Measurements of charmonium production in p$+$p, p$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{\rm NN}}}$~=~200~GeV with the STAR experiment

We present the first results from the STAR MTD of mid-rapidity charmonium measurements via the di-muon decay channel in p$+$p, p$+$Au, and Au$+$Au collisions at $\sqrt{s_{_{\rm NN}}}=200$~GeV at RHIC. The inclusive $J/\psi$ production cross section in p$+$p collisions can be described by the Non-Relativistic QCD (NRQCD) formalism coupled with the color glass condensate effective theory (CGC) at low transverse momentum ($p_T$) and next-to-leading order NRQCD at high $p_T$. The nuclear modification factor in p$+$Au collisions for inclusive $J/\psi$ is below unity at low $p_T$ and consistent with unity at high $p_T$, which can be described by calculations including both nuclear PDF and nuclear absorption effects. The double ratio of inclusive $J/\psi$ and $\psi(2S)$ production rates for $0<p_T<10$~GeV/$c$ at mid-rapidity between p$+$p and p$+$Au collisions is measured to be 1.37~$\pm$~0.42~$\pm$~0.19. The nuclear modification factor in Au$+$Au collisions for inclusive $J/\psi$ shows significant $J/\psi$ suppression at high $p_T$ in central collisions and can be qualitatively described by transport models including dissociation and regeneration contributions.


Introduction
The J/ψ dissociation by the color-screening effect in the hot and dense medium [1] was initially proposed as direct evidence of the quark-gluon plasma formation. However, the interpretation of J/ψ suppression observed in heavy-ion collisions has remained a challenge due to the contribution of regenerated J/ψ from the coalescence of deconfined cc pairs in the medium as well as cold nuclear matter effects. Quantifying the cold and hot nuclear matter effects at the RHIC requires precise measurements of charmonium production in p+p, p+Au, and Au+Au collisions. The Muon Telescope Detector (MTD), which provides both the muon triggering and identification capabilities at mid-rapidity, opens the door to measuring quarkonia via the di-muon decay channel at STAR. Using the MTD di-muon trigger, the STAR experiment recorded data corresponding to an integrated luminosity of 14. modification factors for inclusive J/ψ production over a broad kinematic range in both p+Au and Au+Au collisions at √ s NN = 200 GeV; and (ii) the first measurement of the double ratio of inclusive ψ(2S ) and J/ψ production rates at mid-rapidity between p+p and p+Au collisions at √ s NN = 200 GeV.
2. Inclusive J/ψ measurements in p+p and p+Au collisions at √ s NN = 200 GeV Figure 1 shows the production cross section of inclusive J/ψ in p+p collisions at √ s = 200 GeV via the di-muon decay channel for the transverse momentum (p T ) range of 1 < p T < 10 GeV/c (red circles), along with a similar measurement via the di-electron decay channel (blue squares) in 0 < p T < 14 GeV/c. These results are consistent in the overlapping p T range. The experimental results can be well described by CGC+NRQCD [2] and NLO NRQCD [3] calculations for prompt J/ψ at low and high p T ranges, respectively. While an improved color evaporation model (ICEM) calculation for direct J/ψ [4] can describe the data for p T < 3 GeV/c, it generally underestimates the yield at higher p T . Figure 2 shows the nuclear modification factor, R pAu , of inclusive J/ψ in 0-100% central p+Au collisions. The measured R pAu is generally consistent with the previous R dAu result reported by the PHENIX experiment [5] within statistical and systematic uncertainties. The largest deviation between these results is 1.4σ in the range of 3 < p T < 5 GeV/c. This overall consistency suggests similar cold nuclear matter effects in p+Au and d+Au collisions. Calculations, taking into account the nuclear PDF effect using the nCTEQ15 [6,7,8] or EPS09NLO [6,7,8,9] nuclear PDF sets, can touch the upper limit of the data within uncertainties. However, the model calculation including an additional nuclear absorption effect [10] is favored by the data. The new STAR result for 0 < p T < 10 GeV/c follows the global trend of results by HERA [11], PHENIX [12,13], and CDF [14] experiments. The ICEM calculation at √ s = 200 GeV [4] can describe the increasing trend of the ratio with p T . Figure 4 shows the double ratio of ψ(2S ) and J/ψ production rates between p+p and p+Au collisions as a function of rapidity. The new STAR results at |y| < 0.5 is 1.37 ± 0.42(stat) ± 0.19(sys), which is consistent with the published PHENIX results at |y| < 0.35 in d+Au collisions [15]. The co-mover model calculation [16,17] can qualitatively describe the double ratio at forward and backward rapidities in p+Au collisions reported by the PHENIX experiment [13], and is consistent with the new STAR result at midrapidity within uncertainties.

