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

We calculate the $D^0$-${\bar{D}}^0$ 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 $y_{PP+PV}=(0.21\pm 0.07)\mathrm{\%}$, a prediction more precise than those previously obtained in the literature, and much lower than the experimental data $y_{\mathrm{e}\mathrm{x}\mathrm{p}}=(0.61\pm 0.08)\mathrm{\%}$. 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.