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$D^{0} - {\bar{D}}^{0}$ mixing in the Dyson-Schwinger approach

Xiaotong Xie ^*, Hiroyuki Umeeda ^†, and Jinglong Zhu ^‡

Center for Theoretical Physics and College of Physics, Jilin University, Changchun, 130012, China

^*Contact author: jiext23@mails.jlu.edu.cn
^†Contact author: umeeda@jlu.edu.cn
^‡Contact author: zhujl23@mails.jlu.edu.cn

Phys. Rev. D 112, 034014 – Published 14 August, 2025

DOI: https://doi.org/10.1103/jn43-cv1f

Abstract

In view of difficulty to reproduce observables in the $D^{0} - {\bar{D}}^{0}$ mixing via the operator product expansion, we discuss the Dyson-Schwinger approach to this process. Formulated by the parametrization of quark propagators, SU(3) breaking relevant to charm mixing is evaluated in such a way that properly takes account of dynamical chiral symmetry breaking. The ${\bar{D}}^{0} \to D^{0}$ transition is discussed in the vacuum-insertion approximation with locality of the light valence-quark field, represented by the decay constant of $D^{0}$ meson as well as relevant momentum integrals. It is found that dimensionless mass-difference observable in this approach leads to $| x | = (1.3 - 2.9) \times 10^{- 3}$ , the order of magnitude comparable to the HFLAV data, and thereby offering a certain improvement as a theoretical framework.

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References (51)

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Phys. Rev. D 112, 034014– Published 14 August, 2025

Vol. 112, Iss. 3 — 1 August 2025

Received 24 April 2025
Accepted 29 July 2025

DOI: https://doi.org/10.1103/jn43-cv1f

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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$D^{0} - {\bar{D}}^{0}$ mixing in the Dyson-Schwinger approach

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D0−D¯0 mixing in the Dyson-Schwinger approach

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$D^{0} - {\bar{D}}^{0}$ mixing in the Dyson-Schwinger approach