Scaling of factorial moments in cumulative variables

Abstract

A search for power-law fluctuations within the framework of the intermittency method is ongoing to locate the critical point of the strongly interacting matter. In particular, experimental data on proton and pion production in heavy-ion collisions are analyzed in transverse-momentum, pT, space.In this regard, we have studied the dependence of the second scaled factorial moment F2 of particle multiplicity distribution on the number of subdivisions of transverse momentum-interval used in the analysis. The study is performed using a simple model with a power-law two-particle correlation function in pT. We observe that F2 values depend on the size and position of the pT interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, F2 calculated in subdivisions of the cumulative pT becomes independent of the cumulative-pT interval. The scaling behaviour of F2 for the cumulative variable is observed. Moreover, F2 follows a power law with the number of subdivisions of the cumulative-pT interval with the intermittency index close to the correlation function's exponent.