The Chiral Phase Transition in QCD: Critical Phenomena and Long Wavelength Pion Oscillations

Abstract

In QCD with two massless quarks, the chiral phase transition is plausibly in the same universality class as the classical O(4) magnet. To test this hypothesis, critical exponents characterizing the behaviour of universal quantities near the 2nd order critical point can be calculated and compared to results from lattice simulations. Present simulations already allow many qualitative tests; quantitative tests await future simulations with longer correlation lengths. In a heavy ion collision, a long correlation length would lead to large fluctuations in the number ratio of neutral to charged pions. Unfortunately, no equilibrium correlation length gets long enough for this to occur. Modelling the dynamics of the chiral order parameter in a far from equilibrium transition by quenching in the linear sigma model suggests that long wavelength modes of the pion field can be amplified. This could have dramatic phenomenological consequences. Theoretical advances include attempts to relax the quench approximation and to include expansion and quantum effects. Long wavelength pion oscillations arise in a number of theoretical treatments; however, all involve idealizations and are at best qualitative guides. It is up to experimentalists to determine whether such phenomena occur; detection in a heavy ion collision would imply an out of equilibrium chiral transition.