First measurement of the ratio of $ψ(2S)$-to-$J/ψ$ inclusive production in $p\mathrm{Ar}$ and $pp$ collisions at $\sqrt{s_{\mathrm{NN}}} =113\,\mathrm{GeV}$ with SMOG2
A measurement of the $ψ(2S)$-to-$J/ψ$ production cross-section ratio is performed in proton-argon ($p\mathrm{Ar}$) and proton-proton ($pp$) collisions in fixed-target mode at $\sqrt{s_{\mathrm{NN}}}=113\,\mathrm{GeV}$. Data samples were collected by the LHCb experiment during argon and hydrogen gas injections in the SMOG2 storage cell, resulting in $p\mathrm{Ar}$ and $pp$ collisions, respectively. The $ψ(2S)$-to-$J/ψ$ production cross-section ratio is measured as a function of the charmonium transverse momentum, $p_{\mathrm{T}}$, and rapidity in the centre-of-mass system, $y^{*}$. The $ψ(2S)$-to-$J/ψ$ ratio in $p\mathrm{Ar}$ collisions over that in $pp$ collisions is measured to be $0.90 \pm 0.04 \pm 0.02$ for $-2.3<y^{*}<0.0$ and $0<p_{\mathrm{T}}<8\mathrm{GeV}/c$, indicating the emergence of nuclear effects in the $p\mathrm{Ar}$ system. This study acts as a baseline for the interpretation of future measurements with larger systems accessible by the LHCb experiment.