Nonperturbative Dynamics in D-meson Mixing

Abstract: Theoretical predictions for the $D^0\overline{D^0}$ mixing parameters fall significantly short of experimental measurements, with discrepancies spanning several orders of magnitude. This gap is mainly due to the Glashow-Iliopoulos-Maiani (GIM) mechanism, which suppresses leading-order contributions by high powers of $m_s/m_c$. However, higher-order corrections and nonperturbative effects could reduce this suppression, especially through flavor $SU(3)_F$ symmetry breaking. In this work, we investigate the long-distance contributions from QCD condensates, including, for the first time, the effects of mixed quark-gluon and four-quark condensates. Our results show an increase in the predicted values of $D^0\overline{D^0}$ mixing parameters by two orders of magnitude compared to perturbative NLO result, providing valuable insights into nonperturbative QCD dynamics. Although the theoretical estimates still fall below experimental values, this study represents an important step toward narrowing the gap between theory and observation, highlighting the significance of higher-order $1/m_c$ QCD effects in understanding $D^0\overline{D^0}$ mixing.