Shadowing effects on $J/\psi$ and $\mathrm{{\rm Y}}$ production at energies available at the CERN Large Hadron Collider

Background: Proton-nucleus collisions have been used as a intermediate baseline for the determination of cold-medium effects. They lie between proton-proton collisions in vacuum and nucleus-nucleus collisions which are expected to be dominated by hot-matter effects. Modifications of the quark densities in nuclei relative to those of the proton are well established, although those of the gluons in the nucleus are not well understood. The effect of these modifications on quarkonium production are studied in proton-lead collisions at the CERN Large Hadron Collider (LHC) at a center-of-mass energy of 5.02 TeV.

Purpose: The possibility of whether the LHC proton-lead data can be described by nuclear modifications of the parton densities, referred to as shadowing, alone is examined. The results are compared to the nuclear modification factor and to the forward-backward ratio, as a function of both transverse momentum, $p_T$, and rapidity, $y$.

Methods: The color evaporation model of quarkonium production is employed at next-to-leading order (NLO) in the total cross section and leading order in the transverse momentum dependence. The EPS09 NLO modifications are used as a standard of comparison. The effect of the proton parton density and the choice of shadowing parametrization on the $p_T$ and rapidity dependence of the result is studied. The consistency of the shadowing calculations at LO and NLO are checked. The size of the mass and scale uncertainties relative to the uncertainty on the shadowing parametrization is also investigated. Finally, whether the expected cold-matter effect in nucleus-nucleus collisions can be modeled as the product of proton-nucleus results at forward and backward rapidity is studied.

Results: The rapidity and $p_T$ dependence of the nuclear modification factor is found to be generally consistent with the NLO calculations in the color evaporation model. The forward-backward ratio is more difficult to describe with shadowing alone. The LO and NLO calculations are inconsistent for EPS09, while other available parametrizations are consistent. The mass and scale uncertainties on quarkonium production are larger than those of the nuclear parton densities.

Conclusions: While shadowing is consistent with the nuclear suppression factors within the uncertainties, it is not consistent with the measured forward-backward asymmetry, especially as a function of transverse momentum. Data from $p+p$ collisions at the same energy are needed.

Figure 1

The gluon distribution function at the factorization scale for $J/\psi$ (a) and $\mathrm{{\rm Y}}$ (b) production. The CT10 (black solid curve), CTEQ5M (blue dashed curve), CTEQ6M (red dot-dashed curve), and MSTW (magenta dot-dot-dot-dash-dashed curve) are compared, all calculated with the same input parameters.

Figure 2

The $J/\psi p_T$ distribution at forward rapidity in $p+p$ collisions (a) and the $p_T$-integrated $y$ distribution (b). Results from CT10 (black solid curve), CTEQ5M (blue dashed curve), CTEQ6M (red dot-dashed curve), and MSTW (magenta dot-dot-dot-dash-dashed curve) are compared, all calculated with the same input parameters and using the same value of $F_C$ as for CT10.

Figure 3

The ratios of $J/\psi$ production as a function of $p_T$ at forward rapidity in $p+p$ collisions (a) and $y$ integrated over all $p_T$ (b) relative to CT10 for CTEQ5M (blue dashed curve), CTEQ6M (red dot-dashed curve), and MSTW (magenta dot-dot-dot-dash-dashed curve).

Figure 4

The $\mathrm{{\rm Y}}$ distribution at forward rapidity in $p+p$ collisions (a) and the $p_T$-integrated $y$ distribution (b). Results from CT10 (black solid curve), CTEQ5M (blue dashed curve), CTEQ6M (red dot-dashed curve), and MSTW (magenta dot-dot-dot-dash-dashed curve) are compared, all calculated with the same input parameters and using the same value of $F_C$ as for CT10.

Figure 5

The ratios of $\mathrm{{\rm Y}}$ production as a function of $p_T$ at forward rapidity in $p+p$ collisions (a) and $y$ integrated over all $p_T$ (b) relative to CT10 for CTEQ5M (blue dashed curve), CTEQ6M (red dot-dashed curve), and MSTW (magenta dot-dot-dot-dash-dashed curve).

Figure 6

Gluon shadowing ratios calculated for Pb nuclei ($A=208$) calculated at the central value of the fitted factorization scales for $J/\psi$ (a) and $\mathrm{{\rm Y}}$ (b). The EPS09 NLO set is shown by the black solid curve, while the uncertainty band is outlined by the black dotted curves. The NLO nDS and nDSg parametrizations are given in the blue dashed and dot-dashed curves, respectively. The LO EKS98 parametrization is given in the magenta dot-dot-dash-dashed curves. The NLO FGS-H and FGS-L results are given by the red dot-dash-dash-dashed and dot-dot-dot-dashed curves, respectively.

