A bstract A search for the doubly heavy $$ {\Xi}_{bc}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>bc</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> baryon using its decay to the D 0 pK – final state is performed using proton-proton collision data at a centre-of-mass energy of 13 TeV collected by the LHCb experiment between 2016 and 2018, corresponding to an integrated luminosity of 5.4 fb − 1 . No significant signal is found in the invariant mass range from 6.7 to 7.2 GeV/ c 2 . Upper limits are set at 95% credibility level on the ratio of the $$ {\Xi}_{bc}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>bc</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> production cross-section times its branching fraction to D 0 pK − relative to that of the $$ {\Lambda}_b^0\to {D}^0{pK}^{-} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Λ</mml:mi><mml:mi>b</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:msup><mml:mi>pK</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math> decay. The limits are set as a function of the $$ {\Xi}_{bc}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>bc</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> mass and lifetime hypotheses, in the rapidity range from 2.0 to 4.5 and in the transverse momentum region from 5 to 25 GeV/ c . Upper limits range from 1 . 7 × 10 − 2 to 3 . 0 × 10 − 1 for the considered $$ {\Xi}_{bc}^0 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>Ξ</mml:mi><mml:mi>bc</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math> mass and lifetime hypotheses.