Adiabatic expansion of nuclear matter gas to describe violation of Feynman scaling law in multiple particle production

The main features of the rapidity density distribution of the produced hadrons in multiple particle production in nucleon collisions are; (a) the distribution in the forward region (ȳ ≥ 0) has a shape similar to the Fermi distribution, (b) the distribution in the most forward region reaches almost the maximum rapidity ymax = ln(√s/M) (M : nucleon mass), and (c) the shrinkage of the distribution from the maximum rapidity increases with the incident energy (i.e. violation of Feynman scaling law). These features are possible to be described by the assumptions that; (1) a fireball of the gas (made of nuclear matter, with the temperature Ti and with the shape of the incident nucleon with Lorentz contraction) is produced in the collision, (2) the fireball makes the adiabatic expansion, and (3) the constituent particles of the gas obey the Maxwell-Boltzmann distribution of the temperature Tf in the final state.

DESCRIPTION OF (PSEUDO-)RAPIDITY DENSITY AND TRANSVERSE MOMENTUM DISTRIBUTIONS IN A WIDE ENERGY RANGE $(\sqrt{s} = 22.4\hbox{--}7000~{\rm GeV})$

The rapidity density and transverse momentum distributions of produced particles in multiple particle production are formulated assuming that the produced particles are emitted isotropically from several emitting centers. The energy distribution of produced particles in the rest frames of respective emitting centers is that of the Tsallis statistics. The distribution of emitting centers is flat with slanting cuts at both shoulders on the rapidity axis in the center of mass system. The formulation includes six adjustable parameters, among which four are energy dependent and more important and are determined so that the transverse momentum and the (pseudo-)rapidity density distributions fit to the data at various energies. The energy dependences of the four parameters, determined empirically, reproduce quite well the energy dependence of the average transverse momentum, that of the pseudo-rapidity density at η* = 0 and that of the charged multiplicity. The energy dependence of the inelasticity is either increasing or decreasing from the assumed value of K = 0.5 at [Formula: see text], due to lack of experimental data at the most-forward rapidity region. The pseudo-rapidity density distribution at LHC energy [Formula: see text] expected by the present formulation is compared with those by the other models.