\begin{document}$ {{{{\varOmega}_{bc}^{0}}}} $\end{document} baryon and a search for the \begin{document}$ {{{{\varXi}_{bc}^{0}}}} $\end{document} baryon are performed using \begin{document}$ pp $\end{document} collision data collected via the \begin{document}$ {\rm{LHCb}} $\end{document} experiment from 2016 to 2018 at a centre-of-mass energy of \begin{document}$ 13 \;{\rm{TeV}} $\end{document}, corresponding to an integrated luminosity of 5.2\begin{document}$ \;{\rm{f}}{{\rm{b}}^{ - 1}} $\end{document}. The baryons are reconstructed via their decays to \begin{document}$ {{{{\varLambda}^+_c}}} {{{{\pi}^-}}} $\end{document} and \begin{document}$ {{{{\varXi}^+_c}}} {{{{\pi}^-}}} $\end{document}. No significant excess is found for invariant masses between 6700 and 7300\begin{document}$ \;{\rm{MeV}}/{c^2} $\end{document}, in a rapidity range from 2.0 to 4.5 and a transverse momentum range from 2 to 20\begin{document}$ \;{\rm{MeV}}/{c} $\end{document}. Upper limits are set on the ratio of the \begin{document}$ {{{{\varOmega}_{bc}^{0}}}} $\end{document} and \begin{document}$ {{{{\varXi}_{bc}^{0}}}} $\end{document} production cross-section times the branching fraction to \begin{document}$ {{{{\varLambda}^+_c}}}{{{{\pi}^-}}} $\end{document} (\begin{document}$ {{{{\varXi}^+_c}}}{{{{\pi}^-}}} $\end{document}) relative to that of the \begin{document}$ {{{{\varLambda}^0_b}}} $\end{document} (\begin{document}$ {{{{\varXi}_{b}^{0}}}} $\end{document}) baryon, for different lifetime hypotheses, at 95% confidence level. The upper limits range from \begin{document}$ 0.5\times10^{-4} $\end{document} to \begin{document}$ 2.5\times10^{-4} $\end{document} for the \begin{document}$ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $\end{document} (\begin{document}$ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varLambda}^+_c}}}{{{{\pi}^-}}}}}}} $\end{document}) decay, and from \begin{document}$ 1.4\times10^{-3} $\end{document} to \begin{document}$ 6.9\times10^{-3} $\end{document} for the \begin{document}$ {{{{{{{{\varOmega}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $\end{document} (\begin{document}$ {{{{{{{{\varXi}_{bc}^{0}}}}{{\rightarrow }}{{{{\varXi}^+_c}}}{{{{\pi}^-}}}}}}} $\end{document}) decay, depending on the considered mass and lifetime of the \begin{document}$ {{{{\varOmega}_{bc}^{0}}}} $\end{document} (\begin{document}$ {{{{\varXi}_{bc}^{0}}}} $\end{document}) baryon."> Search for the doubly heavy baryons <inline-formula><tex-math id="M1-1">\begin{document}${\boldsymbol \varOmega_{\boldsymbol{bc}}^{\bf 0}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M1-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M1-1.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M2-1">\begin{document}$ {\boldsymbol\varXi_{\boldsymbol{bc}}^{\bf 0} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M2-1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M2-1.png"/></alternatives></inline-formula> decaying to <inline-formula><tex-math id="M3">\begin{document}${ \boldsymbol \varLambda_c^+\pi^- }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ {\boldsymbol\varXi_c^+\pi^- }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/552ba4e5-a89a-48a6-9e28-fc99bb67bf91/CPC-2021-0260_M4.png"/></alternatives></inline-formula> -
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