Isospin fluctuations in QCD and relativistic heavy-ion collisions

Abstract

We address the role of fluctuations in strongly interacting matter during the dense stages of a heavyion 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 τ 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 freezeout, 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.

Electromagnetic Probes at Rhic-Ii

“…When extrapolated into the finite-µ q plane, the isoscalar quark susceptibility develops a maximum while the isopin susceptibility remains monotonic. Since the susceptibilities can be related to the space-like static limit of the corresponding correlation function in the ω and ρ channels, valuable information on the soft part of the spectral functions may be inferred [52] or at least tested for a given model. Whether the lattice results for the isoscalar susceptibility are related to an in-medium reduced ω mass e.g.…”

Charge fluctuations and electric mass in a hot meson gas

“…(D1) can be rewritten with a result corresponding to Eq. (29). For the moment we ignore the symmetrization operator A in Eq.…”

“…(31), we consider the general expression of Eq. (29) for the case of two interacting particles. This result is obtained in [42] after carrying out the trace over particle states, i.e.…”

“…Equivalently, the CF or susceptibility are related to the electromagnetic current-current correlation function [29,30] Π µν (ω, k) = i dtd 3 x e −i(ωt−kx) J µ (x, t)J ν (0)…”

Comparing different hard-thermal-loop approaches to quark number susceptibilities

“…In view of the ongoing search for quark-gluon plasma signals in the early stages of ultrarelativistic heavy-ion collisions, quark number susceptibilities (QNS) have recently received enhanced attention because of their direct connection with fluctuations of conserved charges which could in principle discriminate against a purely hadronic phase [1][2][3]. Concurrently, new results for QNS have become available from lattice gauge theory [4,5] which considerably improve upon previous studies [6], and moreover extend them to higher T /T c .…”