Decays $f_1 \to a_0 \pi,\pi \pi \pi(\eta)$ and $f_1 \to K K \pi$ in the chiral $U(3) \times U(3)$ quark NJL model

TL;DR

This paper calculates decay branching fractions of the $f_1$ meson into various channels within the $U(3) imes U(3)$ NJL model, accounting for intermediate states and quark mass differences, aligning well with experimental data.

Contribution

It provides the first comprehensive calculation of $f_1$ meson decay branching fractions in the NJL model without arbitrary parameters, including intermediate states and quark mass effects.

Findings

Calculated decay branching fractions agree with experimental data.

Decays $f_1 o ho o 3 ext{pions}$ occur due to $u$ and $d$ quark mass differences.

Intermediate channels with scalar mesons are effectively incorporated.

Abstract

The branching fractions of the axial vector meson decays $f_1 \to a_0 \pi,\pi\pi\eta$, $f_1 \to \rho \pi,\pi\pi\pi$ and $f_1 \to KK\pi$ are calculated in the standard $U(3) \times U(3)$ quark NJL model. The intermediate channels with the states $a_0(980)\pi$ and $f_0(500)\eta$ are taken into account in the decay $f_1 \to \pi\pi\eta$. In the case of the scalar mesons, the $\bar{q}q$ representation as a chiral symmetric partners of the pseudoscalar mesons is used. It is shown that the decays $f_1 \to \rho \pi$ and $f_1 \to3\pi$ occur due to the mass difference of the $u$ and $d$ quarks. All the results are obtained without using any additional arbitrary parameters and are in satisfactory agreement with the known experimental data.