General Charge Balance Functions, A Tool for Studying the Chemical Evolution of the Quark-Gluon Plasma

In the canonical picture of the evolution of the quark-gluon plasma during a high-energy heavy-ion collision, quarks are produced in two waves. The first is during the first fm/c of the collision, when gluons thermalize into the QGP. After a roughly isentropic expansion that roughly conserves the number of quarks, a second wave ensues at hadronization, 5-10 fm/c into the collision. Since each hadron contains at least two quarks, the majority of quark production occurs at this later time. For each quark produced in a heavy-ion collision, an anti-quark of the same flavor is created at the same point in space-time. Charge balance functions identify, on a statistical basis, the location of balancing charges for a given hadron, and given the picture above one expects the distribution in relative rapidity of balancing charges to be characterized by two scales. After first demonstrating how charge balance functions can be created using any pair of hadronic states, it will be shown how one can identify and study both processes of quark production. By considering balance functions of several hadronic species, and by performing illustrative calculations, this class of measurement appears to hold the prospect of providing the field's most stringent insight into the chemical evolution of the QGP.