Geometrical scaling of inclusive charged hadron $p_{\mathrm{T}}$ spectra in Pb-Pb collsions at 2.76 TeV

Abstract

In Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV, we report on a geometrical scaling in the transverse momentum ($p_{\mathrm{T}}$) spectra of inclusive charged hadrons at 0-5$\%$, 5-10$\%$, 10-20$\%$, 20-30$\%$, 30-40$\%$, 40-50$\%$, 50-60$\%$, 60-70$\%$ and 70-80$\%$ centralities. This geometrical scaling is exhibited when these spectra are expressed in terms of a new scaling variable, $p_{\mathrm{T}}^{\prime }=p_{\mathrm{T}}(191.5/N_A{)}^{1/(3\lambda +6)}$, where $N_A$ is the number of participating nucleon pairs, $\lambda$ is the scaling parameter. With the method of ratios, this scaling parameter is determined to be 1.68. We then use a single Tsallis distribution to parameterize the spectra at different centralities, and find that the Tsallis temperature $T$ is proportional to $N_A^{1/(3\lambda +6)}$, which is exactly the prediction of the geometrical scaling. The geometrical scaling also predicts that the charged-particle density per participating nucleon pair ($(d{N}_{\mathrm{ch}}/d\eta )/N_A$) grows as a power of $N_A$, $N_A^{2/(3\lambda +6)}$, which is confirmed by the data collected by the ALICE collaboration.

Comments: 6 pages, 5 EPS figures included. In v2, another table is added, and the fifth reference has been changed