Isospin Fluctuations in QCD and Relativistic Heavy-Ion Collisions

We address the role of fluctuations in strongly interacting matter during the dense stages of a heavy-ion collision through its electromagnetic emission. Fluctuations of isospin charge are considered in a thermal system at rest as well as in a moving hadronic fluid at fixed proper time within a finite bin of pseudo-rapidity. In the former case, we use general thermodynamic relations to establish a connection between fluctuations and the space-like screening limit of the retarded photon self-energy, which directly relates to the emissivities of dileptons and photons. Effects of hadronic interactions are highlighted through two illustrative calculations. In the latter case, we show that a finite time scale $\tau$ inherent in the evolution of a heavy-ion collision implies that equilibrium fluctuations involve both space-like and time-like components of the photon self-energy in the system. Our study of non-thermal effects, explored here through a stochastic treatment, shows that an early and large fluctuation in isospin survives only if it is accompanied by a large temperature fluctuation at freeze-out, an unlikely scenario in hadronic phases with large heat capacity. We point out prospects for the future which include: (1) A determination of the Debye mass of the system at the dilute freeze-out stage of a heavy-ion collision, and (2) A delineation of the role of charge fluctuations during the dense stages of the collision through a study of electromagnetic emissivities.