Decay rates $f_{1}(1285)to rho^{0}pi^{+} pi^{-}$ and $a_{1}(1260)toomegapi^{+}pi^{-}$ in the Nambu -- Jona-Lasinio model

The anomalous decays $f_1(1285)torho^0pi^+pi^-$ and $a_1(1260)toomegapi^+pi^-$ violating natural parity for vectors and axial-vectors are studied in the framework of the Nambu -- Jona-Lasinio model. We consider the Lagrangian with $U(2)_Ltimes U(2)_R$ 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 $Gamma (f_1(1285)torho^0pi^+pi^-)=2.78, mbox{MeV}$ and $Gamma (a_1(1260)toomegapi^+pi^-)=87, mbox{keV}$. Our result on the $f_1(1285)torho^0pi^+pi^-$ decay rate is in a good agreement with experiment. It is shown that a strong suppression of the $a_1(1260)toomega pipi$ decay is a direct consequence of destructive interference between box and triangle anomalies.