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A bstract The inclusive production of the J/ ψ and ψ (2S) charmonium states is studied as a function of centrality in p-Pb collisions at a centre-of-mass energy per nucleon pair $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 8 . 16 TeV at the LHC. The measurement is performed in the dimuon decay channel with the ALICE apparatus in the centre-of-mass rapidity intervals − 4 . 46 < y cms < − 2 . 96 (Pb-going direction) and 2 . 03 < y cms < 3 . 53 (p-going direction), down to zero transverse momentum ( p T ). The J/ ψ and ψ (2S) production cross sections are evaluated as a function of the collision centrality, estimated through the energy deposited in the zero degree calorimeter located in the Pb-going direction. The p T -differential J/ ψ production cross section is measured at backward and forward rapidity for several centrality classes, together with the corresponding average 〈 p T 〉 and $$ \left\langle {p}_{\mathrm{T}}^2\right\rangle $$ p T 2 values. The nuclear effects affecting the production of both charmonium states are studied using the nuclear modification factor. In the p-going direction, a suppression of the production of both charmonium states is observed, which seems to increase from peripheral to central collisions. In the Pb-going direction, however, the centrality dependence is different for the two states: the nuclear modification factor of the J/ ψ increases from below unity in peripheral collisions to above unity in central collisions, while for the ψ (2S) it stays below or consistent with unity for all centralities with no significant centrality dependence. The results are compared with measurements in p-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5 . 02 TeV and no significant dependence on the energy of the collision is observed. Finally, the results are compared with theoretical models implementing various nuclear matter effects.
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