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Anomalous $U(1)_A$ couplings and the Columbia plot
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abstract
When the quark masses are lighter than those in QCD, the standard lore is that a chiral transition of first order must emerge for three, light flavors. Recently, however, numerical simulations on the lattice suggest that the chiral transition is of second order in the chiral limit. Using an extended linear sigma model in the mean field approximation, we study the relation between terms which break the anomalous, $U(1)_A$ symmetry and the order of the chiral phase transition, especially how a chiral transition of second order can arise for three, massless flavors. We note that in an (unphysical) region of the "Columbia" phase diagram, when the strange quark mass is light and negative, corresponding to topological angle $\theta=\pi$, the $CP$ symmetry is spontaneously broken.
Forward citations
Cited by 2 Pith papers
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On the nature of the QCD chiral phase transition with imaginary chemical potential
First-order chiral regions observed on coarse staggered lattices disappear in tricritical points as the lattice spacing decreases at imaginary chemical potential, implying a second-order continuum transition.
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Quark mass dependence of a QCD critical point and structure of the Columbia plot
In a truncated Dyson-Schwinger setup, the QCD critical point moves to higher temperature and lower baryon chemical potential as light quark masses decrease toward the chiral limit.
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