The production of the $f_1(1285)\gamma$ and $a_1(1260)\gamma$ in colliding $e^{+}{e}^{-}$-beams in threshold domain

The processes $e^{+}{e}^{-}\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}(f_1(1285),a_1(1260))\gamma$ in threshold domain are considered in the framework of the extended Nambu–Jona-Lasinio model. The channels with the ground $\rho (770)$, $\omega (782)$ and radially excited $\rho (1450)$, $\omega (1420)$ intermediate meson states are taken into account. It is shown that in the process $e^{+}{e}^{-}\to f_1(1285)\gamma$, the probability of the subprocesses with $\rho$-mesons significantly exceeds the probability of the subprocesses with $\omega$-mesons, whereas, in the process $e^{+}{e}^{-}\to a_1(1260)\gamma$, $\rho$- and $\omega$-channels give approximately equal contributions. The mechanism of this effect is discussed. The radiative decay widths of $\rho (1450)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}{f}_1(1285)\gamma$, $\omega (1420)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}{f}_1(1285)\gamma$, $\rho (1450)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}{a}_1(1260)\gamma$ and $\omega (1420)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}{a}_1(1260)\gamma$ are calculated.