Multi-particle correlations, cumulants, and moments sensitive to fluctuations in rare-probe azimuthal anisotropy in heavy ion collisions

Correlations of two or more particles have been an essential tool for understanding the hydrodynamic behavior of the quark-gluon plasma created in ultra-relativistic nuclear collisions. In this paper, we extend that framework to introduce a mathematical construction of multi-particle correlators that utilize correlations between arbitrary numbers of particles of interest (e.g. particles selected for their strangeness, heavy flavor, and conserved charges) and inclusive reference particles to estimate the azimuthal anisotropies of rare probes. To estimate the fluctuations and correlations in the azimuthal anisotropies of these particle of interest, we use these correlators in a system of cumulants, raw moments, and central moments. We finally introduce two classes of observables that can compare the fluctuations in the azimuthal anisotropies of particles of interest with reference particles at each order.