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 $\Gamma (f_1\to\pi^+\pi^-\gamma)=346\,\mbox{keV}$ 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.
Highlights
The anomalous radiative decay f1 → ρ0γ of the axialvector IGðJPCÞ 1⁄4 0þð1þþÞf1ð1285Þ meson has been described recently [1], with dynamics determined by the effective meson Lagrangian
The model reproduces the nontrivial structure of the f1ργ vertex, and fixes fully the values of the coupling constants involved
The decay width that has been obtained, Γf1→ργ 1⁄4 311 keV, is compatible with the recently published value Γf1→ρ0γ 1⁄4 453 Æ 177 keV [10] measured for the first time in photo-production from a proton target using the CLAS detector at Jefferson Laboratory
Summary
The anomalous radiative decay f1 → ρ0γ of the axialvector IGðJPCÞ 1⁄4 0þð1þþÞf1ð1285Þ meson has been described recently [1], with dynamics determined by the effective meson Lagrangian. It would be interesting to analyze as well the role of these anomalies in the f1ð1285Þ → πþπ−γ decay. This transition has not been measured yet, a clear signal of f1ð1285Þ has been seen in the effective mass spectrum of the πþπ−γ system in the reaction π−N → π−πþπ−γN at a pion beam with the momentum pπ− 1⁄4 37 GeV=c studied at the VES spectrometer of IHEP [12]. An earlier attempt of the theoretical description of the f1ð1285Þ → πþπ−γ decay width can be found in [14] It is made in the framework of the Uð2ÞL × Uð2ÞR chiral theory of mesons.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
