We address the issue of whether a region of disordered chiral condensate (DCC), in which the chiral condensate has components along the pion directions, can form. We consider a system going through the chiral phase transition either via a quench, or via relaxation of the high temperature phase to the low temperature one within a given time scale (of order $\sim 1 \rm{ fm/c}$). We use a density matrix based formalism that takes both thermal and quantum fluctuations into account non-perturbatively to argue that if the $O(4)$ linear sigma model is the correct way to model the situation in QCD, then it is very unlikely at least in the Hartree approximation, that a large ($> 10\ \rm{ fm}$) DCC region will form. Typical sizes of such regions are $\sim 1 -2 \ \rm{ fm}$ and the density of pions in such regions is at most of order $\sim 0.2 / \rm{ fm}^3$. We end with some speculations on how large DCC regions may be formed.
Categories: hep-ph