The production of prompt $D^0$ mesons in proton-lead collisions in the forward and backward configurations at a center-of-mass energy per nucleon pair of $\sqrt{s_\mathrm{NN}} = 8.16~\mathrm{TeV}$ is measured by the LHCb experiment. The nuclear modification factor of prompt $D^0$ mesons is determined as a function of the transverse momentum $p_\mathrm{T}$, and rapidity in the nucleon-nucleon center-of-mass frame $y^*$. In the forward rapidity region, significantly suppressed production with respect to $pp$ collisions is measured, which provides significant constraints of nuclear parton distributions and hadron production down to the very low Bjorken-$x$ region of $\sim 10^{-5}$. In the backward rapidity region, a suppression with a significance of 2.0 - 3.8 standard deviations compared to nPDF expectations is found in the kinematic region of $p_\mathrm{T}>6~\mathrm{GeV}/c$ and $-3.25<y^*<-2.5$, corresponding to $x\sim 0.01$.
Double-differential cross-sections for prompt $D^0$ mesons in intervals of $p_\mathrm{T}$ and $y^\ast$ in forward rapidity regions.
Double-differential cross-sections for prompt $D^0$ mesons in intervals of $p_\mathrm{T}$ and $y^\ast$ in forward rapidity regions.
Double-differential cross-sections for prompt $D^0$ mesons in intervals of $p_\mathrm{T}$ and $y^\ast$ in backward rapidity regions.
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