Theoretical aspects of $D^0-\bar{D}^0$ mixing

TL;DR

This paper investigates the theoretical analysis of $D^0-ar{D}^0$ mixing using operator product expansion and quark-hadron duality, highlighting the suppression of contributions and comparing exclusive and inclusive width differences in a simplified model.

Contribution

It examines the role of quark-hadron duality in $D^0-ar{D}^0$ mixing and compares exclusive and inclusive width differences within the 't Hooft model, providing insights into the observed mixing.

Findings

Exclusive width difference is enhanced relative to inclusive contributions.

The order of magnitude of the width difference aligns qualitatively with observations.

Quark-hadron duality plays a significant role in the analysis.

Abstract

Observables in the $D^0-\bar{D}^0$ mixing can be theoretically analyzed by the operator product expansion (OPE), in which $1/m_c$ is regarded as an expansion parameter. Since the contributions of four-quark operators are strongly suppressed by the Glashow-Iliopoulos-Maiani (GIM) mechanism, the order of magnitude of the width difference is still not reproduced in the OPE analysis. In view of this issue, quark-hadron duality, an assumption that is tacitly made in the OPE, is studied for the $D^0-\bar{D}^0$ mixing. In particular, the exclusive width difference and the inclusive counterpart can be compared within the 't Hooft model, two-dimensional QCD in the large-$N_c$ limit. It is shown that the order of magnitude of the exclusive width difference is enhanced relative to the 4D-like inclusive contributions of the four-quark operators, that is qualitatively consistent with the realistic observation of the $D^0-\bar{D}^0$ mixing.