The anomalous decay $f_1(1285)\to \rho \gamma$ and related processes

Abstract

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, ${\Gamma }_{f_1\to {\rho }^0\gamma }=311\text{mbox}keV$, ${\Gamma }_{f_1\to \omega \gamma }=34.3\text{mbox}keV$, ${\Gamma }_{a_1\to {\rho }^0\gamma }=26.8\text{mbox}keV$, ${\Gamma }_{a_1\to \omega \gamma }=238\text{mbox}keV$, 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 ${\Gamma }_{f_1\to {\rho }^0\gamma }=453\pm 177\text{mbox}keV$, but disagrees with the PDG-based estimate of ${\Gamma }_{f_1\to {\rho }^0\gamma }=1326\pm 313\text{mbox}keV$. The calculations presented require a minimum of theoretical input, and are shown to be consistent with the non-renormalization theorems of QCD.

Comments: 7 pages, 1 figure, appear in Physical Review D