Medium effects on charmonium production at ultrarelativistic energies available at the CERN Large Hadron Collider

We investigate with a transport approach the cold and hot nuclear matter effects on the charmonium transverse momentum distributions in relativistic heavy ion collisions. The newly defined nuclear modification factor $r_{AA}={\langle p_T^2\rangle }_{AA}/{\langle p_T^2\rangle }_{pp}$ and elliptic flow $v_2$ for $J/\psi$ are sensitive to the nature of the hot medium and the thermalization of heavy quarks. From Super Proton Synchrotron (SPS) through Relativistic Heavy Ion Collider (RHIC) to Large Hadron Collider (LHC) colliding energies, we observe dramatic changes in the centrality dependence of $r_{AA}$. We find that, at LHC energy, the finally observed charmonia are dominated by the regeneration from thermalized heavy quarks.

Figure 1

The parametrization of inclusive (solid line) and prompt (dashed line) $J/\psi$ production cross sections as a function of transverse momentum in 2.76 TeV $p+p$ collisions. The thick (red online) and thin (black online) lines represent midrapidity and forward rapidity, respectively. The data at forward rapidity are from the ALICE Collaboration [59].

Figure 2

The B decay fraction as a function of $J/\psi$ transverse momentum in $p+p$ collisions. The data are from the CDF [64] and CMS [65] Collaborations, and the straight line is our linear parametrization.

Figure 3

The $J/\psi$ nuclear modification factor as a function of centrality for 2.76 TeV Pb+Pb collisions at forward rapidity (upper panel) and midrapidity (lower panel). The dot-dashed lines represent the initial fraction. The thick and thin dashed lines represent the regeneration fraction with the upper and lower limits of charm quark cross-sections $d{\sigma }_{c\overline{c}}^{pp}/dy=0.8$ and $0.65$ mb at mid rapidity and $0.5$ and $0.4$ mb at forward rapidity. The shaded bands represent the full results. The data points are taken from the ALICE experiment [59].

Figure 4

The $J/\psi$ nuclear modification factor as a function of centrality for 2.76 TeV Pb+Pb collisions at forward rapidity and in different transverse momentum bins. The dot-dashed lines are the initial fraction, the thick and thin dashed lines are the regeneration fraction with charm quark cross sections $d{\sigma }_{c\overline{c}}^{pp}/dy=0.5$ and $0.4$ mb, and the bands are the full result. The data are from the ALICE Collaboration [21].

Figure 5

The $J/\psi$ nuclear modification factor as a function of centrality for 2.76 TeV Pb+Pb collisions at midrapidity and in a high transverse momentum bin. The line is the model calculation and the data are from the CMS collaboration [18].

Figure 6

The $J/\psi$ nuclear modification factor as a function of transverse momentum for 2.76 TeV Pb+Pb collisions at forward rapidity and in different centrality bins. The dot-dashed lines are the initial fraction, the thick and thin dashed lines are the regeneration fraction with charm quark cross sections $d{\sigma }_{c\overline{c}}^{pp}/dy=0.5$ and $0.4$ mb, and the bands are the full result. The data are from the ALICE Collaboration [21].

Figure 7

The $J/\psi$ nuclear modification factor as a function of transverse momentum for 2.76 TeV Pb+Pb collisions at midrapidity and in a minimum bias event. The dot-dashed line is the initial fraction, the thick and thin dashed lines are the regeneration fraction with charm quark cross sections $d{\sigma }_{c\overline{c}}^{pp}/dy=0.8$ and $0.65$ mb, and the band is the full result. The data are from the CMS Collaboration [20].

Figure 8

The newly defined nuclear modification factor $r_{AA}={\langle p_T^2\rangle }_{AA}/{\langle p_T^2\rangle }_{pp}$ for $J/\psi$'s as a function of centrality at SPS, RHIC, and LHC energies. The bands at LHC are due to the uncertainty in the charm quark cross section $0.4<d{\sigma }_{c\overline{c}}^{pp}/dy<0.5$ mb at forward rapidity (lower panel) and $0.65<d{\sigma }_{c\overline{c}}^{pp}/dy<0.8$ mb at midrapidity (upper panel), and the data are from NA50 [5], PHENIX [71], and ALICE [72] Collaborations.

Figure 9

The newly defined nuclear modification factor $r_{AA}={\langle p_T^2\rangle }_{AA}/{\langle p_T^2\rangle }_{pp}$ for $J/\psi$'s as a function of centrality at LHC energy and at forward rapidity. The upper and lower panels are the comparisons between pQCD and thermal charm quark distributions and between with and without shadowing effect. The bands are again due to the uncertainty in the charm quark cross section $0.4<d{\sigma }_{c\overline{c}}^{pp}/dy<0.5$ mb, and the data are from the ALICE Collaboration [72].

Figure 10

The elliptic flow $v_2$ for prompt (upper panel) and inclusive (lower panel) $J/\psi$'s in $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. The calculation is with impact parameter $b=8.4$ fm, corresponding to the minimum bias event. The dot-dashed, dashed, and solid lines represent the initial, regeneration, and total contributions. In the lower panel, the thick and thin lines indicate the total results including thermal bottom decay and pQCD bottom decay, respectively. The experimental data are taken from the ALICE experiment [74].