  A search for the doubly heavy baryons $\it{\Xi}_{bc}^{\rm0}$ and
$\it{\Omega}_{bc}^{\rm0}$ is performed using $pp$ collision data collected with
the LHCb experiment from 2016 to 2018 at a centre-of-mass energy of $13TeV$,
corresponding to an integrated luminosity of 5.2$fb^{-1}$. The baryons are
reconstructed via their decays to $\it{\Lambda_{c}^{+}\pi^{-}}$ and
$\it{\Xi_{c}^{+}\pi^{-}}$. No significant excess is found for invariant masses
between 6700 and 7300$MeV/c^2$, in the rapidity range from 2.0 to 4.5 and the
transverse momentum range from 2 to 20$GeV/c$. Upper limits are set on the
ratio of the $\it{\Xi}_{bc}^{\rm0}$ and $\it{\Omega}_{bc}^{\rm0}$ production
cross-section times its branching fraction to $\it{\Lambda_{c}^{+}\pi^{-}}$
($\it{\Xi_{c}^{+}\pi^{-}}$) relative to that of the $\it{\Lambda_b^{\rm0}}$
($\it{\Xi_b^{\rm0}}$) baryon, for different lifetime hypotheses, at $95\%$
confidence level. The upper limits range from $0.5\times10^{-4}$ to
$2.5\times10^{-4}$ for the
$\it{\Xi}_{bc}^{\rm0}\rightarrow\it{\Lambda_{c}^{+}\pi^{-}}$
($\it{\Omega}_{bc}^{\rm0}\rightarrow\it{\Lambda_{c}^{+}\pi^{-}}$) decay, and
from $1.4\times10^{-3}$ to $6.9\times10^{-3}$ for the
$\it{\Xi}_{bc}^{\rm0}\rightarrow\it{\Xi_{c}^{+}\pi^{-}}$
($\it{\Omega}_{bc}^{\rm0}\rightarrow\it{\Xi_{c}^{+}\pi^{-}}$) decay, depending
on the considered mass and lifetime of the $\it{\Xi}_{bc}^{\rm0}$
($\it{\Omega}_{bc}^{\rm0}$) baryon.
