Bound states of charm and anticharm quarks, known as charmonia, have a rich spectroscopic structure that can be used to probe the dynamics of hadron production in high-energy hadron collisions. Here, the cross section ratio of excited ($\psi$(2S)) and ground state (J/$\psi$) vector mesons is measured as a function of the charged-particle multiplicity in proton-lead (pPb) collisions at a center-of-mass (CM) energy per nucleon pair of 8.16 TeV. The data corresponding to an integrated luminosity of 175 nb$^{-1}$ were collected using the CMS detector. The ratio is measured separately for prompt and nonprompt charmonia in the transverse momentum range 6.5 $\lt$$p_\text{T}$$\lt$ 30 GeV and in four rapidity ranges spanning $-$2.865 $\lt$$y_\text{CM}$$\lt$ 1.935. For the first time, a statistically significant multiplicity dependence of the prompt cross section ratio is observed in proton-nucleus collisions. There is no clear rapidity dependence in the ratio. The prompt measurements are compared with a theoretical model which includes interactions with nearby particles during the evolution of the system. These results provide additional constraints on hadronization models of heavy quarks in nuclear collisions.
Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -2.865 < y_{CM} < -2$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$
Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -2 < y_{CM} < -1$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$
Normalized $\sigma_{\psi(2S)}/\sigma_{J/\psi}$ in $6.5<p_T<30.0\,GeV$ and $ -1 < y_{CM} < 1$ as functions of normalized $\text{N}^{{\text{corr.}}}_{\text{track}}$
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