Impact of $J/\psi$ pair production at the LHC and predictions in nonrelativistic QCD

For $J/\psi$ pair production at hadron colliders, we present the full next-to-leading order (NLO) calculations with the color-singlet channel in nonrelativistic QCD. We find that the NLO result can reasonably well describe the LHCb measured cross section, but exhibits very different behaviors from the CMS data in the transverse momentum distribution and mass distribution of the $J/\psi$ pair. Moreover, by adding contributions of gluon fragmentation and quark fragmentation, which occur at even higher order in ${\alpha }_s$, it is still unable to reduce the big differences. In particular, the observed flat distribution in the large invariant mass region is hard to explain. New processes or mechanisms are needed to understand the CMS data for $J/\psi$ pair production.

Figure 1

Typical Feynman diagrams for $J/\psi$ pair production in the color-singlet channel, including LO (a), NLO (b–e), as well as single quark or gluon fragmentation diagrams beyond NLO (f–i).

Figure 2

Comparison between LO, $\overline{\mathrm{HC}}$, and full NLO results of the cross section $p_T$ distribution in $J/\psi$ pair production.

Figure 3

Scale dependence of total cross sections for LO and NLO at LHCb, where ${\mu }_0=m_T$.

Figure 4

Differential cross sections in bins of the $J/\psi$ pair invariant mass at LHCb. The data are taken from Ref. [8]. The green and blue lines denote the LO and NLO theoretical results, respectively.

Figure 5

Differential cross sections in bins of the transverse momentum of $J/\psi$ pair at CMS. The data are taken from Ref. [9]. The blue band denotes the NLO results, where the uncertainties are due to scale choices as mentioned in the text, and the yellow band, solid, dash dotted lines represent the fragmentation contributions including all relevant channels by three sets of different CO matrix elements. The dashed line represents the fragmentation contribution by taking the ${{}^{1}S}_0^{[8]}$-dominant CO matrix elements.

Figure 6

Differential cross sections in bins of the $J/\psi$ pair invariant mass at CMS. The data are taken from Ref. [9]. The green and blue bands denote the LO and NLO theoretical results, respectively, where the uncertainties are due to scale choices as mentioned in the text. The yellow band, solid, dash dotted lines represent the sum of the quark and gluon fragmentation from all relevant channels by three groups of different CO matrix elements. The dashed line represents the fragmentation contribution by taking the ${{}^{1}S}_0^{[8]}$-dominant CO matrix elements.

Figure 7

Differential cross sections in bins of the $J/\psi$ pair $|\mathrm{\Delta }y|$ at CMS. The data are taken from Ref. [9]. The green and blue bands denote the LO and NLO theoretical results, respectively, where the uncertainties are due to scale choices as mentioned in the text.