Dissipation at the two-loop level: Undressing the chiral condensate

Abstract

A simple and consistent real time analysis of the long-wavelength chiral condensate fields in the background of hard thermal modes is presented in the framework of the linear sigma model. Effective evolution equations are derived for the inhomogeneous condensate fields coupled to a heat bath. The multiple effects of the thermal background on the disoriented chiral condensate are studied using linear response theory. I determine the temperature dependence of the equilibrium condensate, and examine the modification of the sigma and pion dispersion relations as these mesons traverse a hot medium. I calculate the widths by determining the dissipative coefficients at nonzero temperature at one- and two-loop order with resummed meson masses. My results show that not only decay processes, but elastic scattering processes are significant at high temperatures, yielding to short relaxation times in the phase transition region. The relaxation times obtained are shorter than in previous estimates, making the observation of disoriented chiral condensate signals questionable. Throughout this work Goldstone's theorem is satisfied when chiral symmetry is spontaneously broken.