Scaling properties of fractional momentum loss of high-pThadrons in nucleus-nucleus collisions atsNNfrom 62.4 GeV to 2.76 TeV

Measurements of the fractional momentum loss $({S}_{\mathrm{loss}}\ensuremath{\equiv}\ensuremath{\delta}{p}_{T}/{p}_{T})$ of high-transverse-momentum-identified hadrons in heavy-ion collisions are presented. Using ${\ensuremath{\pi}}^{0}$ in $\mathrm{Au}+\mathrm{Au}$ and $\mathrm{Cu}+\mathrm{Cu}$ collisions at $\sqrt{{s}_{{}_{NN}}}=62.4$ and 200 GeV measured by the PHENIX experiment at the Relativistic Heavy Ion Collider and and charged hadrons in $\mathrm{Pb}+\mathrm{Pb}$ collisions measured by the ALICE experiment at the Large Hadron Collider, we studied the scaling properties of ${S}_{\mathrm{loss}}$ as a function of a number of variables: the number of participants, ${N}_{\mathrm{part}}$, the number of quark participants, ${N}_{\mathrm{qp}}$, the charged-particle density, $d{N}_{\mathrm{ch}}/d\ensuremath{\eta}$, and the Bjorken energy density times the equilibration time, ${\ensuremath{\varepsilon}}_{\mathrm{Bj}}{\ensuremath{\tau}}_{0}$. We find that the ${p}_{T}$, where ${S}_{\mathrm{loss}}$ has its maximum, varies both with centrality and collision energy. Above the maximum, ${S}_{\mathrm{loss}}$ tends to follow a power-law function with all four scaling variables. The data at $\sqrt{{s}_{{}_{NN}}}=200$ GeV and 2.76 TeV, for sufficiently high particle densities, have a common scaling of ${S}_{\mathrm{loss}}$ with $d{N}_{\mathrm{ch}}/d\ensuremath{\eta}$ and ${\ensuremath{\varepsilon}}_{\mathrm{Bj}}{\ensuremath{\tau}}_{0}$, lending insight into the physics of parton energy loss.