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