Study of $\chi_{\mathrm{c}}$ production in pPb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 8.16 TeV

Production of prompt P-wave charmonium states $\chi_\mathrm{c1}$(1P) and $\chi_\mathrm{c2}$(1P) is studied in proton-lead (pPb) collisions at a center-of-mass energy per nucleon pair of $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}$ = 8.16 TeV. The analysis is based on data corresponding to an integrated luminosity of 175 nb$^{-1}$ collected by the CMS experiment at the CERN LHC. The $\chi_\mathrm{c}$ states are measured via their decay $\chi_\mathrm{c}$ $\to$ J$/\psi\,\gamma$. The J$/\psi$ meson is reconstructed via its decay to a muon pair, while the photon is reconstructed through its conversion to an electron-positron pair. The ratio of production cross sections times branching fractions for the two charmonium states, [$\sigma(\chi_\mathrm{c2}) \mathcal{B}(\chi_\mathrm{c2}$ $\to$ J$/\psi \, \gamma$)] / [$\sigma(\chi_\mathrm{c1}) \mathcal{B}(\chi_\mathrm{c1}$ $\to$ J$/\psi \, \gamma)$], is reported in the rapidity range $\vert y($J$/\psi)\vert$ $\lt$ 2.4 for the transverse momentum range 6.5 $\lt$ $p_{\mathrm{T}}$(J$/\psi$) $\lt$ 30 GeV. The $\chi_\mathrm{c2}$-to-$\chi_\mathrm{c1}$ ratio is found to be independent of event charged-particle multiplicity, as well as of the rapidity and $p_\mathrm{T}$ of the J$/\psi$. The consistency of this ratio with proton-proton measurements at $\sqrt{s}$ = 7 TeV indicates an absence of strong relative modification for $\chi_\mathrm{c}$ states in pPb collisions, in contrast to the behavior observed in the $\psi$(2S)-to-J$/\psi$ ratio.