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The inclusive production of the $\psi$(2S) charmonium state was studied as afunction of centrality in p-Pb collisions at the nucleon-nucleon center of massenergy $\sqrt{s_{\rm NN}}$ = 5.02 TeV at the CERN LHC. The measurement wasperformed with the ALICE detector in the center of mass rapidity ranges$-4.46<y_{\rm cms}<-2.96$ and $2.03<y_{\rm cms}<3.53$, down to zero transversemomentum, by reconstructing the $\psi$(2S) decay to a muon pair. The $\psi$(2S)production cross section $\sigma_{\psi(\rm 2S)}$ is presented as a function ofthe collision centrality, which is estimated through the energy deposited inforward rapidity calorimeters. The relative strength of nuclear effects on the$\psi$(2S) and on the corresponding 1S charmonium state J/$\psi$ is thenstudied by means of the double ratio of cross sections $[\sigma_{\psi(\rm2S)}/\sigma_{\rm J/\psi}]_{\rm pPb}/[\sigma_{\psi(\rm 2S)}/\sigma_{\rmJ/\psi}]_{\rm pp}$ between p-Pb and pp collisions, and by the values of thenuclear modification factors for the two charmonium states. The results show alarge suppression of $\psi$(2S) production relative to the J/$\psi$ at backward(negative) rapidity, corresponding to the flight direction of the Pb-nucleus,while at forward (positive) rapidity the suppressions of the two states arecomparable. Finally, comparisons to results from lower energy experiments andto available theoretical models are presented.

Centrality dependence of $\mathbf{\psi}$(2S) suppression in p-Pb collisions at $\mathbf{\sqrt{{\textit s}_{\rm NN}}}$ = 5.02 TeV