Scaling of hadronic transverse momenta in a hydrodynamic treatment of relativistic heavy ion collisions

The transverse momenta of hadrons in central nucleus-nucleus collisions are evaluated in a boost invariant hydrodynamics with transverse expansion. Quark gluon plasma is assumed to be formed in the initial state which expands and cools via a first order phase transition to a rich hadronic matter and ultimately undergoes a freeze-out. The average transverse momentum of pions, kaons, and protons is estimated for a wide range of multiplicity densities and transverse sizes of the system. For a given system it is found to scale with the square-root of the particle rapidity density per unit transverse area, and consistent with the corresponding values seen in $p\overline{p}$ experiments at 1800 GeV, suggesting a universal behaviour. The average transverse momentum shows only an approximate scaling with multiplicity density per nucleon which is at variance with the $p\overline{p}$ data.