Various Cold Nuclear Matter (CNM) effects, such as nuclear shadowing or partonic energy loss, can modify the production of J/ψ in heavy-ion collisions with respect to what is measured in elementary colliding systems. The study of p-Pb collisions at the Large Hadron Collider (LHC) energy scale represents a crucial tool to assess the influence of Cold Nuclear Matter on J/ψ production in order to achieve a more correct interpretation of Pb-Pb collision results. The ALICE detector at the LHC is

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... ble of reconstructing J/ψ mesons at central rapidity through their e + e − decay channel down to zero transverse momentum (p T ), and has measured the fraction of J/ψ produced from the decay of beauty-flavoured hadrons (non-prompt J/ψ) in p-Pb collisions down to p T = 1.3 GeV/c. In this paper, the results obtained by ALICE from the measurement of the prompt and non-prompt J/ψ yields at mid-rapidity in p-Pb collisions at √ s NN = 5.02 TeV will be discussed in comparison to different theoretical predictions including CNM effects.