# $D^0$-$\overline{D}^0$ mixing parameter $y$ in the factorization-assisted topological-amplitude approach

## TL;DR

This paper calculates the $D^0$-$ar{D}^0$ mixing parameter $y$ using the FAT approach, considering various decay modes, and finds the predicted value is lower than experimental measurements, indicating other decay channels are important.

## Contribution

The study provides a more precise theoretical prediction of $y$ in the FAT approach, highlighting the limited contribution of $VV$ modes and the need to consider additional decay channels.

## Key findings

- $VV$ contribution to $y$ is negligible (~10^{-4})
- $PP$ and $PV$ modes contribute up to 0.21%
- Predicted $y$ value is lower than experimental data

## Abstract

We calculate the $D^0$-$\overline{D}^0$ mixing parameter $y$ in the factorization-assisted topological-amplitude (FAT) approach, considering contributions from $D^{0}\to PP$, $PV$, and $VV$ modes, where $P$ ($V$) stands for a pseudoscalar (vector) meson. The $D^{0}\to PP$ and $PV$ decay amplitudes are extracted in the FAT approach, and the $D^{0}\to VV$ decay amplitudes with final states in the longitudinal polarization are estimated via the parameter set for $D^{0}\to PV$. It is found that the $VV$ contribution to $y$, being of order of $10^{-4}$, is negligible, and that the $PP$ and $PV$ contributions amount only up to $y_{PP+PV}=(0.21\pm0.07)\%$, a prediction more precise than those previously obtained in the literature, and much lower than the experimental data $y_{\rm exp}=(0.61\pm0.08)\%$. We conclude that $D^{0}$ meson decays into other two-body and multi-particle final states are relevant to the evaluation of $y$, so it is difficult to understand it fully in an exclusive approach.