Exclusive $\eta$ production in proton-proton collisions at energies available at the GSI Facility for Antiproton and Ion Research

Abstract

The cross sections for the $p p \to p p \eta$ reaction are evaluated at energies relevant for the HADES, PANDA, and SIS100 experiments at GSI-FAIR. Consideration includes the $\eta$-bremsstrahlung mechanism involving intermediate proton exchange via the $\pi^{0}$, $\eta$, $\rho^{0}$, and $\omega$ exchanges and the mechanism involving the nucleon resonances $N(1535)$, $N(1650)$, $N(1710)$, and $N(1880)$ excited via the pseudoscalar- and/or vector-meson exchanges, depending on the model. The role of the $\omega \omega$- and $\rho^{0} \rho^{0}$-fusion processes with the reggeized vector-meson exchanges is also discussed. The calculation is done in an effective Lagrangian approach. To determine the parameters of the model, the $\gamma p \to \eta p$ and $\pi^{-} p \to \eta n$ reactions are studied and the results are then compared with the Crystal Ball and CLAS data. For the $p p \to p p \eta$ reaction, the model results are compared with the energy dependence of the cross section measured far from the threshold and with the differential distributions $d\sigma/d\cos{\theta_{\eta}}$ and $d\sigma/dp_{\eta}$ measured by the DISTO Collaboration. The comparison shows that the $N(1535)$ resonance is the dominant contribution and that other contributions are also important due to interference effects. Assuming that the $\rho$ exchange is the dominant resonant excitation process, the model is able to describe the available data, e.g., it reproduces the shape of the angular distributions measured by the DISTO Collaboration. Predictions are given for the HADES experiment at center-of-mass energy of $\sqrt{s} = 3.46$ GeV, which can be verified in the near future, and for planned PANDA and SIS100 experiments at higher energies.