${\boldsymbol{ U_A(1) }}$ symmetry restoration at high baryon density

Abstract：

We study the relation between chiral and $ U_A(1) $ symmetries in the quark-meson model. Although quarks and mesons are described in mean field approximation, the topological susceptibility characterizing the $ U_A(1) $ breaking comprises two components: one controlled by the condensate and the other by the meson fluctuation. The $ U_A(1) $ restoration is governed by the competition of these components. In a hot medium, the condensates melt. However, the fluctuation is enhanced. Therefore, the $ U_A(1) $ symmetry cannot be solely restored via the temperature effect. Nevertheless, the baryon density reduces the condensates and fluctuation, and thereby, the $ U_A(1) $ symmetry can only be restored in a dense or dense and hot medium. The strange condensate plays a weak role in the susceptibility, and the chiral and $ U_A(1) $ symmetry restorations occur almost at the same critical point.