Phenomenology of inelastic hadron-hadron interactions

A review is given of basic theoretical models describing multiple processes with small transverse momenta (psub(t)), which are the basic processes of hadron-hadron interactions at high energies. All the models are phenomenological ones. The first phenomenological level is related to the concepts of quarks and gluons as constituents of elementary particles. Further development of the quark-gluon model proceeds in the multiperipheral approach. The multiperipheral cluster model is compared in most detail with experiments on pp and π-p processes in the energy range from 28 to 200 GeV. The agreement has proved to be very good, that is demonstrated on the example of the following characteristics: total cross sections, distributions in rapidity and pairing masses, rapidity correlations, distributions in rapidity ranges, azimuthal correlations. Advances of the cluster model in describing the experiments with small psub(t) are pointed out and the need for further development of the quark approach is stressed