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

Abstract

The branching fractions of the axial vector meson decays $f_1 \to a_0 π,ππη$, $f_1 \to ρπ,πππ$ and $f_1 \to KKπ$ are calculated in the standard $U(3) \times U(3)$ quark NJL model. The intermediate channels with the states $a_0(980)π$ and $f_0(500)η$ are taken into account in the decay $f_1 \to ππη$. 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 $f_1 \to ρπ$ and $f_1 \to3π$ 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.