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

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.