Unified Balance Functions

The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve as a probe of the diffusivity of light quarks as well as the evolution of the systems formed in heavy-ion collisions. In this work, we reexamine the formulation of general balance functions and consider how to best define and measure these correlation functions in terms of differences of conditional densities of unlike-sign and like-sign particle pairs. We define general balance functions in terms of associated particle functions and show these obey a simple sum rule. We additionally proceed to distinguish between balance functions expressed as differences of conditional densities valid irrespective of experimental acceptance boundaries and bound balance functions that explicitly account for the limited acceptance of experiments. General balance functions are additionally extended to accommodate strange, baryon, as well as charm and bottom quantum numbers based on the densities of these quantum numbers.