Isospin-symmetry breaking and baryon-isospin correlations from the Polyakov–Nambu–Jona-Lasinio model

Abstract

We present a study of the 1+1 flavor system of strongly interacting matter in terms of the Polyakov−Nambu−Jona-Lasinio model. We find that though the small isospin symmetry breaking brought in through unequal light quark masses is too small to affect the thermodynamics of the system in general, it may have significant effect in baryon-isospin correlations and have a measurable impact in heavy-ion collision experiments. PACS numbers: 12.38.Aw, 12.38.Mh, I. INTRODUCTIONSignatures of phases of matter with deconfined color charges is under critical investigation for last few decades, both theoretically and experimentally. Quantum Chromodynamics (QCD) is the formulation for first principle studies of strongly interacting matter. Along with the local color symmetry, the quark sector has few global symmetries also. In the chiral limit for two light flavors u and d, we have global vector and axial vector symmetry SU V (2) ⊗ SU A (2). For non-zero quark masses, the axial symmetry SU A (2) is explicitly broken, while for non-zero quark mass difference vector (isospin) symmetry SU V (2) is explicitly broken. At low energies the isospin symmetry breaking (ISB) has relevance in many aspects of hadronic observables [1]. Apart from the quark mass difference, ISB effects may be brought in by electromagnetic contributions as well. Low energy π − K scattering has been studied considering the inclusion of electromagnetic correction into the effective Lagrangian [2]. In the chiral quark model, ISB of valence and sea quark distributions in protons and neutrons has been studied in [3,4] and thermodynamics has been discussed in [5]. ISB may also have significant effect in the context of existence of CP violating phase [6]. Some Lattice QCD investigation of the effect of unequal quark masses was done in Ref. [7] and recently the effect of ISB on different hadronic observables were studied in Ref. [8,9]. Within the framework of chiral perturbation theory the isospin breaking effect in quark condensates has been studied considering m u = m d and electromagnetic corrections as well, where the authors have given an analysis of scalar susceptibilities [10,11]. Both of the above-mentioned effects have been incorporated also in Nambu−Jona-Lasinio (NJL) model [12] to study the influence of the isospin symmetry breaking on the orientation of chiral symmetry breaking.In the context of high energy heavy ion collisions where strongly interacting matter is supposed to exist in a state of thermal and chemical equilibrium, the ISB effects have not been explored much. Fluctuations and correlations of conserved charges are important and sensitive probes for heavy ion physics. Most of the theoretical studies in this respect are in isospin symmetric limit (see e.g. [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]). Here we present our first case study of ISB effect on fluctuations and correlations of strongly interacting matter within the framework of the Polyakov loop enhanced Nambu−Jona-Lasinio (PNJL) model. We discuss the possible ...

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

“…On the contrary to what happens at finite baryonic density, systems with finite isospin density does not suffer with the sign problem and hence are easily accessible to lattice QCD based calculations. Initial results of lattice QCD at finite temperature and isospin density appeared in early 2000's [6,7] and they were also investigated by other available techniques, such as chiral perturbation theory (χPT) [8][9][10][11][12][13][14][15][16][17], Hard Thermal Loop perturbation theory (HTLPt) [18], Nambu-Jona-Lasinio (NJL) model [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and its Polyakov loop extended version PNJL [36,37], quark meson model (QMM) [38][39][40][41] and the results were largely in qualitative agreement. However, all of the early lattice QCD calculations have been done considering unphysical pion masses and/or an unphysical flavour content.…”

Reparametrizing the Polyakov–Nambu–Jona-Lasinio model

“…In ref. [56] it was shown that though in general a small amount of mass difference between the two light quarks does not affect the thermodynamics of the system much, it might have a significant effect on baryon-isospin correlations. Studies of various thermodynamic quantities and fluctuation and correlations of conserved charges incorporating finite volume effects have been reported in ref.…”

Isospin symmetry breaking and Baryon-Isospin correlations in effective mean field models.

“…From this one is able to undestand the presence of m 2 scaling for some correlators. The detail analysis is shown in [9].…”