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Inclusive $\psi$(2S) production is measured in p-Pb collisions at thecentre-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm{NN}}}=8.16$ TeV,using the ALICE detector at the CERN LHC. The production of $\psi$(2S) isstudied at forward ($2.03 < y_{\rm cms} < 3.53$) and backward ($-4.46 < y_{\rmcms} < -2.96$) centre-of-mass rapidity and for transverse momentum $p_{\rm{T}}$$<$ 12 GeV/$c$ via the decay to muon pairs. In this paper, we report theintegrated as well as the $y_{\rm cms}$- and $p_{\rm T}$-differential inclusiveproduction cross sections. Nuclear effects on $\psi$(2S) production are studiedvia the determination of the nuclear modification factor that shows a strongsuppression at both forward and backward centre-of-mass rapidities. Comparisonswith corresponding results for inclusive J/$\psi$ show a similar suppressionfor the two states at forward rapidity (p-going direction), but a strongersuppression for $\psi$(2S) at backward rapidity (Pb-going direction). As afunction of $p_{\rm T}$, no clear dependence of the nuclear modification factoris found. The relative size of nuclear effects on $\psi$(2S) productioncompared to J/$\psi$ is also studied via the double ratio of production crosssections $[\sigma_{\psi(2S)}/\sigma_{\rm{J/}\psi}]_{\rmpPb}/[\sigma_{\psi(2S)}/\sigma_{\rm{J/}\psi}]_{\rm pp}$ between p-Pb and ppcollisions. The results are compared with theoretical models that includevarious effects related to the initial and final state of the collision systemand also with previous measurements at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV.

Measurement of nuclear effects on $\psi\rm{(2S)}$ production in p-Pb collisions at $\sqrt{\textit{s}_{\rm NN}} = 8.16$ TeV