Production of primordial $J/\psi$ in relativistic $p+p$ and heavy-ion collisions

$J/\psi$ observables of $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ and 2.76 TeV are calculated using the pythia event generator for the production of $c$ and $\overline{c}$ 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 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.

Figure 1

The Wigner function for a $P$ state as a function of $r/\sigma$ for $\sigma p=1$ and 2.

Figure 2

The transverse momentum at $\left|y\right|<1$ and rapidity distribution of charm quarks in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ and 2.76 TeV from the FONLL and from the tuned pythia calculations.

Figure 3

The distribution of the relative momentum in the center-of-mass frame of charm quark pair from the tuned pythia calculations for $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ and 2.76 TeV.

Figure 4

$J/\psi$ production in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ including the feed-down from ${\chi }_c$ and ${\psi }^{\prime }$ in comparison with the experimental data from the PHENIX Collaboration [46].

Figure 5

$J/\psi$ production in $p+p$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$ including the feed-down from ${\chi }_c,{\psi }^{\prime }$, and $B$ mesons in comparison with the experimental data from the ALICE Collaboration [47].

Figure 6

The percentages of $J/\psi$ coming from ${\chi }_c$ and ${\psi }^{\prime }$ decays in $p+p$ collisions at $\sqrt{s}=200\mathrm{GeV}$ and 2.76 TeV, compared with the experimental data from the PHENIX [48] and CDF [11] collaborations and the global averages of the $p+A$ measurements [50]. The contribution from $B$ decay is excluded.

Figure 7

Primordial rapidity distributions of $J/\psi$ in $0–20\%$ central Au+Au collisions at $\sqrt{s}=200\mathrm{GeV}$ (top) and in $0–20\%$ central Pb+Pb collisions at $\sqrt{s}=2.76\mathrm{TeV}$ (bottom). For the dashed curve the creation of charmonium from $c$ and $\overline{c}$ from different initial collisions is excluded. For the dotted line we do not exclude this mixing. The solid lines show calculations in which the Wigner density has been modified to simulate QGP effects. For orientation we display as well the experimental data from the PHENIX Collaboration [51].