Dynamics of the $O(4)$ critical point in QCD

TL;DR

This paper presents a real-time simulation of the $O(4)$ critical point in QCD, revealing the dynamical behavior of axial charge and order parameters, and extracting a critical exponent consistent with theoretical predictions.

Contribution

It provides the first detailed dynamical simulation of the $O(4)$ critical point in QCD, connecting lattice results with effective theories and critical exponents.

Findings

Extracted dynamical critical exponent $=1.47 \u00b1 0.01$

Confirmed compatibility with theoretical expectation $=d/2$

Matched lattice results to superfluid effective theory at low temperatures

Abstract

We perform a real-time simulation of the $O(4)$ critical point of QCD, which lies in the dynamic universality class of Model G. The axial charge and the order parameter $\phi_a =(\sigma, \vec{\pi})$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below $T_c$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $\zeta=1.47 \pm 0.01 ({\rm stat})$, which is compatible with the theoretical expectation of $\zeta = d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.