Does the NJL chiral phase transition affect the elliptic flow of a fluid at fixed $\eta/s$?

TL;DR

This study investigates whether the chiral phase transition influences the elliptic flow in heavy-ion collisions, finding that when shear viscosity to entropy ratio is fixed, the flow remains unaffected by the phase transition.

Contribution

It demonstrates that the chiral phase transition does not significantly alter elliptic flow when ta/s is held constant, despite initial suppression effects.

Findings

Elliptic flow $v_2$ is suppressed by field dynamics but not when ta/s is fixed.

The relation between $v_2$ and ta/s$ remains unaffected by the chiral phase transition.

Field dynamics generate constituent mass but do not alter $v_2$ at fixed ta/s.

Abstract

We have derived and solved numerically the Boltzmann-Vlasov transport equations that includes both two-body collisions and the chiral phase transition by mean of NJL-field dynamics. The scope is to understand if the field dynamics supply new genuine effects on the build-up of the elliptic flow $v_2$, a measure of the asymmetry in the momentum space, and in particular if it can affect the relation between $v_2$ and the shear viscosity to entropy ratio $\eta/s$. Solving the transport equation with a constant cross section for the condition of $Au+Au$ collisions at $\sqrt{s_{NN}}=200$ AGeV it is shown a sizable suppression of $v_2$ due to the attractive nature of the field dynamics that generates the constituent mass. However the key result is that if $\eta/s$ of the system is kept fixed by an appropriate local renormalization of the cross section the $v_2$ does not depend on the details of the collisional and/or field dynamics and in particular it is not affected significantly by the chiral phase transition.