  We analyze the neutral meson mixing by directly solving the dispersion
relation obeyed by the mass and width differences of the two meson mass
eigenstates. We solve for the parameters $x$ and $y$, proportional to the mass
and width differences in the charm mixing, respectively, taking the box-diagram
contributions to $x(s)$ and $y(s)$ at large mass squared $s$ of a fictitious
$D$ meson as inputs. The SU(3) symmetry breaking is introduced through physical
thresholds of different $D$ meson decay channels for $y(s)$. These
threshold-dependent effects, acting like nonperturbative power corrections in
QCD sum rules, stabilize the solutions of $y(s=m_D^2)$ with the $D$ meson mass
$m_D$. We then calculate $x(s)$ through the dispersive integration of $y(s)$,
and show that our predictions $x(m_D^2)\approx 0.21\%$ and $y(m_D^2)\approx
0.52\%$ are close to the data in both $CP$-conserving and $CP$-violating cases.
It is observed that the channel containing di-kaon states provides the major
source of SU(3) breaking, which enhances $x(m_D^2)$ and $y(m_D^2)$ by four
orders of magnitude relative to the perturbative results. We also predict the
coefficient ratio $q/p$ involved in the charm mixing with $|q/p|-1\approx
2\times 10^{-4}$ and $Arg(q/p)\approx 6\times 10^{-3}$ degrees, which can be
scrutinized by precise future measurements. The formalism is extended to
studies of the $B_{s(d)}$ meson mixing and the kaon mixing, and the small
deviations of the obtained width differences from the perturbative inputs
explain why the above mixing can be understood via short-distance dynamics. We
claim that the puzzling charm mixing is attributed to the strong
Glashow-Iliopoulos-Maiani suppression on perturbative contributions, instead of
to breakdown of the quark-hadron duality, which occurs only at 15\% level.
