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

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 $f_1\to 3\pi$ 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.