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

TL;DR

This paper investigates the decay rates of specific anomalous meson decays within the Nambu--Jona-Lasinio model, providing theoretical estimates that align well with experimental data and explaining the suppression mechanisms involved.

Contribution

The study offers a novel calculation of decay widths for $f_1(1285)$ and $a_1(1260)$ mesons using the NJL model with chiral symmetry, including anomaly effects and interference phenomena.

Findings

Decay width of $f_1(1285) o ho^0 o ext{pions}$ matches experimental data.

Strong suppression of $a_1(1260) o ext{omega} ext{pions}$ explained by anomaly interference.

Theoretical framework successfully incorporates anomalous triangle diagrams.

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 $\Gamma (f_1(1285)\to\rho^0\pi^+\pi^-)=2.78\, \mbox{MeV}$ and $\Gamma (a_1(1260)\to\omega\pi^+\pi^-)=87\, \mbox{keV}$. 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.