Shear and bulk viscous coefficients of a hot and chirally imbalanced quark matter using NJL model

The shear <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>η</a:mi></a:math> and bulk <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>ζ</c:mi></c:math> viscous coefficients have been calculated in a hot and chirally asymmetric quark matter quantified in terms of a chiral chemical potential (CCP) using the two-flavor Nambu-Jona–Lasinio (NJL) model. This is done by employing the one-loop Green-Kubo formalism where the viscous coefficients have been extracted from the long-wavelength limit of the in-medium spectral function corresponding to the energy momentum tensor (EMT) current correlator calculated using the real time formalism of finite temperature field theory. The momentum dependent thermal width of the quark/antiquark that enters into the expression of the viscosities as a dynamical input containing interactions, has been obtained from the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>2</e:mn><e:mo stretchy="false">→</e:mo><e:mn>2</e:mn></e:math> scattering processes mediated via the collective mesonic modes in scalar and pseudoscalar channels encoded in respective in-medium polarization functions having explicit temperature and CCP dependence. Several thermodynamic quantities such as pressure, energy density, entropy density (<h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mi>s</h:mi></h:math>), specific heat and isentropic speed of sound have also been calculated at finite CCP. The temperature and CCP dependence of the viscosity to entropy density ratios <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>η</j:mi><j:mo>/</j:mo><j:mi>s</j:mi></j:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi>ζ</l:mi><l:mo>/</l:mo><l:mi>s</l:mi></l:math> have also been studied.