Associated Quarkonium Hadroproduction at High-Energy Colliders

Quarkonium production in proton-proton collision is interesting in profiling the partons inside the nucleon. Recently, the impact of double parton scatterings (DPSs) was suggested by experimental data of associated quarkonium production (J/psi+Z, J/psi+W, and J/psi+J/psi) at the LHC and Tevatron, in addition to single parton scatterings (SPSs). In this proceedings contribution, we review the extraction of the effective parameter of the DPS through the evaluation of the SPS contributions under quark-hadron duality.


The double parton scattering
Let us parametrize the DPS. If we assume two uncorrelated parton scatterings, the DPS cross section can be written as with δ AB = 1 for the case where we have A = B in the final state, where A or B (or both) is a quarkonium.
The CEM is a model to calculate heavy quarkonium production processes based on quark-hadron duality [4,[30][31][32][33]. In this model, the quarkonium Q is produced as a quark-antiquark pair QQ having its invariant mass below the open-heavy flavor threshold 2m thr. . The cross section in the model is given by where we assume universal parameters P [34], obtained from the fit of the single inclusive J/ψ hadroproduction data. A caveat is that the single-quarkonium production cross section predicted by the model overshoots the experimental data at high transverse momentum p T [2,4,34]. It is understood that the dominance of the gluon fragmentation in the model yields too hard a p T spectrum, which should also apply to the associated quarkonium production with vector bosons, discussed in the next section.
4. Analysis of the ATLAS data for J/ψ + Z and J/ψ + W productions in the CEM Let us now consider the J/ψ + Z and J/ψ + W productions. As we mentioned in the previous section, the single quarkonium production in the CEM is dominated by the gluon fragmentation topologies at large p T , which also happens for the cases of J/ψ + Z and J/ψ + W. Since the CEM predictions overshoot the experimental data at high p T , we can set conservative upper limits to the SPS contribution of both these processes. The SPS is evaluated at NLO in α s with MadGraph5 aMC@NLO [35].  Table I shows the results of the associated J/ψ productions with vector bosons. We see that the NLO CEM SPS predictions alone are smaller than the ATLAS experimental data (see also Fig. 1).

Analysis of di-J/ψ production in the CEM
Let us now evaluate the di-J/ψ production in the CEM. The regions of the phase space of interest are at the large invariant mass M ψψ and rapidity separation ∆y, where the experimental data of CMS and ATLAS are overshooting the color singlet model SPS prediction [11,12,18,27].
By computing the SPS contribution to the di-J/ψ production at LO, we obtain the result of Fig. 2. No particular enhancements at large M ψψ and ∆y are seen in the CEM. Our result is suggesting the dominance of the DPS in these regions of the di-J/ψ production. By assuming the dominance of the DPS, the σ eff value extracted from the CMS [11] (σ eff = (8.2 ± 2.0 stat ± 2.9 sys ) mb [18]), D0  [19,20] are also displayed for comparison.  (σ eff = (4.8 ± 0.5 stat ± 2.5 sys ) mb) [10], and ATLAS Collaborations (σ eff = (6.3 ± 1.6 stat ± 1.0 sys ) mb) [12] are all consistent with each other, as well as with those of the J/ψ + W and J/ψ + Z productions. In Fig. 3, we summarize the extractions of σ eff from different processes and experimental data.

Conclusion
To summarize, we analyzed the production processes of J/ψ + W/Z (NLO) and J/ψ + J/ψ (LO) in the CEM. For the case of J/ψ+ W/Z, it is possible to extract the DPS yield from the experimental data by setting an upper limit on the SPS contribution. We obtained σ eff = (4.7 +2.4 −1.5 ) mb (J/ψ + Z), and σ eff = (6.1 +3.3 −1.9 ) mb (J/ψ + W), which emphasizes the importance of the DPS and is compatible with other extractions from other central rapidity quarkonium data. This σ eff is also in agreement with the enhancement of the di-J/ψ production at large ∆y and invariant mass.