD) picture. It contributes to a gauge invariant anomalous tri-axial (AAA) vertex as a pure surface term.

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