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

TL;DR

This paper calculates the decay amplitude and width of the anomalous radiative decay $f_1(1285) o ^+^-$ using the NJL model, highlighting the dominant role of the $ ho^0$-resonance exchange over $a_1(1260)$ exchange.

Contribution

It introduces a novel calculation of the decay process within the NJL model emphasizing the significance of the $ ho^0$-resonance exchange, contrasting with previous models.

Findings

Decay width $$ of 346 keV was obtained.

Spectral di-pion mass distribution was derived.

$ ho^0$-resonance exchange is the dominant contribution.

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.