Quark Number Susceptibility : Revisited with Fluctuation-Dissipation Theorem in mean field theories

TL;DR

This paper revisits quark number susceptibilities using the fluctuation-dissipation theorem within mean field theories, clarifying the calculation of static correlators and susceptibilities with implicit mean field dependencies.

Contribution

It provides a rigorous diagrammatic approach to compute quark number susceptibilities in mean field theories, including the implicit dependence of mean fields on chemical potential.

Findings

Diagrammatic calculation of static correlators is feasible with proper mean field dependence.

Explicit analytical method for mean field dependence on chemical potential.

Reinforces the connection between fluctuations and thermodynamic susceptibilities.

Abstract

Fluctuations of conserved quantum numbers are associated with the corresponding susceptibilities because of the symmetry of the system. The underlying fact is that these fluctuations as defined through the static correlators become identical to the direct calculation of these susceptibilities defined through the thermodynamic derivatives, due to the fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show that a diagrammatic calculation of the static correlators associated with the conserved quark number fluctuations and the corresponding susceptibilities are possible in case of mean field theories, if the implicit dependence of the mean fields on the quark chemical potential are taken into account appropriately. As an aside we also give an analytical prescription for obtaining the implicit dependence of the mean fields on the quark chemical potential.