Forward $D$ predictions for $p\mathrm{P}\mathrm{b}$ collisions, and sensitivity to cold nuclear matter effects

Predictions are provided for double differential cross sections and forward-backward ratios of $D^0$ production in $p\mathrm{P}\mathrm{b}$ (forward) and $\mathrm{P}\mathrm{b}$$p$ (backward) collisions at 5.02~TeV. The effect of nuclear corrections on the ratio of differential cross sections ratios is estimated to be $\simeq$ (10-30)% in the kinematically accessible region of LHCb, and interestingly this ratio is approximately flat with respect to $p_T(D^0)$ due to a compensation of shadowing and anti-shadowing effects arising from the input nuclear PDFs. In comparison to $J\mathrm{/}\psi (\to {\mu }^{-}{\mu }^{+})$ measurements which have already been performed with the available data, the cross section for $D^0(\to K^{-}{\pi }^{+})$ production is expected to be two-orders of magnitude higher.