A measurement of the lifetimes of the $Omega^{0}_{c}$ and $Xi^{0}_{c}$ baryons is reported using proton-proton collision data at a centre-of-mass energy of $13text{ TeV}$, corresponding to an integrated luminosity of $5.4text{ fb}^{-1}$ collected by the LHCb experiment. The $Omega^{0}_{c}$ and $Xi^{0}_{c}$ baryons are produced directly from proton interactions and reconstructed in the $pK^{-}K^{-}pi^{+}$ final state. The $Omega^{0}_{c}$ lifetime is measured to be $276.5pm13.4pm4.4pm0.7text{ fs}$, and the $Xi^{0}_{c}$ lifetime is measured to be $148.0pm2.3pm2.2pm0.2text{ fs}$, where the first uncertainty is statistical, the second systematic, and the third due to the uncertainty on the $D^{0}$ lifetime. These results confirm previous LHCb measurements based on semileptonic beauty-hadron decays, which disagree with earlier results of a four times shorter $Omega^{0}_{c}$ lifetime, and provide the single most precise measurement of the $Omega^{0}_{c}$ lifetime.
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