Properties and uses of factorial cumulants in relativistic heavy-ion collisions

We discuss properties and applications of factorial cumulants of various particle numbers and for their mixed channels measured by event-by-event analysis in relativistic heavy-ion collisions. After introducing the factorial cumulants for systems with multiparticle species, their properties are described. The uses of factorial cumulants in the study of critical fluctuations are discussed. We point out that factorial cumulants play useful roles in understanding fluctuation observables when they have underlying physics approximately described by the binomial distribution. As examples, we suggest novel utilization methods of the factorial cumulants in the study of the momentum cut and rapidity window dependences of fluctuation observables.