The anomalous decays $f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-}$ and $a_1(1260)\to \omega {\pi }^{+}{\pi }^{-}$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu–Jona-Lasinio model. We consider the Lagrangian with $U(2{)}_L\times U(2{)}_R$ chiral symmetric four-quark interactions. The theory is bosonized, and corresponding effective meson vertices are obtained in the leading order of $1/N_c$ and derivative expansions. The uncertainties related with the surface terms of anomalous quark triangle diagrams are fixed by the corresponding symmetry requirements. We make a numerical estimate of the decay widths $\mathrm{\Gamma }(f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-})=2.74\mathrm{MeV}$ and $\mathrm{\Gamma }(a_1(1260)\to \omega {\pi }^{+}{\pi }^{-})=293\mathrm{keV}$. Our result on the $f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-}$ decay rate is in good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)\to \omega \pi \pi$ decay is a direct consequence of destructive interference between box and triangle anomalies.

• Received 28 May 2018

DOI:https://doi.org/10.1103/PhysRevD.98.014037

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Published by the American Physical Society