Measurement of the relative yields of $ψ(2S)$ to $ψ(1S)$ mesons produced at forward and backward rapidity in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV

The PHENIX Collaboration has measured the ratio of the yields of $ψ(2S)$ to $ψ(1S)$ mesons produced in $p$$+$$p$, $p$$+$Al, $p$$+$Au, and $^{3}$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV over the forward and backward rapidity intervals $1.2<|y|<2.2$. We find that the ratio in $p$$+$$p$ collisions is consistent with measurements at other collision energies. In collisions with nuclei, we find that in the forward ($p$-going or $^{3}$He-going) direction, the relative yield of $ψ(2S)$ mesons to $ψ(1S)$ mesons is consistent with the value measured in \pp collisions. However, in the backward (nucleus-going) direction, the $ψ(2S)$ is preferentially suppressed by a factor of $\sim$2. This suppression is attributed in some models to breakup of the weakly-bound $ψ(2S)$ through final state interactions with comoving particles, which have a higher density in the nucleus-going direction. These breakup effects may compete with color screening in a deconfined quark-gluon plasma to produce sequential suppression of excited quarkonia states.