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

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 ${\varphi }_a=(\sigma ,\vec{\pi })$ 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 $\zeta =1.47\pm 0.01(\mathrm{stat})$, 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.

Comments: 33 pages, 13 figures