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

Abstract

While the prompt J/$\psi$ cross section and polarization have been measured with good precision as a function of transverse momentum, $p_{\mathrm{T}}$, those of the directly produced J/$\psi$ are practically unknown, given that the cross sections and polarizations of the ${\chi }_{c1}$ and ${\chi }_{c2}$ mesons, large indirect contributors to J/$\psi$ production, are only known with rather poor accuracy. The lack of precise measurements of the ${\chi }_{cJ}$ polarizations induces large uncertainties in the level of their feed-down contributions to the prompt J/$\psi$ 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/$\psi$, $\psi$(2S) and ${\chi }_c$ cross sections and polarizations, faithfully respecting all the correlations and uncertainties. In particular, it is seen that the ${\chi }_{cJ}$ polarizations and feed-down fractions to J/$\psi$ production have a negligible dependence on the J/$\psi$ $p_{\mathrm{T}}$, with average values ${\lambda }_{\vartheta }^{{\chi }_{c1}}=0.55\pm 0.23$, ${\lambda }_{\vartheta }^{{\chi }_{c2}}=-0.39\pm 0.22$, $R^{{\chi }_{c1}}=(18.8\pm 1.4)\%$ and $R^{{\chi }_{c2}}=(6.5\pm 0.5)\%$. The analysis also shows that $(67.2\pm 1.9)\%$ of the prompt J/$\psi$ yield is due to directly-produced mesons, of polarization constrained to remarkably small values, ${\lambda }_{\vartheta }^{\mathrm{J}/\psi }=0.04\pm 0.06$.

arXiv commentSubmitted to Eur. Phys. J. C

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