Anomalous decay $f_1(1285)\to {\pi }^{+}{\pi }^{-}\gamma$ in the Nambu - Jona-Lasinio model

Abstract

Using the Nambu--Jona-Lasinio model with the $U(2)\times U(2)$ chiral symmetric effective four-quark interactions, we derive the amplitude of the radiative decay $f_1(1285)\to {\pi }^{+}{\pi }^{-}\gamma$, find the decay width $\Gamma (f_1\to {\pi }^{+}{\pi }^{-}\gamma )=346\text{mbox}keV$ and obtain the spectral di-pion effective mass distribution. It is shown that in contrast to the majority of theoretical estimates (which consider the $a_1(1260)$ meson exchange as the dominant one), the most relevant contribution to this process comes out from the ${\rho }^0$-resonance exchange related with the triangle $f_1{\rho }^0\gamma$ anomaly. The spectral function is obtained to be confronted with the future empirical data.

Comments: 6 pages, 4 figures