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

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 $ϕ_a =(σ, \vecπ)$ 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 $ζ=1.47 \pm 0.01 ({\rm stat})$, which is compatible with the theoretical expectation of $ζ= d/2$ (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.

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