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 $pp\ensuremath{\rightarrow}pp{f}_{1}(1285)$ and $p\overline{p}\ensuremath{\rightarrow}p\overline{p}{f}_{1}(1285)$ 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 $\ensuremath{\omega}\ensuremath{\omega}\ensuremath{\rightarrow}{f}_{1}(1285)$ and ${\ensuremath{\rho}}^{0}{\ensuremath{\rho}}^{0}\ensuremath{\rightarrow}{f}_{1}(1285)$ fusion processes are the dominant production mechanisms. The vertex for the $VV\ensuremath{\rightarrow}{f}_{1}$ coupling is derived from an effective coupling Lagrangian. The ${g}_{\ensuremath{\rho}\ensuremath{\rho}{f}_{1}}$ coupling constant is extracted from the decay rate of ${f}_{1}(1285)\ensuremath{\rightarrow}{\ensuremath{\rho}}^{0}\ensuremath{\gamma}$ using the vector-meson-dominance ansatz. We assume ${g}_{\ensuremath{\omega}\ensuremath{\omega}{f}_{1}}={g}_{\ensuremath{\rho}\ensuremath{\rho}{f}_{1}}$, equality of these two coupling constants, based on arguments from the naive quark model and vector-meson dominance. The amplitude for the $VV\ensuremath{\rightarrow}{f}_{1}$ 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 $\ensuremath{\gamma}p\ensuremath{\rightarrow}{f}_{1}(1285)p$ 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 perform a Monte Carlo feasibility simulation of the $pp\ensuremath{\rightarrow}pp{f}_{1}$ reaction for $\sqrt{s}=3.46\text{ }\text{ }\mathrm{GeV}$ with the ${f}_{1}$ decaying into the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (not shown explicitly) and ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}(\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0})$ final states using the PLUTO event generator. The latter ${f}_{1}$ decay is especially promising as a peak in the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\eta}$ mass distribution should be observable by HADES.