From prompt to direct J/$ψ$ production: new insights on the $χ_{c1}$ and $χ_{c2}$ polarizations and feed-down contributions from a global-fit analysis of mid-rapidity LHC data

Abstract

While the prompt J/$ψ$ cross section and polarization have been measured with good precision as a function of transverse momentum, $p_{\rm T}$, those of the directly produced J/$ψ$ are practically unknown, given that the cross sections and polarizations of the $χ_{c1}$ and $χ_{c2}$ mesons, large indirect contributors to J/$ψ$ production, are only known with rather poor accuracy. The lack of precise measurements of the $χ_{cJ}$ polarizations induces large uncertainties in the level of their feed-down contributions to the prompt J/$ψ$ yield, because of the polarization-dependent acceptance corrections. The experimental panorama of charmonium production can be significantly improved through a consistent and model-independent global analysis of existing measurements of J/$ψ$, $ψ$(2S) and $χ_{c}$ cross sections and polarizations, faithfully respecting all the correlations and uncertainties. In particular, it is seen that the $χ_{cJ}$ polarizations and feed-down fractions to J/$ψ$ production have a negligible dependence on the J/$ψ$ $p_{\rm T}$, with average values $λ_\vartheta^{χ_{c1}} = 0.55 \pm 0.23$, $λ_\vartheta^{χ_{c2}} = -0.39 \pm 0.22$, $R^{χ_{c1}} = (18.8 \pm 1.4)\%$ and $R^{χ_{c2}} = (6.5 \pm 0.5)\%$. The analysis also shows that $(67.2 \pm 1.9)\%$ of the prompt J/$ψ$ yield is due to directly-produced mesons, of polarization constrained to remarkably small values, $λ_\vartheta^{{\rm J}/ψ} = 0.04 \pm 0.06$.