Methodology for analyzing proton multiplicity fluctuations with azimuthal partitions in heavy-ion collisions

A primary objective in high-energy heavy-ion collisions is to investigate the phase transition between confined and deconfined color matter. Complementary to the cumulants of conserved charges integrated over the full azimuth, we introduce a novel experimental approach to explore particle fluctuations in azimuthal partitions, which are potentially sensitive to the first-order phase transition in heavy-ion collisions. We evaluate proton multiplicity (Nw) fluctuations in azimuthal partitions of width w to quantitatively estimate the clustering tendency among these protons. The Δσ2 observable is defined as the normalized difference between the variance of the Nw distribution and the binomial baseline. We demonstrate the feasibility and characteristics of this observable through simulations using a multiphase transport (AMPT) and MUSIC+FIST models. We also use a Gaussian correlation model to illustrate that the dependence of Δσ2 on w can be parameterized to accurately extract the strength and the range of the input interaction among protons.