Abstract
We propose $D$ mesons as probes to investigate finite-volume effects for chiral symmetry breaking at zero and finite temperature. By using the $2+1$-flavor linear-sigma model with constituent light quarks, we analyze the Casimir effects for the $\sigma$ mean fields: The chiral symmetry is rapidly restored by the antiperiodic boundary for light quarks, and the chiral symmetry breaking is catalyzed by the periodic boundary. We also show the phase diagram of the $\sigma$ mean fields on the volume and temperature plane. For $D$ mesons, we employ an effective model based on the chiral-partner structure, where the volume dependence of $D$ mesons is induced by the $\sigma$ mean fields. We find that $D_s$ mesons are less sensitive to finite volume than $D$ mesons, which is caused by the insensitivity of $\sigma_s$ mean fields. An anomalous mass shift of $D$ mesons at high temperature with the periodic boundary will be useful in examinations with lattice QCD simulations. The dependence on the number of compactified spatial dimensions is also studied.
Highlights
Chiral symmetry breaking induced by the chiral condensate is a unique property in the low-energy QCD
By using the 2 þ 1-flavor linear sigma model with constituent light quarks, we analyze the Casimir effects for the σ mean fields; the chiral symmetry is rapidly restored by the antiperiodic boundary for light quarks, and the chiral symmetry breaking is catalyzed by the periodic boundary
We find that Ds mesons are less sensitive to finite volume than D mesons, which is caused by the insensitivity of σs mean fields
Summary
Chiral symmetry breaking induced by the chiral condensate is a unique property in the low-energy QCD. It is related to the properties of many hadrons, such as masses and decay constants. Under an extreme environment such as high temperature/density, the chiral symmetry is partially restored by the external effects, and hadron properties are simultaneously modified. An intuitive scenario connecting the chiral symmetry to hadron properties is the chiral-partner structure, which means that the masses of partners become degenerate in the chiralrestored phase. The chiral-partner structure for D mesons was first suggested in Refs. [1,2], and it was later extended to strange
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