Production of primordial $J/\psi$ in relativistic $p+p$ and heavy-ion collisions
Résumé
$J/\psi$ observables of p+p collisions at $\sqrt{s}=$ 200 GeV and 2.76 TeV are calculated using the PYTHIA event generator for the production of $c$ and $\bar c$ and the Wigner density formalism. The charm quark momentum from PYTHIA is tuned in such a way that the transverse momentum and rapidity distribution correspond to the Fixed-Order Next-to-Leading Logarithm (FONLL) calculations and hence to the experimental data for open charm mesons. Using the Wigner density of the charmonium wave function we calculate for each charm quark pair the probability to form a charmonium. As a result, the experimental data on the total $J/\psi$ yield, its rapidity and transverse momentum distribution as well as the fractions of feed-down from excited states of charmonium are reproduced. Applying the same approach to relativistic heavy-ion collisions, we find, if quark gluon plasma (QGP) effects are ignored, a considerable enhancement of the primordial $J/\psi$'s.