Figure 7

The $J/\psi$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ for ALICE at forward rapidity [2] (a) and $p_T$-integrated $R_{p\mathrm{Pb}}\left(y\right)$ from ALICE [1, 2], $\left|y\right|>0$ in the blue points and midrapidity in magenta, and LHCb [4] (red points) (b) are given. The ratios are shown for CT10 (black solid curves), CTEQ5M (blue dashed curves), CTEQ6M (red dot-dashed curves), and MSTW (magenta dot-dot-dot-dash-dashed curves).

Figure 8

The $J/\psi$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b), and central (c) rapidity [2]. In (d), the ALICE results on $R_{p\mathrm{Pb}}\left(y\right)$ [1, 2] are given, $\left|y\right|>0$ in the blue points and midrapidity in magenta, along with those of LHCb [4] (red points). The EPS09 NLO uncertainty band is shown.

Figure 9

The $J/\psi$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region, $2.96<y_{\mathrm{cms}}<3.53$ (a) and $R_{\text{FB}}\left(y\right)$ (b). The EPS09 NLO uncertainty band is shown with the ALICE [1] (blue) and LHCb [4] (red) data.

Figure 10

The $\mathrm{{\rm Y}}$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b), and central (c) rapidity. The ratio $R_{p\mathrm{Pb}}\left(y\right)$ from ALICE [3] (blue) and LHCb [5] (red) is shown in (d). The EPS09 NLO uncertainty band is shown.

Figure 11

The $\mathrm{{\rm Y}}$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region (a) and $R_{\text{FB}}\left(y\right)$ (b). The EPS09 NLO uncertainty band is shown, along with the ALICE [3] (blue) and LHCb [5] (red) data.

Figure 12

The EPS09 central results, as well as the uncertainty bands, are shown in (a), (c), and (e). In all cases, the solid red curve shows the central NLO result, while the dashed red curves delineate the NLO uncertainty band. The dot-dashed blue curve is the LO central result, while the dotted curves outline the LO uncertainty band. The nDS and nDSg results are presented in (b), (d), and (f). The red solid curves show the NLO nDS result, while the dashed red curves are the nDSg results. The blue dot-dashed and dotted curves show the nDS and nDSg LO results. (Top) The LO (blue) and NLO (red) gluon shadowing parametrizations. (Middle) The calculated $J/\psi R_{p\mathrm{Pb}}\left(y\right)$ at $\sqrt{s_{{}_{NN}}}=5$ TeV compared to the ALICE midrapidity (magenta) [2] and $\left|y\right|>0$ (blue) [1] data and the LHCb [4] (red) data. (Bottom) The calculated $\mathrm{{\rm Y}}{R}_{p\mathrm{Pb}}\left(y\right)$ at $\sqrt{s_{{}_{NN}}}=5$ TeV compared to the ALICE [3] (blue) and LHCb [5] (red) data.

Figure 13

The $J/\psi$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b), and central (c) rapidity [2]. In (d), the ALICE results on $R_{p\mathrm{Pb}}\left(y\right)$ [1, 2] are given, $\left|y\right|>0$ in the blue points and midrapidity in magenta, along with those of LHCb [4] (red points). The results are shown for central EPS09 NLO (black curves), nDS NLO (blue dashed curves), nDSg NLO (blue dot-dashed curves), and EKS98 LO (magenta dot-dot-dash-dashed curves), FGS-H (red dot-dash-dash-dashed curves), and FGS-L (red dot-dot-dot-dashed curves).

Figure 14

The $J/\psi$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region (a) and $R_{\text{FB}}\left(y\right)$ (b). The data from ALICE [1] (blue) and LHCb [4] (red) are shown. The ratios are for central EPS09 NLO (black curves), nDS NLO (blue dashed curves), nDSg NLO (blue dot-dashed curves) and EKS98 LO (magenta dot-dot-dash-dashed curves), FGS-H (red dot-dash-dash-dashed curves), and FGS-L (red dot-dot-dot-dashed curves).

Figure 15

The $\mathrm{{\rm Y}}$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b) and central (c) rapidity. The ratio $R_{p\mathrm{Pb}}\left(y\right)$ is compared to the ALICE [3] (blue) and LHCb [5] (red) data in (d). The ratios are for central EPS09 NLO (black curves), nDS NLO (blue dashed curves), nDSg NLO (blue dot-dashed curves) and EKS98 LO (magenta dot-dot-dash-dashed curves), FGS-H (red dot-dash-dash-dashed curves), and FGS-L (red dot-dot-dot-dashed curves).

Figure 16

The $\mathrm{{\rm Y}}$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region (a) and $R_{\text{FB}}\left(y\right)$ (b). The ALICE [3] (blue) and LHCb [5] (red) data are shown in (b). The ratios are shown for central EPS09 NLO (black curves), nDS NLO (blue dashed curves), nDSg NLO (blue dot-dashed curves), EKS98 LO (magenta dot-dot-dash-dashed curves), FGS-H (red dot-dash-dash-dashed curves), and FGS-L (red dot-dot-dot-dashed curves).

