Deciphering the universal scaling of particle transverse momentum spectra in heavy-ion collisions
We systematically investigate the scaling properties of the transverse momentum spectra for pions, kaons, and protons in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV, as well as in U+U collisions at $\sqrt{s_{NN}}$ = 193 GeV, across different centrality classes, using experimental data from the collaborations at the Relativistic Heavy Ion Collider (RHIC). Universal scaling emerges when the particle transverse momentum spectra are scaled by global physical quantities, i.e., the average total particle multiplicity and mean transverse momentum, confirming recent scaling findings from the data at the Large Hadron Collider (LHC) by the ExTrEMe collaboration. The scaling behavior breaks down in the high $p_{T}$ region and in peripheral collisions. We provide a natural explanation for these observations by invoking the Cooper-Frye formula, which is used for hadronization in hydrodynamics. Furthermore, we demonstrate the equivalence between the scaling found by the ExTrEMe collaboration and the Hwa-Yang scaling which was proposed two decades ago.