We work out the low-energy expansion of the anomalous $f_1(1285)\to\rho\gamma$ decay amplitude by using the Nambu--Jona-Lasinio model with $U(2)\times U(2)$ chiral symmetric four-quark interactions in the one-quark-loop approximation. The related processes $f_1(1285)\to\omega\gamma$, $a_1(1260)\to\omega\gamma$, and $a_1(1260)\to\rho\gamma$, are also considered. An effective meson Lagrangian responsible for $f_1\rho\gamma$, $f_1\omega\gamma$, $a_1\rho\gamma$ and $a_1\omega\gamma$ interactions is found. The predicted radiative decay widths, $\Gamma_{ f_1\to\rho^0\gamma}=311\ \mbox{ keV}$, $\Gamma_{ f_1\to\omega\gamma}=34.3\ \mbox{ keV}$, $\Gamma_{ a_1\to\rho^0\gamma}=26.8\ \mbox{ keV}$, $\Gamma_{ a_1\to\omega\gamma}=238\ \mbox{ keV}$, allow an experimental test of the hypothesis that $f_1(1285)$ and $a_1(1260)$-mesons have a quark-antiquark nature. At present, only the $f_1(1285)\to\rho\gamma$ decay has been measured. Our result is in remarkably good agreement with the recent data of CLAS Collaboration $\Gamma_{ f_1\to\rho^0\gamma}=453\pm 177\ \mbox{ keV}$, but disagrees with the PDG-based estimate of $\Gamma_{ f_1\to\rho^0\gamma}=1326\pm 313\ \mbox{ keV}$. The calculations presented require a minimum of theoretical input, and are shown to be consistent with the non-renormalization theorems of QCD.
Categories: hep-ph