Scaling of factorial moments in cumulative variables

TL;DR

This paper investigates the scaling behavior of factorial moments in cumulative transverse momentum variables, demonstrating that transforming to cumulative variables reveals power-law scaling and intermittency consistent with underlying correlations.

Contribution

It introduces a method to analyze factorial moments in cumulative variables, showing that this transformation uncovers scale-invariant behavior in particle production data.

Findings

F2 depends on pT interval size and position in original variables

Transforming to cumulative variables makes F2 independent of interval choice

F2 exhibits power-law scaling with the number of subdivisions 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, $p_T$, space. In this regard, we have studied the dependence of the second scaled factorial moment $F_2$ 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 $p_T$. We observe that $F_2$ values depend on the size and position of the $p_T$ interval. However, when we convert the non-uniform transverse-momentum distribution to uniform one using cumulative transformation, $F_2$ calculated in subdivisions of the cumulative $p_T$ becomes independent of the cumulative-$p_T$ interval. The scaling behaviour of $F_2$ for the cumulative variable is observed. Moreover, $F_2$ follows a power law with the number of subdivisions of the cumulative-$p_T$ interval with the intermittency index close to the correlation function's exponent.