Multiplicity dependence of ${\sigma }_{\psi (2S)}\mathrm{/}{\sigma }_{J\mathrm{/}\psi }$ in $pp$ collisions at $\sqrt{s}=13$ TeV

The ratio of production cross-sections of $\psi (2S)$ over $J\mathrm{/}\psi$ mesons as a function of charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy $\sqrt{s}=13$ TeV is measured with a data sample collected by the LHCb detector, corresponding to an integrated luminosity of 658 pb${}^{-1}$. The ratio is measured for both prompt and non-prompt $\psi (2S)$ and $J\mathrm{/}\psi$ mesons. When there is an overlap between the rapidity ranges over which multiplicity and charmonia production are measured, a multiplicity-dependent modification of the ratio is observed for prompt mesons. No significant multiplicity dependence is found when the ranges do not overlap. For non-prompt production, the $\psi (2S)-to-J\mathrm{/}\psi$ production ratio is roughly independent of multiplicity irrespective of the rapidity range over which the multiplicity is measured. The results are compared to predictions of the co-mover model and agree well except in the low multiplicity region. The ratio of production cross-sections of $\psi (2S)$ over $J\mathrm{/}\psi$ mesons are cross-checked with other measurements in di-lepton channels and found to be compatible.