Account for axial vector mesons in the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays

Abstract

The rates and spectra of the anomalous $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays are calculated. The approach is based on the effective meson Lagrangian obtained in the Nambu-Jona-Lasinio model with vector and axial-vector mesons by integrating out quark fields. The resulting action is affected by mixing between members of pseudoscalar $J^{PC}=0^{-+}$ and axial-vector $1^{++}$ nonets that violates some low-energy theorems. In this note we point out that a gauge covariant procedure to diagonalize this mixing allows for consistent description of the $\eta \to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ decays.

arXiv comment8 pages, 6 figuras

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Cited by in corpus (2)

• ${\eta }^{{(}^{\prime })}\to {\pi }^{+}{\pi }^{-}{\gamma }^{(\ast )}$ in large-$N_c$ chiral perturbation theory
• Gauge-covariant diagonalization of $\pi$-$a_1$ mixing and the resolution of a low energy theorem