First measurement of the ratio of $\psi (2S)$-to-$J\mathrm{/}\psi$ inclusive production in $p\mathrm{A}\mathrm{r}$ and $pp$ collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=113\mathrm{G}\mathrm{e}\mathrm{V}$ with SMOG2

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