= Solution
Useful examples with no net <quark flavor> are the <eta c meson> $\eta_c=c\bar c$ and the <eta b meson> $\eta_b=b\bar b$. Examples with nonzero <quark flavor> are the <kaon> $K^+=u\bar s$ and the <D meson> $D^+=c\bar d$. These are <pseudoscalar mesons>: in the lowest <quark model> configuration the constituent <spins> combine to $S=0$, the relative <orbital angular momentum> is $L=0$, and the total <angular momentum> and <parity> are $J^P=0^-$. For the self-conjugate examples, <meson parity and charge conjugation> also gives $C=(-1)^{L+S}=+1$. Electrical neutrality alone would not imply zero net <quark flavor>; for example $K^0=d\bar s$ has strangeness.
Restoring <reduced Planck constant>, <decay width> and <mean lifetime> satisfy $\Gamma\tau=\hbar$. Thus the representative numbers correspond to
$$
\tau_{20\,\mathrm{MeV}}=\frac{6.582\times10^{-22}\ \mathrm{MeV\,s}}{20\ \mathrm{MeV}}=3.29\times10^{-23}\ \mathrm s,\qquad
\Gamma_{1\,\mathrm{ps}}=6.582\times10^{-10}\ \mathrm{MeV}.
$$
The <mean lifetimes> differ by at least $3.0\times10^{10}$. Hidden-heavy-flavor <quarkonium> can undergo <quark>-<antiquark> <annihilation> into <gluons>, followed by <hadronization>. A $0^{-+}$ color-singlet state can annihilate into two <gluons>. A lightest open-flavor <meson> cannot simply annihilate through the <strong interaction>, which conserves net <quark flavor>. With no lighter accessible final state carrying that flavor, it must undergo a <weak interaction> changing a constituent's flavor. The small <weak interaction> amplitude, <CKM matrix> factors and available <Lorentz-invariant phase space> produce a much smaller <decay width>.
\b[Qualification.] A <decay width> of order tens of MeV is not a universal property of flavor-neutral <pseudoscalar mesons>. The <neutral pion> has $\Gamma\simeq7.8\ \mathrm{eV}$ and decays predominantly by the <electromagnetic interaction>, a concrete counterexample. Its <mass> lies below the lightest allowed hadronic final state. The examples above illustrate the intended annihilation-versus-open-flavor comparison; the numerical scale depends on thresholds and selection rules.<Review of Particle Physics by Particle Data Group (2022)>[Meson summary tables: neutral-pion width and heavy pseudoscalar properties]{ref}
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