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

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