2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008

Gauge-covariant diagonalization of pi-a1‚Äč mixing and the resolution of a low energy theorem

Authors: A. A. Osipov, M. M. Khalifa, B. Hiller

Ref.: Acta Phys.Polon.Supp. (2020)

Abstract: Using a recently proposed gauge covariant diagonalization of $\pi a_1$-mixing we show that the low energy theorem $F^{\pi}=e f_\pi^2 F^{3\pi}$ of current algebra, relating the anomalous form factor $F_{\gamma \to \pi^+\pi^0\pi^-} = F^{3\pi}$ and the anomalous neutral pion form factor $F_{\pi^0 \to \gamma\gamma}=F^\pi$, 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 $\gamma \pi {\bar 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.