Deconfinement and chiral restoration in non-local PNJL models at zero and imaginary chemical potential

Abstract

We study the deconfinement and chiral restoration transitions in the context of non-local PNJL models, considering the impact of the presence of dynamical quarks on the scale parameter appearing in the Polyakov potential. We show that the corresponding critical temperatures are naturally entangled for both zero and imaginary chemical potential, in good agreement with lattice QCD results. We also analyze the Roberge Weiss transition, which is found to be first order at the associated endpoint.PACS numbers: 12.39. Ki, 11.30.Rd, 12.38.Mh The detailed understanding of the behavior of strongly interacting matter at finite temperature and baryon density represents an issue of great interest in particle physics [1]. From the theoretical point of view, this problem can be addressed through lattice QCD calculations [2-4], which have been significantly improved in the last years. However, this ab initio approach is not yet able to provide a full understanding of the QCD phase diagram. One well-known difficulty is given by the so-called sign problem, which arises when dealing with finite real chemical potentials. Thus, it is worth to develop alternative approaches, such as the study of effective models that show consistency with lattice QCD results and can be extrapolated into regions not accessible by lattice techniques.One of these effective theories, proposed quite recently, is the so-called Polyakov-Nambu-JonaLasinio (PNJL) model [5][6][7][8][9][10][11], an extension of the well-known NJL model [12] in which quarks are coupled to the Polyakov loop (PL), providing a common framework to study both the chiral and deconfinement transitions. As a further improvement over the (local) PNJL model, extensions that include covariant non-local quark interactions have also been considered [13][14][15]. The non-local character of the interactions arises naturally in the context of several successful approaches to low-energy quark dynamics, and leads to a momentum dependence in the quark propagator that can be made consistent [16] with lattice results. It has been shown [17][18][19][20] that non-local models

Deconfinement and chiral restoration in nonlocal SU(3) chiral quark models

“…[45,46]). Something similar happens in the region of imaginary chemical potential, where the entanglement between both transitions occurs in a natural way within nonlocal models [24], while in the PNJL model it can be obtained only after e.g. the inclusion of an eight-quark interaction [47].…”

Chiral phase transition in two-flavor QCD from an imaginary chemical potential

“…Results have first been obtained within a staggered fermion formulation of QCD, but efforts have been undertaken to confirm their universality also within a Wilson fermion approach [35,[37][38][39] leading to the same qualitative phase diagram [35]. The Roberge-Weiss endpoint transition, or variants of it, also has been studied in many other different contexts and QCD-like theories [40][41][42][43][44][45][46][47][48][49][50][51].…”

Roberge-Weiss endpoint at the physical point ofNf=2+1QCD

“…ii) Early studies have shown that the RW endpoint transition is first order for small quark masses, second order for intermediate masses, and again first order for large masses; the three regions are separated by two tricritical points [13][14][15]. The emergence of this interesting structure has induced many further studies in effective models [28][29][30][31][32][33][34][35][36][37][38][39][40] which try to reproduce the essential features of QCD. Moreover, interesting proposals have been made on the connection of this phase structure with that present at µ B = 0 (the so-called Columbia plot) and on the possibility to exploit the whole phase structure at imaginary chemical potential in order to clarify currently open issues on the phase structure at µ B = 0, like the order of the chiral transition for N f = 2 [21,24].…”