Effect of chiral imbalance on the electrical conductivity of hot and dense quark matter using Green-Kubo Method within the 2-flavour gauged NJL model

TL;DR

This study investigates how chiral imbalance influences the electrical conductivity of hot, dense quark matter using the NJL model and Green-Kubo method, revealing a strong dependence at low temperatures.

Contribution

It introduces a calculation of electrical conductivity considering chiral imbalance within the NJL model using the Green-Kubo approach, including spectral functions and scattering effects.

Findings

Electrical conductivity to temperature ratio depends significantly on chiral chemical potential.

Chiral imbalance affects the spectral function and scattering amplitudes in the model.

Results highlight the importance of chiral imbalance at low temperatures.

Abstract

The electrical conductivity of hot and dense quark matter is calculated using the 2-flavour gauged Nambu-Jona--Lasinio (NJL) model in the presence of a chiral imbalance quantified in terms of a chiral chemical potential (CCP). To this end, the in-medium spectral function corresponding to the vector current correlator is evaluated employing the real time formulation of finite temperature field theory. Taking the long wavelength limit of the spectral function we extract the electrical conductivity using the Green-Kubo relation. The thermal widths of the quarks/antiquarks that appear in the expression of electrical conductivity are calculated by considering the $2\to2$ scattering in the NJL model. The scattering amplitudes containing the polarization functions of the mesonic modes in the scalar and pseudoscalar channels are also evaluated by considering finite value of CCP. We find that the ratio of electrical conductivity to temperature has significant dependence on CCP especially in the low temperature region.