$\phi$ Meson Production in Heavy-Ion Collisions at SIS Energies

Phi meson production in heavy-ion collisions at SIS/GSI energies ($\sim 2$ GeV/nucleon) is studied in the relativistic transport model. We include contributions from baryon-baryon, pion-baryon, and kaon-antikaon collisions. The cross sections for the first two processes are obtained in an one-boson-exchange model, while that for the last process is taken to be of Breit-Wigner form through the phi meson resonance. The dominant contribution to phi meson production in heavy ion collisions at these energies is found to come from secondary pion-nucleon collisions. Effects due to medium modifications of kaon masses are also studied and are found to reduce the phi meson yield by about a factor of two, mainly because of increased phi decay width as a result of dropping kaon-antikaon masses. In this case, the $\phi/K^-$ ratio is about 4%, which is a factor of 2-3 below preliminary experimental data from the FOPI collaboration at GSI. Including also the reduction of phi meson mass in medium increases this ratio to about 8%, which is then in reasonable agreement with the data