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 $Γ(f_1(1285)\toρ^0π^+π^-)=2.78\, \mbox{MeV}$ and $Γ(a_1(1260)\toωπ^+π^-)=87\, \mbox{keV}$. 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.

10 pages, 6 figuras

References in corpus (8)

• The contribution of axial-vector mesons to hyperfine structure of muonic hydrogen
• Exclusive photoproduction of $f_1(1285)$ meson off proton in the JLab kinematics
• Analysis of recent CLAS data on $f_1(1285)$ photoproduction
• The anomalous decay $f_1(1285)\to \rho \gamma$ and related processes
• $\tau \to f_1(1285){\pi }^{-}{\nu }_{\tau }$ decay in the extended Nambu -- Jona-Lasinio model
• Triangle singularity in $\tau \to f_1(1285)\pi {\nu }_{\tau }$ decay
• Anomalous decay $f_1(1285)\to {\pi }^{+}{\pi }^{-}\gamma$ in the Nambu - Jona-Lasinio model
• The production of the $f_1(1285)\gamma$ and $a_1(1260)\gamma$ in colliding $e^{+}{e}^{-}$-beams in threshold domain

Cited by in corpus (4)

• Central exclusive diffractive production of axial-vector $f_1(1285)$ and $f_1(1420)$ mesons in proton-proton collisions
• Theoretical description of the $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1380)$, $\mathbf{J}/\mathbf{\psi }\to \mathbf{\eta }({\mathbf{\eta }}^{\prime }){\mathbf{h}}_1(1170)$ and $\mathbf{J}/\mathbf{\psi }\to {\mathbf{\pi }}^0{\mathbf{b}}_1(1235{)}^0$ reactions
• Role of the triangle mechanism in the ${\Lambda }_b\to {\Lambda }_c{\pi }^{-}{f}_0(980)$ reaction
• Electromagnetic interactions of mesons induced by the axial-vector -- pseudoscalar mixings