# Bulk viscosity of two-flavor quark matter from the Kubo formalism

## TL;DR

This paper calculates the bulk viscosity of two-flavor quark matter at strong coupling using the Kubo formalism, highlighting the importance of multi-loop contributions near the Mott transition.

## Contribution

It introduces a detailed calculation of bulk viscosity incorporating multi-loop effects within the NJL model, emphasizing their dominance near the Mott temperature.

## Key findings

- Multi-loop contributions dominate near the Mott line.
- At high temperatures, one-loop bulk viscosity is dominant.
- Multi-loop bulk viscosity exceeds shear viscosity near the Mott temperature.

## Abstract

We study the bulk viscosity of quark matter in the strong coupling regime within the two-flavor Nambu--Jona-Lasinio model. The dispersive effects that lead to non-zero bulk viscosity arise from quark-meson fluctuations above the Mott transition temperature, where meson decay into two quarks is kinematically allowed. We adopt the Kubo-Zubarev formalism and compute the equilibrium imaginary-time correlation function for pressure in the $O(1/N_c)$ power counting scheme. The bulk viscosity of matter is expressed in terms of the Lorentz components of the quark spectral function and includes multi-loop contributions which arise via re-summation of infinite geometrical series of loop diagrams. We show that the multi-loop contributions dominate the single-loop contribution close to the Mott line, whereas at high temperatures the one-loop contribution is dominant. The multi-loop bulk viscosity dominates the shear viscosity close to the Mott temperature by factors 5 to 20, but with increasing temperature the shear viscosity becomes the dominant dissipation mechanism of stresses as the one-loop contribution becomes the main source of bulk viscosity.