Quark number susceptibility: Revisited with fluctuation-dissipation theorem in mean field theories

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 the 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.

Dilepton and photon production in the presence of a nontrivial Polyakov loop

“…In this instance, identities similar to eq. (3.23) hold for a n a (E) and a n a (E) separately, and are again equal to those in the PNJL model, [57,58,99]. )…”

“…We can also make contact with results from Polyakov Nambu-Jona-Lasino (PNJL) models [56][57][58], especially with the computation of dilepton production by Islam, Majumder, Haque, and Mustafa [99]. To do so we need a simple identity.…”

“…In refs. [57,58,99] this effective distribution function was obtained by taking the derivative of the free energy, when = 1, with respect to a given energy E. Since the free energy involves a sum over all colors, it is clear that defining the effective statistical distribution function in this way automatically gives a sum over all n a (E) (or n a (E)), which appears on the left hand side of eq. (3.23).…”

“…[56][57][58]99], when = 1 the effective statistical distribution function is defined as the right hand side of eq. (3.23); e.g., eqs.…”

“…There are various models which can be used to study the region near T c , which we call the "semi" Quark-Gluon Plasma. This includes Parton Hadron String Dynamics [50][51][52][53][54][55], Polyakov loop models [56][57][58], the functional renormalization group [59][60][61][62][63][64][65][66][67][68][69][70], background field methods [71][72][73], and lastly, matrix models [74][75][76][77][78][79][80][81][82][83][84][85].…”