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By assuming the existing of memory effects and long-range interactions in thehot and dense matter produced in high energy heavy ion collisions, thenonextensive statistics together with the relativistic hydrodynamics includingphase transition is used to discuss the transverse momentum distributions ofcharged particles produced in heavy ion collisions. It is shown that thecombined contributions from nonextensive statistics and hydrodynamics can givea good description to the experimental data in Au+Au collisions at sqrt(s_NN )=200 GeV and in Pb+Pb collisions at sqrt(s_NN) )= 2.76 TeV for pi^(+ -) , K^(+-) in the whole measured transverse momentum region, and for p(p-bar) in theregion of p_T<= 2.0 GeV/c. This is different from our previous work, where, byusing the conventional statistics plus hydrodynamics, the describable region isonly limited in p_T<= 1.1 GeV/c.

A description of the transverse momentum distributions of charged particles produced in heavy ion collisions at RHIC and LHC energies