Inclusive, prompt and non-prompt $\mathrm{J}\mathrm{/}\psi$ production at midrapidity in p$-$Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02$ TeV

A measurement of inclusive, prompt, and non-prompt $\mathrm{J}\mathrm{/}\psi$ production in p$-$Pb collisions at a nucleon$-$nucleon centre-of-mass energy $\sqrt{s_{\mathrm{N}\mathrm{N}}}=5.02$ TeV is presented. The inclusive $\mathrm{J}\mathrm{/}\psi$ mesons are reconstructed in the dielectron decay channel at midrapidity down to a transverse momentum $p_{\mathrm{T}}=0$. The inclusive $\mathrm{J}\mathrm{/}\psi$ nuclear modification factor $R_{\mathrm{p}\mathrm{P}\mathrm{b}}$ is calculated by comparing the new results in p$-$Pb collisions to a recently measured proton$-$proton reference at the same centre-of-mass energy. Non-prompt $\mathrm{J}\mathrm{/}\psi$ mesons, which originate from the decay of beauty hadrons, are separated from promptly produced ${\rm J}/\psi$onastatisticalbasisfor$p_{\rm T}$largerthan1.0GeV\mathrm{/}$c$. These results are based on the data sample collected by the ALICE detector during the 2016 LHC p$-$Pb run, corresponding to an integrated luminosity ${\cal L}_{\rm int} = 292 \pm 11 ; {\rm \mu b}^{-1}$, which is six times larger than the previous publications. The total uncertainty on the $p_{\mathrm{T}}$-integrated inclusive $\mathrm{J}\mathrm{/}\psi$ and non-prompt $\mathrm{J}\mathrm{/}\psi$ cross section are reduced by a factor 1.7 and 2.2, respectively. The measured cross sections and $R_{\mathrm{p}\mathrm{P}\mathrm{b}}$ are compared with theoretical models that include various combinations of cold nuclear matter effects. From the non-prompt $\mathrm{J}\mathrm{/}\psi$ production cross section, the $\mathrm{b}\bar{\mathrm{b}}$ production cross section at midrapidity, $\mathrm{d}{\sigma }_{\mathrm{b}\bar{\mathrm{b}}}\mathrm{/}\mathrm{d}y$, and the total cross section extrapolated over full phase space, ${\sigma }_{\mathrm{b}\bar{\mathrm{b}}}$, are derived.