Two-flavor condensates in chiral dynamics: Temperature and isospin density effects

Abstract

Isospin density and thermal corrections for several condensates are discussed, at the one-loop level, in the frame of chiral dynamics with pionic degrees of freedom. The evolution of such objects give an additional insight into the condensed-pion phase transition, that occurs basically when |µI| > mπ, being |µI| the isospin chemical potential. Calculations are done in both phases, showing a good agreement with lattice results for such condensates.This paper is an extension of our previous analysis of pion dynamics, according to chiral perturbation theory, in the presence of isospin chemical potential and temperature. In the first article [1] we discussed the evolution of the masses and decay constants from the perspective of the first phase (|µ I | < m π ). In the second paper [2], we proposed a scheme of calculation in the second phase for the pion masses (|µ I | > m π ). The method allowed us to explore the regions where the chemical potential is close to the phase transition point (|µ I | m π ) and also where |µ I | ≫ m π . The validity of this approach is restricted to values of µ I less than the η or ρ masses.Here we would like to address the thermal and density behavior of several condensates that can be buit in this frame, as well as the validity of the Gell-Mann-Oakes-Renner (GMOR) relation, completing in this way the discussion of the pion properties. We compare our results with those obtained through lattice measurements.This analysis is relevant since some of these condensates are sharp signals for the occurrence of the phase transition, i.e., phenomenological order parameters. Natural scenarios where this dynamics can play a role are in the core of neutron stars (especially during the cooling period), possible asymmetries in the pion multiplicity in the central rapidity region at RHIC or ALICE, etc.As in the previous articles, we introduce the chemical potential following [3,4]. Even though, these articles deal with QCD with two colors rather than QCD with three colors, it is clear that both problems are intimately related. The introduction of in-medium processes via isospin chemical potential has been studied at zero temperature [5,6] in both phases (|µ I | ≶ m π ) at tree level.Different approaches, such as Lattice QCD [7,8,9,10], Ladder QCD [11] and Nambu-Jona-Lasinio model based analysis [12,13,14,15,16] have confirmed the appearance of an interesting and non-trivial phase structure as function of temperature and chemical potentials, in particular isospin, chemical potential.

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

“…As suggested by the heuristic argument in the previous section, the pion condensate induces an axial condensate that points in the orthogonal direction, −φ 2φ1 T . This feature has also been observed in the context of the NJL model [15] and previously in χ PT near the critical isospin chemical potential [22] at next-to-leading order.…”

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

“…This followed various studies by other available theoretical tools yielding qualitatively similar results. These studies include chiral perturbation theory (χPT) [8][9][10][11][12][13][14][15][16][17][18][19][20], Hard Thermal Loop perturbation theory (HTLPt) [21], Nambu-Jona-Lasinio (NJL) model and its Polyakov loop extended version PNJL [43,44], quark meson model (QMM) [45][46][47][48]. Recently, early lattice QCD results have been modified by using an improved lattice action with staggered fermions at physical quark masses and results for finite isospin density are presented in Refs [49][50][51][52].…”

Electrical neutrality and $$\beta $$-equilibrium conditions in dense quark matter: generation of charged pion condensation by chiral imbalance

“…In connection with the physics of neutron star matter and experiments on heavy-ion collision, there has recently appeared an interest in the study of quark medium with isospin (isotopic) asymmetry. QCD phase diagram at nonzero values of the isotopic chemical potential μ I has been studied in different approaches, e.g., in lattice QCD approach [40][41][42][43][44][45][46][47][48], in ChPT [49][50][51][52][53], in different QCD-like effective models such as NJL model [34,38,[54][55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71], quark meson model [72,73], also in perturbative QCD (with diagrams resummation) [74,75], in effective theory at asymptotically high isospin density [76], in a random matrix model [77], in hadron resonance gas model [78]. It was shown in these papers that if there is an isospin imbalance then charged pion condensation (PC) phenomenon can be generated in quark matter.…”