J/$\psi$ production at midrapidity in p$-$Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=8.16$ TeV

The production of inclusive, prompt and non-prompt J/$\psi$ was studied for the first time at midrapidity ($-1.37<y_{\mathrm{c}\mathrm{m}\mathrm{s}}<0.43$) in p$-$Pb collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=8.16$ TeV with the ALICE detector at the LHC. The inclusive J/$\psi$ mesons were reconstructed in the dielectron decay channel in the transverse momentum ($p_{\mathrm{T}}$) interval $0<p_{\mathrm{T}}<14$ GeV/$c$ and the prompt and non-prompt contributions were separated on a statistical basis for $p_{\mathrm{T}}>2$ GeV/$c$. The study of the J/$\psi$ mesons in the dielectron channel used for the first time in ALICE online single-electron triggers from the Transition Radiation Detector, providing a data sample corresponding to an integrated luminosity of $689\pm 13\mu {\mathrm{b}}^{-1}$. The proton$-$proton reference cross section for inclusive J/$\psi$ was obtained based on interpolations of measured data at different centre-of-mass energies and a universal function describing the $p_{\mathrm{T}}$-differential J/$\psi$ production cross sections. The $p_{\mathrm{T}}$-differential nuclear modification factors $R_{\mathrm{p}\mathrm{P}\mathrm{b}}$ of inclusive, prompt, and non-prompt J/$\psi$ are consistent with unity and described by theoretical models implementing only nuclear shadowing.