Exclusive $f_{1}(1285)$ meson production for energy ranges available at the GSI-FAIR with HADES and PANDA

We evaluate the cross section for the $p p \to p p f_{1}(1285)$ and $p \bar{p} \to p \bar{p} f_{1}(1285)$ reactions at near threshold energies relevant for the HADES and PANDA experiments at GSI-FAIR. We assume that at energies close to the threshold the $\omega \omega \to f_{1}(1285)$ and $\rho^{0} \rho^{0} \to f_{1}(1285)$ fusion processes are the dominant production mechanisms. The vertex for the $VV \to f_{1}$ coupling is derived from an effective coupling Lagrangian. The $g_{\rho \rho f_1}$ coupling constant is extracted from the decay rate of $f_{1}(1285) \to \rho^{0} \gamma$ using the vector-meson-dominance ansatz. We assume $g_{\omega \omega f_1} = g_{\rho \rho f_1}$, equality of these two coupling constants, based on arguments from the naive quark model and vector-meson dominance. The amplitude for the $VV \to f_{1}$ fusion, supplemented by phenomenological vertex form factors for the process, is given. The differential cross sections at energies close to the threshold are calculated. In order to determine the parameters of the model the $\gamma p \to f_{1}(1285) p$ reaction is discussed in addition and results are compared with the CLAS data. The possibility of a measurement by HADES@GSI is presented and discussed. We performed a Monte Carlo feasibility simulations of the $p p \to p p f_1$ reaction for $\sqrt{s}$ = 3.46 GeV in the $\pi^+ \pi^- \pi^+ \pi^-$ (not shown explicitly) and $\pi^+ \pi^- \pi^+ \pi^- \pi^0$ final states using the PLUTO generator. The latter one is especially promising as a peak in the $\pi^+ \pi^- \eta$ should be observable by HADES.