Detailed rapidity dependence of $J/\psi$ production at energies available at the Large Hadron Collider

$J/\psi$ suppression with rapidity is studied with both a (3+1)-dimensional transport equation and hydrodynamics in detail at $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. In the central rapidity region of the hot medium, the $J/\psi$ nuclear modification factor shows weak rapidity dependence due to the boost invariance of the medium. But in the forward rapidity region for the entire transverse momentum bin, $J/\psi$ regeneration is strongly suppressed due to the decreasing charm pair cross section. This makes $J/\psi R_{AA}\left(y\right)$ decrease with rapidity. The ratio $r_{AA}$ of the mean transverse momentum squared in $AA$ collisions to that in $pp$ collisions increases strongly in the forward rapidity region and is more sensitive to the $J/\psi$ production mechanisms.

Figure 1

Differential inclusive $J/\psi$ production cross section at $\sqrt{s_{NN}}=2.76$ TeV $pp$ collisions, fitted by exponential functions $\frac{d{\sigma }_{J/\psi }^{pp}}{dy}=Aexp[-y^n/\left(2B^2\right)]$. Solid and dashed lines correspond to $n=4$ and $n=2$ respectively. The parameters $A$ and $B$ are listed in Table 1. Data are from the ALICE Collaboration [37].

Figure 2

The prompt $J/\psi$ nuclear modification factor as a function of rapidity for $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. The data are from the CMS Collaboration [38].

Figure 3

The inclusive $J/\psi$ nuclear modification factor as a function of rapidity for $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. Theoretical calculations are in centrality 0–90%. Dotted line includes initially produced charmonium and non-prompt charmonium (B decay), with both cold and hot nuclear matter effects. Black solid line and black dashed line are the total yields of charmonium with both cold and hot nuclear matter effects. They correspond to the cross sections of solid line and dashed line respectively in Fig. 1. For the black solid line, I also shift $\frac{d{\sigma }_{c\overline{c}}^{pp}}{dy}\left(y\right)$ with 10% to consider the the uncertainty of charm pair cross section, which results in the green colored region of $R_{AA}$. Results of EPS09 and nDSg models are cited from [11]. The experimental data are from the ALICE Collaboration [11, 46].

Figure 4

The inclusive $J/\psi$ nuclear modification factor in the $p_T>3$ GeV/$c$ region as a function of rapidity for $\sqrt{s_{NN}}=2.76$ Pb+Pb collisions. Theoretical calculations are in centrality 0–90%. The black dotted line, dashed line, solid line, and green colored region are the same as those in Fig. 3, but for $p_T>3$ GeV/$c$. Results of EPS09 and nDSg models are from [11]. The experimental data are from the ALICE Collaboration [11].

Figure 5

The elliptic flow of prompt $J/\psi$ as a function of rapidity for $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. The black line is for smooth (3+1)D ideal hydro and red dashed line is for smooth (2+1)D viscous hydro. The data are from the CMS Collaboration [48].

Figure 6

The mean transverse momentum squared ratio $r_{AA}$ of prompt $J/\psi$ as a function of rapidity for $\sqrt{s_{NN}}=2.76$ TeV Pb+Pb collisions. Theoretical calculations are for centrality 0–90%. The black solid line and green color region are the same as those in Fig. 3.