Production of $J/\psi +{\chi }_c$ and $J/\psi +J/\psi$ with real gluon emission at the LHC

In the present work we study production of $J/\psi +{\chi }_c$ and $J/\psi +J/\psi$ at the LHC. The first process is forbidden at the leading order in gluon fusion due to the $C$-parity conservation, and the first nonvanishing contribution is given by the process with the additional emission of a real gluon. Considering the direct production of $J/\psi +J/\psi$, where the leading order is allowed, we have found that the contribution from the higher order process with real gluon emission is comparable and even more significant than the leading order. Moreover, account of this higher order effect dramatically changes kinematical distributions. Through the present paper we study in detail different channels of paired $J/\psi +J/\psi$ production: direct $J/\psi +J/\psi$ production, feed-down from the $J/\psi +{\chi }_c$ channel, and double parton scattering. We also try to find kinematical distributions that are most suitable to separate these different channels.

Figure 1

Typical Feynman diagrams for the paired heavy quarkonia production at parton level: (a) diagram for the LO process (only for $J/\psi +J/\psi$); (b)–(d) diagrams for the NLO* process (both $J/\psi +{\chi }_c$ and $J/\psi +J/\psi$ are possible).

Figure 2

Energy dependence of partonic cross section of $gg\to J/\psi +J/\psi$ (solid), $gg\to J/\psi +J/\psi +g$ (dashed), and $gg\to J/\psi +{\chi }_c+g$ (dotted-dashed). The cross sections are evaluated within the kinematical region ${\mathrm{\Delta }}_{\chi }={\mathrm{\Delta }}_{\psi }=1\mathrm{GeV}$. The cross section of $J/\psi +{\chi }_c$ is very small, so in the figure it is multiplied by a factor of 10.

Figure 3

Distribution over invariant mass of the $J/\psi +J/\psi$ pair for $\mathrm{\Delta }=1\mathrm{GeV}$ (left) and $\mathrm{\Delta }=3\mathrm{GeV}$ (right). Solid (blue), dashed (red) and dotted-dashed (green) lines correspond to direct NLO* $J/\psi +J/\psi$, feed-down from $J/\psi +{\chi }_c$ and DPS mechanisms respectively.

Figure 4

Distribution over transverse momenta of a whole $J/\psi +J/\psi$ pair. Notation is the same as in Fig. 3.

Figure 5

Distribution over transverse momentum asymmetry ${\mathcal{A}}_T=|p_{T1}-p_{T2}|/|p_{T1}+p_{T2}|$. Notation is the same as in Fig. 3.

Figure 6

Distribution over rapidity of $J/\psi$. Notation is the same as in Fig. 3.

Figure 7

Distribution over azimuthal asymmetry $|\mathrm{\Delta }\varphi |=|{\varphi }_1-{\varphi }_2|$. Notation is the same as in Fig. 3.

Figure 8

Distribution over rapidity asymmetry $\mathrm{\Delta }y=y_1-y_2$. Notation is the same as in Fig. 3.