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Measurement of $ψ(2S)$ nuclear modification at backward and forward rapidity in $p$$+$$p$, $p$$+$Al, and $p$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

Suppression of the $J/ψ$ nuclear-modification factor has been seen as a trademark signature of final-state effects in large collision systems for decades. In small systems, the nuclear modification was attributed to cold-nuclear-matter effects until the observation of strong differential suppression of the $ψ(2S)$ state in $p/d$$+$$A$ collisions suggested the presence of final-state effects. Results of $J/ψ$ and $ψ(2S)$ measurements in the dimuon decay channel are presented here for $p$$+$$p$, $p$$+$Al, and $p$$+$Au collision systems at $\sqrt{s_{_{NN}}}=200$ GeV. The results are predominantly shown in the form of the nuclear-modification factor, $R_{pA}$, the ratio of the $ψ(2S)$ invariant yield per nucleon-nucleon collision in collisions of proton on target nucleus to that in $p$$+$$p$ collisions. Measurements of the $J/ψ$ and $ψ(2S)$ nuclear-modification factor are compared with shadowing and transport-model predictions, as well as to complementary measurements at Large-Hadron-Collider energies.