Inclusive J/ψ measurements in Au+Au collisions at √ s NN = 200 GeV
Shown in Fig. 5 is the nuclear modification factor R AA of inclusive J/ψ in 0-40% central Au+Au collisions compared with LHC results [18,19]. The strong suppression at RHIC at high p T indicates significant J/ψ dissociation. The hint of the increasing R AA with increasing p T can be explained by the formation-time effect and the feed-down contribution from B hadron decays [20]. The stronger suppression of J/ψ at RHIC at low p T can be explained by less regeneration contribution due to smaller charm production cross section, while the smaller suppression of J/ψ at RHIC at high p T could arise from a smaller dissociation rate due to the lower temperature of the medium. The R AA as a function of the number of participant nucleons (N part ) for p T > 0 GeV/c and p T > 5 GeV/c are compared with the R pAu in Fig. 6. The nuclear modification factors in the most peripheral Au+Au collisions are consistent with those measured in p+Au collisions.
Transport models from Tsinghua [21,22] and Texas A&M University (TAMU) [20,23] groups, including dissociation and regeneration contributions, can qualitatively describe the p T dependence of the RHIC and the LHC data as shown in Fig. 5. Centrality dependences of the J/ψ R AA at the RHIC [24] and the LHC are shown in Fig. 7 for p T > 0 GeV/c and in Fig. 8 for p T > 5 GeV/c. For p T > 0 GeV/c, both models can describe the centrality dependence at the RHIC, but tend to overestimate the suppression at the LHC. For p T > 5 GeV/c, there is tension among models and data. The discontinuities seen in the R AA as a function of N part from the Tsinghua model calculation can be attributed to the complete dissociation of J/ψ when the medium temperature exceeds the dissociation temperature.

Summary
In summary, we presented the first charmonium measurements in the di-muon decay channel at midrapidity at the RHIC. In p+p collisions at √ s = 200 GeV, inclusive J/ψ production cross section can be described by CGC+NRQCD and NLO NRQCD model calculations for prompt J/ψ at low and high p T ranges, respectively. While the ICEM calculation for direct J/ψ can describe the data for p T < 3 GeV/c, it generally underestimates the yield at higher p T . In p+Au collisions at √ s NN = 200 GeV, we observe (i) inclusive J/ψ R pAu is consistent with R dAu suggesting similar cold nuclear matter effects in p+Au and d+Au collisions; (ii) calculations incorporating the nuclear PDF and nuclear absorption effects can well describe R pAu ; and (iii) the double ratio of inclusive J/ψ and ψ(2S ) production rates between p+p and p+Au collisions is 1.37 ± 0.42 ± 0.19. In Au+Au collisions at √ s NN = 200 GeV, we observe (i) significant J/ψ suppression in central collisions at high p T indicating dissociation; (ii) the J/ψ R AA can be qualitatively described by transport models including dissociation and regeneration; and (iii) the R AA in the most peripheral collisions is consistent with the R pAu . These measurements in Au+Au collisions will gain additional statistical precision by combining with the similar amount of data recorded in the RHIC 2016 run.