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 $({N}_{w})$ fluctuations in azimuthal partitions of width $w$ to quantitatively estimate the clustering tendency among these protons. The $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}^{2}$ observable is defined as the normalized difference between the variance of the ${N}_{w}$ distribution and the binomial baseline. We demonstrate the feasibility and characteristics of this observable through simulations using a multiphase transport (AMPT) and $\mathrm{MUSIC}+\mathrm{FIST}$ models. We also use a Gaussian correlation model to illustrate that the dependence of $\mathrm{\ensuremath{\Delta}}{\ensuremath{\sigma}}^{2}$ on $w$ can be parameterized to accurately extract the strength and the range of the input interaction among protons.