Decay rates $f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-}$ and $a_1(1260)\to \omega {\pi }^{+}{\pi }^{-}$ in the Nambu -- Jona-Lasinio model

Abstract

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 $\Gamma (f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-})=2.78\text{mbox}MeV$ and $\Gamma (a_1(1260)\to \omega {\pi }^{+}{\pi }^{-})=87\text{mbox}keV$. Our result on the $f_1(1285)\to {\rho }^0{\pi }^{+}{\pi }^{-}$ decay rate is in a 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.

Comments: 10 pages, 6 figuras