Local multiplicity fluctuations in Pb$-$Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV with ALICE at the LHC

Local multiplicity fluctuations are an useful tool to understand the dynamics of the particle production and the phase-space changes from quarks to hadrons in ultrarelativistic heavy-ion collisions. The study of scaling behavior of multiplicity fluctuations in geometrical configurations in multiparticle production can be performed using the factorial moments and recognized in terms of a phenomenon referred to as intermittency. In this contribution, the analysis of the factorial moment is presented for the multiplicity distributions of charged particles produced in Pb$-$Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV, recorded with the ALICE detector at the LHC. The normalized factorial moments (NFM), $F_{q}$ of the spatial configurations of charged particles in two-dimensional angular ($\eta,\varphi$) phase space are calculated. For a system with dynamic fluctuations due to the characteristic critical behavior near the phase transition, $F_{q}$ exhibits power-law growth with increasing bin number or decreasing bin size which indicates self-similar fluctuations. Relating the $q^{\rm{th}}$ order NFM ($F_{q}$) to the second-order NFM ($F_{2}$), the value of the scaling exponent ($\nu$) is extracted, which indicates the order of the phase transition within the framework of Ginzburg-Landau theory. The dependence of scaling exponent on the $p_{\rm{T}}$ bin width will be presented. The measurements are also compared with the corresponding results from the AMPT model and a Toy Monte Carlo (MC) simulation.