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Chiral transition and the chiral charge density of the hot and dense QCD matter

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential $μ_5$. The chiral quark condensate $\langle \barψ ψ\rangle$ is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by $μ_5$ is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The CEP location $(μ_E,T_E)$ shifts toward larger $T_E$ but constant $μ_E$ as $μ_5$ increases. A technique is then introduced to compute the chiral charge density $n_5$ from the fully dressed quark propagator. We find the $n_5$ generally increases with temperature $T$, quark number chemical potential $μ$ and $μ_5$. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on $n_5$ and find an increase in $n_5$ with smaller system size.