Regularization issues for a cold and dense quark matter model in β equilibrium

Abstract

A regularization scheme that explicitly separates vacuum contributions from medium effects is applied to a Nambu-Jona-Lasinio model with diquark interactions and in β equilibrium. We perform a comparison of this proposed scheme with the more traditional one, where no separation of vacuum and medium effects is done. Our results point to both qualitative and quantitative important differences between these two methods, in particular regarding the phase structure of the model in the cold and dense nuclear matter case.

Cold QCD at finite isospin density: Confronting effective models with recent lattice data

“…This scheme has been applied to the NJL model and successfully shows qualitative agreement with lattice simulations and more elaborated theories, as might be seen in Refs. [57,59,60].…”

“…µ I ∼ Λ [57,58]. On the other hand, the Medium Separation Scheme (MSS), coined in Refs [59,60], is based arXiv:1907.09880v2 [hep-ph] 7 Aug 2019 on a proper separation of medium effects from divergent integrals, originally having explicit medium dependence. This results in the disposal of all divergent integrals into the pure vacuum part i.e.…”

Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data

“…This scheme has been applied to the NJL model and successfully shows qualitative agreement with lattice simulations and more elaborated theories, as might be seen in Refs. [53,67,70,71]. Let us start for example from integral I ∆ of ∆ gap equation:…”

“…Since the steps to obtain these integrals for MSS are described in detail in previous references [53,70,71], here we will just show the final results of each of these integrals:…”

“…As in our previous work [53] we have tried to rectify the regularization issues within NJL model to deal with the cutting of important degrees of freedom near the Fermi surface because of a sharp ultraviolet (UV) cutoff [67][68][69]. Besides the commonly used Traditional Regularization Scheme (TRS) we have used the Medium Separation Scheme (MSS) [67,70,71], which properly separates the medium effects from divergent integrals. For systems with high values of µ I (∼ Λ) the role of MSS becomes more and more important.…”