Figure 17

The ALICE $J/\psi p_T$ distributions [2] at forward (a), backward (b), and midrapidity (c) at NLO in the CEM [13]. The solid red curve is the EPS09 NLO central value while the dashed red curves are the EPS09 NLO uncertainties and the dot-dashed magenta curves are the mass and scale uncertainties.

Figure 18

The mass and scale uncertainties in the $J/\psi$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b), and central (c) rapidity [2]. In (d), the ALICE results [1, 2] on $R_{p\mathrm{Pb}}\left(y\right)$ are given, $\left|y\right|>0$ in the blue points and midrapidity in magenta, along with those of LHCb [4] (red points). The EPS09 NLO uncertainty band is shown in by the red dashed curves, while the uncertainties calculated with method $v1$ are shown in the blue dot-dashed curves, $v2$ in the magenta dot-dash-dash-dashed curves, and $v3$ in the black dot-dot-dot-dashed curves.

Figure 19

The $p+p$ and $p+\mathrm{Pb}J/\psi$ rapidity distributions for the $(H,H)(C,L)$ sets showing the differences leading to the change in the upper limit of the mass and scale uncertainties of method $v1$ around midrapidity. Here the $(H,H)$ results are shown in black ($p+\mathrm{Pb}$ solid curve, $p+p$ dashed curve), while the $(C,L)$ results are given in red ($p+\mathrm{Pb}$, dot-dashed curve; $p+p$, dotted curve).

Figure 20

The mass and scale uncertainties in the $J/\psi$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region (a) and $R_{\text{FB}}\left(y\right)$ (b). The EPS09 NLO uncertainty band is by the red dashed curves while the uncertainties calculated with method $v1$ are shown in the blue dot-dashed curves and $v3$ in the black dot-dot-dot-dashed curves. The ALICE [1] (blue) and LHCb [4] (red) data are also shown.

Figure 21

The mass and scale uncertainties in the $\mathrm{{\rm Y}}$ ratio $R_{p\mathrm{Pb}}\left(p_T\right)$ in the ALICE acceptance at forward (a), backward (b), and central (c) rapidities. The ratio $R_{p\mathrm{Pb}}\left(y\right)$ is compared to the ALICE [3] (blue) and LHCb [5] (red) data in (d). The EPS09 NLO uncertainty band is shown by the red dashed curves, while the uncertainties calculated with method $v1$ are shown in the blue dot-dashed curves, $v2$ in the magenta dot-dash-dash-dashed curves, and $v3$ in the black dot-dot-dot-dashed curves.

Figure 22

The mass and scale uncertainties in the $\mathrm{{\rm Y}}$ forward-backward ratio $R_{\text{FB}}\left(p_T\right)$ in the ALICE overlap region (a) and $R_{\text{FB}}\left(y\right)$ (b). The EPS09 NLO uncertainty band is shown by the red dashed curves, while the uncertainties calculated with method $v1$ are shown in the blue dot-dashed curves and $v3$ in the black dot-dot-dot-dashed curves. The ALICE [3] (blue) and LHCb [5] (red) data are also shown in (b).

Figure 23

The $J/\psi R_{AA}$ (red solid curves) ratio is compared to the product $R_{pA}(+y)\times R_{pA}(-y)$ (blue points) along with the individual $pA$ ratios at forward (magenta dashed curves) and backward (magenta dot-dashed curves) rapidity. Results are compared for the rapidity distributions at LO (a) and NLO (b), as well as for the $p_T$ dependence at NLO (c). Note that no $y$ direction is given to $R_{\mathrm{PbPb}}$ because it is symmetric around $y=0$.

Figure 24

The $\mathrm{{\rm Y}}{R}_{AA}$ (red solid) ratio is compared to the product $R_{pA}(+y)\times R_{pA}(-y)$ (blue points) along with the individual $pA$ ratios at forward (magenta dashed curves) and backward (magenta dot-dashed curves) rapidity. Results are compared for the rapidity distributions at LO (a) and NLO (b), as well as for the $p_T$ dependence at NLO (c). Note that no $y$ direction is given to $R_{\mathrm{PbPb}}$ because it is symmetric around $y=0$.

Figure 25

The $J/\psi$ ratio $R_{d\mathrm{Au}}\left(p_T\right)$ from PHENIX at forward (a), backward (b) and central (c) rapidity [63]. The ratio $R_{d\mathrm{Au}}\left(y\right)$ [64] is shown (d). The EPS09 NLO uncertainty band is compared to the data.

Figure 26

The $\mathrm{{\rm Y}}$ ratio $R_{d\mathrm{Au}}\left(p_T\right)$ for RHIC at forward (a), backward (b), and central (c) rapidities. The ratio $R_{d\mathrm{Au}}\left(y\right)$ is also shown (d). The EPS09 NLO uncertainty band is compared to the PHENIX [65] (blue circles) and STAR [66] (magenta crosses) $R_{d\mathrm{Au}}\left(y\right)$ data in (d).