How Disoriented Chiral Condensates Form: Quenching vs. Annealing

We demonstrate that semiclassical fluctuations, their relaxation, and the chiral phase transition are automatically incorporated in the numerical simulations of the classical equations of motion in the linear σ-model when longitudinal and transverse expansions are included. We find that domains of disoriented chiral condensate with 4–5 fm in size can form through a quench while an annealing leads to domains of smaller sizes. We also demonstrate that quenching cannot be achieved by relaxing a chirally symmetric system through expansion. 25.75.+r, 11.30.Rd, 12.38.Mh Typeset using REVTEX 1 One of the proposed explanations for the Centauro events [1] in high energy cosmic ray experiments is the coherent emission of pions from a large domain of disoriented chiral condensate (DCC) [2]. However, if the system has to go through an equilibrium phase transition, quark masses, though much smaller than the intrinsic QCD scale, prevent DCC domains from reaching a size larger than 1/Tc [3]. As an alternative, Rajagopal and Wilczek [4] proposed that a nonequilibrium phase transition through quenching can generate large DCC domains. Their numerical simulation indeed observed the amplification of the long wavelength modes of the pion fields, but did not shed light on the size of DCC domains. Similar simulations by Gavin, Gocksch, and Pisarski [5] are, however, not conclusive about the exact size of DCC domains, since they only looked at the pion fields averaged over the transverse dimensions which cannot reveal domains smaller than the lattice size. To model a quench, Rajagopal and Wilczek argued that one can evolve the classical fields according to the zero temperature equations of motion from a chirally symmetrical initial condition with short correlation lengths. In this Letter, we shall argue that semiclassical fluctuations introduced in the initial configuration actually render the effective potential to a non-zero temperature one. The interaction between the mean fields and the semiclassical fluctuations as well as their evolution can be automatically included in the numerical simulations of the equations of motion. Using an ensemble averaging technique, we demonstrate the relaxation of the fluctuations and the occurrence of the chiral phase transition due to the longitudinal [6] and transverse expansions which are consistently included in our study, whereas in earlier simulations [4,5] the system only evolves in an approximately constant [7] but non-zero temperature effective potential. By choosing different initial configurations (both the mean fields and the fluctuations), we study the evolution of the system in both quenching [4] and annealing [8,9] scenarios. In the standard linear σ-model, the equations of motion are given by,