Phenomenological model for the ${\gamma }^{\ast }\gamma \to \eta {\pi }^{+}{\pi }^{-}$ reaction in the $f_1(1285)$ energy region

Motivated by the ongoing analysis by the BESIII Collaboration on the single-tagged $e^{+}{e}^{-}\to e^{+}{e}^{-}\eta {\pi }^{+}{\pi }^{-}$ reaction, we present a phenomenological study of the diphoton fusion to $\eta {\pi }^{+}{\pi }^{-}$, focusing on the production mechanism of the $f_1(1285)$ resonance. Contributions from the $f_1(1285)\to a_0(980{)}^{\pm }{\pi }^{\mp }$ and $f_1(1285)\to \sigma \mathrm{/}{f}_0(500)\eta$ channels are included without introducing free parameters within an effective Lagrangian approach. Assuming the destructive interference between the amplitudes, we predict the invariant mass distributions, angular distributions, and total cross sections of the ${\gamma }^{\ast }\gamma \to \eta {\pi }^{+}{\pi }^{-}$ process, which will be tested by the forthcoming BESIII measurements.