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With the experimental data collected by the ALICE collaboration in Pb-Pbcollisions at a center-of-mass energy per nucleon pair 2.76 TeV for sixdifferent centralities (0-5$\%$, 5-10$\%$, 10-20$\%$, 20-40$\%$, 40-60$\%$ and60-80$\%$), we investigate the scaling property of the pion, kaon and protontransverse momentum ($p_{\rm{T}}$) spectra at these centralities. We show thatin the low $p_{\rm{T}}$ region with $p_{\rm T} \leq$ 2.75 (3.10 and 2.35) GeV/cthe pion (kaon and proton) spectra exhibit a scaling behaviour independent ofthe centrality of the collisions. This scaling behaviour arises when thesespectra are presented in terms of a suitable variable, $z=p_{\rm{T}}/K$. Thescaling parameter $K$ is determined by the quality factor method and isparameterized by $a \langle N_{\rm{part}}\rangle^{b}$, where $\langleN_{\rm{part}}\rangle$ is the average value of the number of participatingnucleons, $a$ and $b$ are free parameters, $b$ characterizes the rate at which$\textrm{ln} K$ changes with $\textrm{ln} \langle N_{\rm{part}}\rangle$. Thevalues of $b$ for pions and kaons are consistent within uncertainties, whilethey are smaller than that for protons. In the high $p_{\rm{T}}$ region, due tothe suppression of the spectra, a violation of the proposed scaling is observedgoing from central to peripheral collisions. The more peripheral the collisionsare, the more clearly violated the proposed scaling becomes. In the frameworkof the colour string percolation model, we argue that the pions, kaons andprotons originate from the fragmentation of clusters which are formed bystrings overlapping and the cluster's fragmentation functions are different fordifferent hadrons. The scaling behaviour of the pion, kaon and proton spectrain the low $p_{\rm T}$ region can be simultaneously explained by the colourstring percolation model in a qualitative way.

Universal scaling of the pion, kaon and proton $p_{\rm{T}}$ spectra in Pb-Pb collisions at 2.76 TeV