Dynamics of the O(4) critical point in QCD

Abstract

We perform a Langevin simulation of the $O(4)$ critical point, which lies in the dynamic universality class of ``model G.'' This is the dynamic universality class of the chiral phase transition in QCD with two massless flavors. The axial charge and the order parameter ${\ensuremath{\phi}}_{a}=(\ensuremath{\sigma},\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\pi}})$ 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 $\ensuremath{\zeta}=1.47\ifmmode\pm\else\textpm\fi{}0.01(\text{stat.})$, which is compatible with the theoretical expectation of $\ensuremath{\zeta}=d/2$ (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.