Suppression versus enhancement of heavy quarkonia in $pA$ collisions

We describe the production of heavy quarkonia in $pA$ collisions within the dipole approach by assuming the dominance of the perturbative color-singlet mechanism (CSM) in the $p_T$-integrated cross section. Although accounting for a nonzero heavy $Q\text{−}\overline{Q}$ separation is a higher-twist correction that is usually neglected, we found it to be the dominant source of nuclear effects, significantly exceeding the effects of leading-twist gluon shadowing and energy loss. Moreover, this contribution turns out to be the most reliably predicted, relying on the precise measurements of the dipole cross section at the Hadron-Electron Ring Accelerator (HERA) at DESY. The nuclear suppression of quarkonia has been anticipated to become stronger with energy because the dipole cross section steeply rises. However, the measured nuclear effects remain essentially unchanged within the energy range from that of the BNL Relativistic Heavy Ion Collider (RHIC) to that of the Large Hadron Collider (LHC). A production mechanism is proposed that enhances the charmonium yield. Nuclear effects for the production of $J/\psi$, $\psi \left(2S\right)$, $\mathrm{{\rm Y}}\left(1S\right)$, and $\mathrm{{\rm Y}}\left(2S\right)$ are calculated and are in agreement with data from RHIC and LHC. The dipole description offers a unique explanation for the observed significant nuclear suppression of the $\psi \left(2S\right)\text{-to-}J/\psi$ ratio, which is related to the nontrivial features of the $\psi \left(2S\right)$ wave function.

Figure 1

Ratio (6) of the dipole propagation probability to the one calculated in the frozen approximation. Solid and dashed curves are calculated either with the oscillatory binding potential, or without any potential, respectively.

Figure 2

Multiple-color-exchange interaction of a high-energy $\overline{c}c$ pair propagating through a nucleus.

Figure 3

(left) Symmetric $1^{+}$ state production in glue-glue fusion, $gg\to g{\left\{\overline{c}c\right\}}_{1^{+}}$. (right) Diffractive production of color-octet state $g+N\to g{\left\{\overline{c}c\right\}}_{8^{-}}+N$ with subsequent color-exchange transition $8^{-}\to 1^{+}$ on another nucleon.

Figure 4

From bottom to top, the terms $R^{2N}$, $R^{1N}$ and their sum, Eq. (17), for $p\text{-Au}$ collisions at $\sqrt{s}=200\text{GeV}$. Dotted and dashed curves present calculations without and with gluon shadowing corrections, respectively.

Figure 5

The same as in Fig. 4, but for $p\text{-Pb}$ collisions at $\sqrt{s}=5000\text{GeV}$.

Figure 6

Ratio of the projectile gluon distributions in $p\text{-Pb}$ to $pp$ collisions at $\sqrt{s}=5000\text{GeV}$ vs $x_1$ and $B$. The projectile gluon distribution, ${\tilde{g}}_N(x_1,B$) in $pA$ collisions is DGLAP evolved from the initial scale $4m_c^2$ to $4m_c^2+Q_s^2$, generated by the impact-parameter-dependent saturation momentum $Q_s\left(B\right)$.

Figure 7

Ratio of $p\text{-Au}$ to $pp$ cross sections of $J/\psi$ production at $\sqrt{s}=200\text{GeV}$. The curves from bottom to top present numerical results for the terms in Eq. (17) $R^{\left(2N\right)}$, $R^{\left(1N\right)}$, and their sum, respectively. Gluon shadowing and nonperturbative and perturbative energy-loss effects are included (see text). The data points are from Ref. [4].

Figure 8

The same as in Fig. 7, but for $p\text{-Pb}$ collisions at $\sqrt{s}=5000\text{GeV}$. Data points are from Refs. [5, 6]

Figure 9

The $p_T$-dependent ratio of the differential cross sections of inclusive (but direct) $J/\psi$ production in $pA$ and $pp$ collisions, at $\sqrt{s}=5.02\text{TeV}$ and $y\in (-4.46,-2.96)$. Data points are from Ref. [6].

Figure 10

The same as in Fig. 9, but for $y\in (-1.37,-0.43)$.

Figure 11

The same as in Fig. 9, but for $y\in (2.03,3.53)$.

Figure 12

Ratio of $p\text{-Au}$ to $pp$ cross sections of $\psi \left(2S\right)$ production at $\sqrt{s}=200\text{GeV}$. The curves from bottom to top present numerical results for the terms in Eq. (17) $R^{\left(2N\right)}$, $R^{\left(1N\right)}$, and their sum, respectively. Gluon shadowing, as well as the nonperturbative and perturbative energy-loss effects are included (see text). The data point is from Ref. [85].

Figure 13

The same as in Fig. 12, but for $p\text{-Pb}$ collisions at $\sqrt{s}=5000\text{GeV}$. Data points are from Ref. [86]

Figure 14

The double ratio $R_{pA}^{\left(2S\right)}/R_{pA}^{\left(1S\right)}$ as function of quarkonium energy in the nuclear rest frame, $E_{\overline{Q}Q}=M_{\overline{Q}Q}^2/2x_2{m}_N$. Solid and dashed curves show the results of calculations for charmonium and bottomium, respectively. Green full circles and squares show the results of, respectively, ALICE [86] and LHCb [87] measurements of $R_{pA}^{\psi \left(2S\right)}/R_{pA}^{J/\psi }$ at $\sqrt{s}=5.02\text{TeV}$. The blue empty circle shows the CMS result [88] for $\mathrm{{\rm Y}}\left(2S\right)/\mathrm{{\rm Y}}\left(1S\right)p\text{Pb}$ to $pp$ double ratio at $\sqrt{s}=5.02\text{TeV}$.

Figure 15

The same as in Fig. 7, but for $\mathrm{{\rm Y}}$ production in $p\text{-Au}$ collisions at RHIC at $\sqrt{s}=200\text{GeV}$. The data point is from Rev. [89].

Figure 16

The same as in Fig. 15, but at $\sqrt{s}=5000\text{GeV}$.

Figure 17

Inelastic dipole-nucleon amplitude, squared and summed over final nucleon debris.

Figure 18

Graphical representation of the density matrix, describing color states of the interacting dipole.

Figure 19

Different unitarity cuts of the dipole-nucleon interaction cross section. The unitarity cuts are shown by dashed lines.

Figure 20

Feynman graphs for CSM of $J/\psi$ production.

Figure 21

The cross section of $pp\to J/\psi X$, calculated with Eqs. (B14) and (B15) in comparison with data from Refs. [4, 57] at $\sqrt{s}=200\text{GeV}$.

Figure 22

The same as in Fig. 21 at $\sqrt{s}=5000\text{GeV}$ in comparison with data [90].