Energy density and path-length dependence of the fractional momentum loss in heavy-ion collisions at $\sqrt{s_{NN}}$ from 62.4 to 5020 GeV

In this work a study of the fractional momentum loss ($S_{\mathrm{loss}}$) as a function of the characteristic path length ($L$) and the Bjorken energy density times the equilibration time (${\epsilon }_{\mathrm{Bj}}{\tau }_0$) for heavy-ion collisions at different $\sqrt{s_{NN}}$ is presented. The study has been conducted using inclusive charged particles from intermediate to large transverse momentum ($5<p_T<20$ GeV/$c$). Within uncertainties and for all the transverse momentum values which were explored, the fractional momentum loss is found to increase linearly with ${\left({\epsilon }_{\mathrm{Bj}}{\tau }_0\right)}^{3/8}L$. For identified hadrons, albeit a smaller slope of $S_{\mathrm{loss}}$ vs. ${\left({\epsilon }_{\mathrm{Bj}}{\tau }_0\right)}^{3/8}L$ is observed for (anti)protons at ${p_T}^{}=5\mathrm{GeV}/c,S_{\mathrm{loss}}$ is also found to grow linearly with $L$. The behavior of data could provide important information aimed at understanding the parton energy loss mechanism in heavy-ion collisions and some insight into the expected effect for small systems.

Figure 1

Number of participants distributions obtained from Glauber simulations for Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV. Results for 0–5% (left), 20–30% (middle), and 70–80% (right) are displayed.

Figure 2

Fractional momentum loss ($S_{\mathrm{loss}}$) as a function of ${\epsilon }_{\mathrm{Bj}}{\tau }_0$. Results for three values of transverse momentum measured in $pp$ collisions are displayed: $p_{}^{pp}=5$ GeV/$c$ (left), 10 GeV/$c$ (middle), and 15 GeV/$c$ (right). Data from Pb-Pb at $\sqrt{s_{NN}}=2.76$ [26] and 5.02 TeV [24], Au-Au at 62.4 and 200 GeV, and Cu-Cu at $\sqrt{s_{NN}}=200$ GeV [15] are used for the extraction of the quantities. Systematic uncertainties are displayed as boxes around the data points.

Figure 3

Fractional momentum loss ($S_{\mathrm{loss}}$) as a function of ${\left({\tau }_0{\epsilon }_{\mathrm{Bj}}\right)}^{3/4}{L}^2$. Results for three values of transverse momentum measured in $pp$ collisions are displayed: $p_{}^{pp}=5$ GeV/$c$ (left), 10 GeV/$c$ (middle), and 15 GeV/$c$ (right). Data from Pb-Pb at $\sqrt{s_{NN}}=2.76$ [26] and 5.0 TeV [24], Au-Au at 62.4 and 200 GeV, and Cu-Cu at $\sqrt{s_{NN}}=200$ GeV [15] are used for the extraction of the quantities. Systematic uncertainties are displayed as boxes around the data points.

Figure 4

Fractional momentum loss ($S_{\mathrm{loss}}$) as a function of ${\left({\tau }_0{\epsilon }_{\mathrm{Bj}}\right)}^{3/8}L$. Results for three values of transverse momentum measured in $pp$ collisions are displayed: $p_{}^{pp}=5$ GeV/$c$ (left), 10 GeV/$c$ (middle), and 15 GeV/$c$ (right). Data from Pb-Pb at $\sqrt{s_{NN}}=2.76$ [25, 26] and 5.0 TeV [24], Au-Au at 62.4 and 200 GeV, and Cu-Cu at $\sqrt{s_{NN}}=200$ GeV [15] are used for the extraction of the quantities. Systematic uncertainties are displayed as boxes around the data points. Results for inclusive charged particles measured at different $\sqrt{s_{NN}}$ are displayed in the top panel. The bottom panel shows the results for charged pions, kaons, and (anti)protons in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76\text{TeV}$.