Chiral imbalanced hot and dense quark matter: NJL analysis at the physical point and comparison with lattice QCD

Abstract

Hot and dense quark matter with isospin and chiral imbalances is investigated in the framework of the (3+1)-dimensional Nambu-Jona-Lasinio model (NJL) in the large-Nc limit (Nc is the number of quark colors). Its phase structure is considered in terms of barion -µB, isospin -µI and chiral isospin -µI5 chemical potentials. It is shown in the paper that (i) in the chiral limit there is a duality between chiral symmetry breaking (CSB) and charged pion condensation (PC) phenomena. (ii) At the physical point, i.e. at nonzero bare quark mass m0, and temperature this duality relation is only approximate, although rather accurate. (iii) We have shown that the chiral isospin chemical potential µI5 in dense quark matter generates charged pion condensation both at zero and nonzero m0, and at µI5 = 0 this phase might be observed up to temperatures as high as 100 MeV. (iv) Pseudo-critical temperature of the chiral crossover transition rises in the NJL model with increasing µI5. (v) It has been found an agreement between particular sections of the phase diagram in the framework of NJL model and corresponding ones in lattice QCD simulations. Two different plots from different lattice simulations that are completely independent and are not connected at the first sight are in reality dual to each other, it means that lattice QCD simulations support the hypothesis that in real quark matter there exists the (approximate) duality between CSB and charged PC. Moreover, we can reverse the logic and we can predict the increase of pseudo-critical temperature with chiral chemical potential, the much debated effect recently, just by the duality notion, hence bolster confidence in this result (lattice QCD showed this feature for unphysically large pion mass) and put it on the considerably more solid ground.

Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities

“…The dualities of the QCD phase diagram, in particular, the duality between chiral symmetry breaking and pion condensation phenomena has been found in the framework of the (1+1)-dimensional QCD motivated toy model in Reference [68][69][70][71]. Then it was shown to exist in the framework of effective models in References [26,97,[101][102][103][104][105].…”

“…And the QCD phase structure at non-zero isospin imbalance is comparatively well-known [20][21][22][87][88][89] and one knows that the critical temperature of PC phase is an increasing function of isospin chemical potential at least to the values of several hundred MeV. One also knows that the duality is valid only in the chiral limit (m π = 0) and is a very good approximation but not exact in the physical point (m π ≈ 140 MeV) [26] (the duality is almost exact if ν > m π /2, at least from one hundred to several hundred MeV). So one can conclude using the duality and lattice QCD results at isospin imbalance that critical temperature of chiral symmetry breaking phase should be an increasing function of chiral chemical potential µ 5 .…”

“…It is believed that the chiral imbalance can be created at high temperatures in the heavy-ion collisions due to the Adler-Bell-Jackiw anomaly and nontrivial gluon field configurations. Moreover, in strong magnetic field or under rotation, due to the so-called chiral separation [24] or chiral vortical [25] effects, chiral density can be produced in dense quark matter [26][27][28]. Chiral imbalance can also be generated in parallel electric and magnetic fields [29][30][31].…”

“…Moreover, there is another type of chiral imbalance, when chiral densities of u and d quarks are different, it is called chiral isospin imbalance n I5 . It can be shown that chiral isospin imbalance can be produced in magnetized or rotating dense quark matter [26]. Moreover, in parallel electric and magnetic fields chiral isospin imbalance can be generated as well.…”

Meson Condensation

“…The meson condensed phases can also be studied by a modeling of the strong interaction by contact interaction terms [34][35][36][37][38][39][40][41][45][46][47]50,52,55], see [54] for a brief recent review. These models stem from the original work by Nambu and Jona Lasinio [113][114][115] of a pre-QCD Lagrangian for the description of the strong interaction by contact interaction terms:…”