Bulk viscosity and the phase transition of the linear sigma model

Abstract

In this work, we deal with the critical behavior of the bulk viscosity in the linear sigma model (LσM) as an example of a system which can be treated by using different techniques. Starting from the Boltzmann-Uehling-Uhlenbeck equation, we compute the bulk viscosity over entropy density of the LσM in the large-N limit. We search for a possible maximum of ξ/s at the critical temperature of the chiral phase transition. The information about this critical temperature, as well as the effective masses, is obtained from the effective potential. We find that the expected maximum ( as a measure of the conformality loss) is absent in the large-N limit in agreement with other models in the same limit. However, this maximum appears when, instead of the large-N limit, the Hartree approximation within the Cornwall-Jackiw-Tomboulis formalism is used. Nevertheless, this last approach to the L sigma M does not give rise to the Goldstone theorem and also predicts a first-order phase transition instead of the expected second-order one. Therefore, both the large-N limit and the Hartree approximations, should be considered relevant and informative for the study of the critical behavior of the bulk viscosity in the LσM.