Yields of charmonia, bound states of quarks, are observed to be strongly suppressed in heavy-ion collisions relative to proton-proton collisions as a result of their interaction with the quark-gluon plasma produced in such collisions. Understanding the mechanisms responsible for this suppression requires a detailed understanding of charmonium production. To constrain the production mechanisms, it is essential to quantify how charmonium production correlates with jet activity. Measurements of production in the dimuon decay channel are presented for inclusive mesons and for mesons that are either isolated or not isolated from jets, separately for prompt and non-prompt production. Non-isolated mesons are defined by matching candidates to anti- jets with and GeV, reconstructed without signal from the meson, allowing the quantification of jet activity accompanying production. The analysis uses Pb+Pb and collisions at TeV recorded by the ATLAS experiment at the LHC, corresponding to integrated luminosities of 1.82 nb and 0.26 fb, respectively. The yields in Pb+Pb, cross sections in , and nuclear modification factors are presented for non-isolated, isolated, and inclusive up to GeV. Isolated fractions and non-prompt fractions are reported in both and Pb+Pb collisions. Strong suppression is observed to persist up to the highest measured values, with differences observed between non-isolated, isolated, and inclusive . These results provide new constraints on charmonium production mechanisms and their in-medium suppression.

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