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.
Highlights
The QCD perturbation theory is not applicable to the low-energy physics of hadrons (E < 2 GeV). In this region of energies, one applies various phenomenological models based on an approximate chiral symmetry of strong interactions
To extend the calculational scheme up to order Oðp6Þ, it incorporates the lowest resonance spin-1 states implementing the appropriate QCD short-distance constraints [6,7,8]. Another well-known approach is the famous Nambu–Jona-Lasinio (NJL) model [9,10], which incorporates the dynamical mechanism of spontaneous chiral symmetry breaking in hadron matter
We have checked gauge invariance for the a1 → γπþπ− decay amplitude. This symmetry is protected by contributions, which are not generated by the VMD mechanism
Summary
The QCD perturbation theory is not applicable to the low-energy physics of hadrons (E < 2 GeV). The recent progress here is related with the study of the anomalous radiative decays of the axial-vector f1ð1285Þ and a1ð1260Þ mesons [23] These vertices belong to the AVV-type and have several restrictions from the QCD low-energy theorems: the Adler-. This step would provide us the important additional information on the masses and widths of the a1ð1260Þ and f1ð1285Þ mesons, but could shed light on the new internal content of these states These issues [the mixing structure consisting of two components of qqand hadronic composites [46], the meson fusing structures [47], the meson-triangle singularities [32], and so on] are widely discussed in the literature and can be addressed in the framework of the NJL model taken at the next to leading order in the 1=Nc expansion
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