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

In Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV, we report on a geometrical scaling in the transverse momentum ($p_{\rm T}$) 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, $p_{\rm T}^{\prime}=p_{\rm T}(191.5/N_{A})^{1/(3\lambda+6)}$, 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 ($(dN_{\rm ch}/d\eta)/N_{A}$) grows as a power of $N_{A}$, $N_{A}^{2/(3\lambda+6)}$, which is confirmed by the data collected by the ALICE collaboration.

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