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The production of prompt $D^0$ mesons in proton-lead collisions in theforward and backward configurations at a center-of-mass energy per nucleon pairof $\sqrt{s_\mathrm{NN}} = 8.16~\mathrm{TeV}$ is measured by the LHCbexperiment. The nuclear modification factor of prompt $D^0$ mesons isdetermined as a function of the transverse momentum $p_\mathrm{T}$, andrapidity in the nucleon-nucleon center-of-mass frame $y^*$. In the forwardrapidity region, significantly suppressed production with respect to $pp$collisions is measured, which provides significant constraints of nuclearparton distributions and hadron production down to the very low Bjorken-$x$region of $\sim 10^{-5}$. In the backward rapidity region, a suppression with asignificance of 2.0 - 3.8 standard deviations compared to nPDF expectations isfound in the kinematic region of $p_\mathrm{T}>6~\mathrm{GeV}/c$ and$-3.25<y^*<-2.5$, corresponding to $x\sim 0.01$.

Measurement of the prompt $D^0$ nuclear modification factor in $p$Pb collisions at $\sqrt{s_\mathrm{NN}} = 8.16$ TeV