Abstract
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 μ5. The chiral quark condensate leftlangle overline{psi}psi rightrangle 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 μ5 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 critical end point (CEP) location (μE, TE ) shifts toward larger TE but constant μE as μ5 increases. A technique is then introduced to compute the chiral charge density n5 from the fully dressed quark propagator. We find the n5 generally increases with temperature T , quark number chemical potential μ and μ5. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n5 and find an increase in n5 with smaller system size.
Highlights
JHEP06(2020)122 while for NJL model the results differ by regularization schemes [26,27,28,29,30,31]
By solving the quark’s Dyson-Schwinger equations (DSEs), the fully dressed quark propagator is obtained with its complete Dirac structures, rendering thermodynamical properties calculable
The chiral phase diagram is studied in the presence of μ5
Summary
The Dyson-Schwinger equation of quark, namely the gap equation, at finite T , μ and μ5 reads [22]. Γaν is the fully dressed quark-gluon vertex. The fully dressed quark propagator G(p, ωn) can be generally decomposed as the summation of eight Dirac structures associated with coefficients of scalar functions [22]. As a generalization to the case of nonzero μ5, we adopt the same setup as in [52], i.e., taking the Rainbow truncation for the quark-gluon vertex. For our purpose of chiral transition study, we only employ the infrared part This significantly simplifies the calculation since the renormalization constants can be set to 1.0, as mentioned below eq (2.1). The terms F4 and F6 can be set to zero Another useful relation is that the scalar functions satisfy. The number of scalar functions with different n’s to compute are halved
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