# $D$ mesons as a probe of Casimir effect for chiral symmetry breaking

## TL;DR

This paper investigates how $D$ mesons can be used to probe finite-volume effects on chiral symmetry breaking, analyzing the impact of boundary conditions and temperature on the $\sigma$ mean fields and meson masses.

## Contribution

It introduces a novel approach using $D$ mesons as probes for finite-volume effects on chiral symmetry, incorporating the effects of boundary conditions and temperature.

## Key findings

- Chiral symmetry is rapidly restored by antiperiodic boundary conditions.
- Periodic boundary conditions catalyze chiral symmetry breaking.
- $D_s$ mesons are less sensitive to finite volume effects than $D$ mesons.

## 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.