Currently there is much interest in subthreshold production of heavy mesons in relativistic nuclear collisions. It is expected that measurements will reveal the change of the properties of mesons in dense and hot nuclear matter. Recent measurements [1] of f mesons in Ni+Ni and Ru+Ru collisions point to relatively large production cross-sections which could not be understood till now within the framework of transport models [2].
Therefore, we study whether three-body collisions could remarkably contribute to the production of f mesons in heavy-ion collisions. Such processes have the advantage that three nucleons can share their energy. The cross section for the reaction N+2N ® f + 3N is calculated using tree-level diagrams indicated in Fig. 1. If the momentum of an intermediate particle (r, p, B) in a diagram gets on shell its value becomes singular and the diagram describes two consecutive two-body processes. Such two-step processes are usually considered in the transport models. Therefore, we have defined the genuine tree-body process after separating the singular parts from the diagrams. The upper line in Fig. 2 shows the cross section for this genuine process. However, if absorption processes in the medium are included this cross section is strongly diminished and can even take a negative value. The two-step processes with intermediate p and r mesons give together a larger cross section than that calculated with the three-body diagrams, see Fig. 2.
We conclude that genuine three-body processes are not important in nuclear matter as most of the strength can be evaluated via consecutive two-body reactions. In the case considered here the two-step processes slightly overestimate the cross section. However, it is necessary that all intermediate particles which can reach the energy shell are treated properly within transport-model calculations as they essentially contribute to particle production.

Fig. 1 Topology of tree-level diagrams contributing to the three-body f meson production. Further diagrams are used arising from time reordering and particle exchanges.		Fig. 2 Cross section of f meson production by a proton hitting a proton in a proton environment. The thin line gives the three-body cross section without intermediate rescattering whereas the other lines show the results with rescattering. For further details consult [3].

References

[1] R. Kotte (FOPI collaboration), Proc. Int. Workshop XXVIII, Hirschegg, Austria, 2000, p. 112
[2] W.S. Chung, G.Q. Li and C.M. Ko, Nucl. Phys. A 625 (1997) 347
[3] H.W. Barz and B. Kämpfer, Nucl. Phys. A 683 (2001) 594  IKH 05/31/01 © H.W. Barz