Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model

Abstract

<jats:title>Abstract</jats:title><jats:p>In this article, we study the two-flavor Nambu and Jona-Lasinio (NJL) phase diagrams on the <jats:italic>T</jats:italic>–<jats:italic>μ</jats:italic> plane through three regularization methods. In one of these, we introduce an infrared three-momentum cutoff in addition to the usual ultraviolet regularization to the quark loop integrals and compare the obtained phase diagrams with those obtained from the NJL model with proper time regularization and Pauli–Villars regularization. We have found that the crossover appears as a band with a well-defined width in the <jats:italic>T</jats:italic>–<jats:italic>μ</jats:italic> plane. To determine the extension of the crossover zone, we propose a novel criterion, comparing it to another criterion that is commonly reported in the literature; we then obtain the phase diagrams for each criterion. We study the behavior of the phase diagrams under all these schemes, focusing on the influence of the regularization procedure on the crossover zone and the presence or absence of critical end points.</jats:p>

Effects of a Finite Volume in the Phase Structure of QCD

“…For a system with infinite volume, critical temperatures calculated with the local criterion are always higher than the ones calculated with the global criterion [84,85], but with Dirichlet conditions systems with very small volumes, the opposite happens: local criterion critical temperatures are lower than global criterion ones. This feature can be observed by comparing the phase diagrams for L = 4 fm in Figures 3a and 4a A very similar result was obtained for L = 1 fm (Figures 3c and 4c).…”

“…In the proper time regularization, the chiral condensate is transformed through the identity [33,84]…”