Lattice study of QCD at finite chiral density: topology and confinement

Abstract

In this paper we study the properties of QCD at nonzero chiral density ρ5, which is introduced through chiral chemical potential µ5. The study is performed within lattice simulation of QCD with dynamical rooted staggered fermions. We first check that ρ5 is generated at nonzero µ5 and in the chiral limit observe ρ5 ∼ Λ 2 QCD µ5. We also test the possible connection between confinement and topological fluctuations. To this end, we measured the topological susceptibility χ top and string tension σ for various values of µ5. We observed that both string tension and chiral susceptibility grow with µ5 and there is a strong correlation between these quantities. We thus conclude that the chiral chemical potential enhances topological fluctuations and that these fluctuations can indeed be closely related to the strength of confinement.

Chiral perturbation theory for nonzero chiral imbalance

“…Another relevant comment in this context is that the temperature and volume corrections might have to be considered in future lattice analyses. Actually, in [22] the total four-volume of the lattice is fixed at around (1.7 fm) 4 which would amount to an effective temperature T ∼ 116 MeV. According to our expressions above, that would affect mostly the linear term ρ…”

“…From the recent lattice analysis in [22] performed for N f = 2, one concludes that for low and moderate values of µ 5 , ρ 5 (µ 5 ) is very insensitive to the quark masses and its behaviour is pretty much dominated by the linear term ρ 5 ∝ µ 5 . This is consistent with our results above since the dominant O(F 2 ) term shows up only in the linear term (73) and is mass independent.…”

“…D. The chiral charge density and µ5 = 0 stability Another quantity whose µ 5 dependence has been studied in the lattice is the chiral charge density [18,22], defined as…”

“…This is consistent with our results above since the dominant O(F 2 ) term shows up only in the linear term (73) and is mass independent. Actually, in [22], that term is estimated simply as 4f 2 π , which is adequate regarding its order of magnitude, but as we have seen in detail here, at that order the contributions from the Z and κ 0 terms have to be considered in addition to that of the pion decay constant. Another relevant comment in this context is that the temperature and volume corrections might have to be considered in future lattice analyses.…”

“…Thus, in [18] the chiral charge density and the chiral magnetic effect have been investigated, while the dependence of the chiral restoration temperature with µ 5 has been studied through the chiral condensate, scalar susceptibility and Polyakov loop for N c = 2 [19] and N c = 3 [20]. The chiral anomaly in the lattice has been also studied in [21] while in more recent lattice analysis, updated results for N f = 2 are provided on the chiral charge density, as well as the topological susceptibility and charge [22].…”