# Critical behavior of the bulk viscosity in QCD

## TL;DR

This paper investigates the critical behavior of bulk viscosity in QCD near a potential critical point, estimating its divergence and sensitivity to assumptions about the phase diagram's alignment.

## Contribution

It provides a quantitative estimate of the bulk viscosity's critical divergence in QCD and highlights the importance of the phase diagram's orientation assumptions.

## Key findings

- Bulk viscosity diverges as $(\xi/\xi_0)^{x_\xi}$ with $x_\xi \,\approx 3$.
- The proportionality constant $a$ is approximately $10^{-4}$.
- Critical bulk viscosity can approach shear viscosity if the phase diagram assumptions are altered.

## Abstract

We study the behavior of the bulk viscosity $\zeta$ in QCD near a possible critical endpoint in the phase diagram. We verify the expectation that $(\zeta/s)\sim a(\xi/\xi_0)^{x_\zeta}$, where $s$ is the entropy density, $\xi$ is the correlation length, $\xi_0$ is the non-critical correlation length, $a$ is a constant and $x_\zeta\simeq 3$. Using a recently developed equation of state that includes a critical point in the universality class of the Ising model we estimate the constant of proportionality $a$. We find that $a$ is typically quite small, $a\sim O(10^{-4})$. We observe, however, that the result is sensitive to the commonly made assumption that the Ising temperature axis is approximately aligned with the QCD baryon chemical potential axis. If this is not the case, then the critical $\zeta/s$ can approach the non-critical value of $\eta/s$, where $\eta$ is the shear viscosity, even if the enhancement of the correlation length is modest, $\xi/\xi_0\sim 2$.