$J/\psi$ production cross section and its dependence on charged-particle multiplicity in $p+p$ collisions at $\sqrt{s}$ = 200 GeV

We present a measurement of inclusive $J/\psi$ production at mid-rapidity ($|y|<1$) in $p+p$ collisions at a center-of-mass energy of $\sqrt{s}$ = 200 GeV with the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The differential production cross section for $J/\psi$ as a function of transverse momentum ($p_T$) for $0<p_T<14$ GeV/$c$ and the total cross section are reported and compared to calculations from the color evaporation model and the non-relativistic Quantum Chromodynamics model. The dependence of $J/\psi$ relative yields in three $p_T$ intervals on charged-particle multiplicity at mid-rapidity is measured for the first time in $p+p$ collisions at $\sqrt{s}$ = 200 GeV and compared with that measured at $\sqrt{s}$ = 7 TeV, PYTHIA8 and EPOS3 Monte Carlo generators, and the Percolation model prediction.


Introduction
Quarkonia are bound states of heavy quark-antiquark pairs (QQ). Their production in p+p collisions can be factorized into hard and soft processes associated with short and long distance strong interactions, respectively. The former is related to production of QQ from hard parton scatterings and can be calculated by perturbative Quantum Chromodynamics (pQCD). The latter involves evolution of QQ into bound quarkonium states and is usually parameterized by phenomenological models such as the Color-Evaporation Model (CEM), Color Singlet Model, and Non-Relativistic Quantum Chromodynamics (NRQCD) including both color singlet and octet intermediate states (for a recent review see [1]). With sizable theoretical uncertainties, these model calculations can describe the measurement results of quarkonium production cross sections from the Tevatron and Large Hadron Collider (LHC) experiments [2,3,4,5]. Precise measurements of quarkonium production over a wide kinematic range at RHIC energies can provide new constraints on model calculations and insights into the quarkonium production mechanism.
Recent studies at the LHC have revealed a faster-than-linear increase in J/ψ and D-meson relative yields with charged-particle multiplicity (n ch ) at mid-rapidity in p+p collisions at √ s = 7 TeV [6,7], suggesting a strong correlation between hard parton scatterings producing heavy flavor particles and soft underlying processes producing all other particles. By including Multiple-Partonic Interactions (MPI) [8,9,10], i.e. several interactions at the parton level occurring in a single p+p collision, PYTHIA8 [11] and EPOS3 [12] Monte Carlo (MC) generators can produce an increase in relative yields of heavy flavor particles with n ch , but underestimate the observed yields at large n ch [7]. Additional effects have been suggested to explain the measurement results at the LHC. For example, collective expansion implemented in EPOS3 MC generator [13] is found to modify the p T distribution of final state particles in high multiplicity p+p collisions at √ s = 7 TeV, producing a faster-than-linear increase for D-meson relative yields at intermediate and high p T [7]. Such an effect is however expected to be small at RHIC energies. On the other hand, the percolation model [14] produces particles through interactions of color strings, which are more suppressed for soft processes than hard processes due to the different size of the color strings. It can also produce a faster-than-linear increase in relative yields of heavy flavor particles with n ch that is qualitatively consistent with the LHC results. Such an increase is predicted to be similar at different energies by the percolation model. Measurements of relative yields of heavy flavor particles versus n ch at RHIC energies can help constrain model calculations and provide knowledge of the energy dependence of MPI in p+p collisions.
In this letter, we present measurement results of inclusive J/ψ production at mid-rapidity (|y| < 1) in p+p collisions at √ s = 200 GeV with the STAR experiment at RHIC [15]. Both the differential production cross section for J/ψ as a function of transverse momentum (p T ) and the total cross section are obtained with higher precision than the previously published results [16,17]. The dependence of J/ψ relative yields on n ch at mid-rapidity is also determined, for the first time, for p+p collisions at RHIC energies. These results are compared to calculations from various theoretical models and MC generators.

STAR experiment and data analysis
The data used in this measurement were collected with minimum-bias (MB) and high-tower (HT) triggers in p+p collisions at √ s = 200 GeV by the STAR experiment in 2012. The MB triggers select non-single diffractive p+p collisions with a coincidence signal from the two Vertex Position Detectors (VPD) [18] or the two Beam Beam Counters (BBC) [19]. The VPD and BBC are located on both sides of the p+p collision region and covering the pseudo-rapidity region of 4.4 < |η| < 4.9 or 3.3 < |η| < 5.0, respectively. About 300 million events triggered by the VPD are analyzed to study J/ψ production with p T < 1.5 GeV/c, while 2.66 million events triggered by the BBC are used to obtain the n ch distribution in MB p+p collisions. The HT triggers select p+p collisions producing at least one high-p T particle with large energy deposition in the Barrel Electromagnetic Calorimeter (BEMC) [20]. Data collected by the HT0 (HT2) trigger with an energy threshold of E T > 2.6 (4.2) GeV, corresponding to an integrated luminosity of 1.36 (23.5) pb −1 , are analyzed to study J/ψ production with p T > 1.5 (4.0) GeV/c. The vertex positions of p+p collisions along the beam line direction can be reconstructed from TPC tracks (V T PC z ) or from VPD signals (V V PD z ). A cut of |V T PC z | < 50 cm is applied to ensure good TPC acceptance for all the events. An additional cut of |V T PC z − V V PD z | < 6 cm is applied to reduce the pile-up background from out-of-time collisions for the VPD-triggered MB events.
The main detectors used in the data analysis are the Time Projection Chamber (TPC) [21], Time-Of-Flight detector (TOF) [22], and BEMC, all with full azimuthal coverage. The TPC records trajectories of charged particles with p T > 0.2 GeV/c and |η| < 1 in a 0.5 T solenoid magnetic field and determines their momenta and ionization energy losses (dE/dx). Tracks are required to have a maximum distance of the closest approach to the collision point of 1 cm, a minimum of 20 TPC hits (out of a maximum of 45), and a minimum of 11 TPC hits for dE/dx calculation. The TOF (VPD) provides the stop (start) time of flight information for charged particles from the collision vertices to the TOF, while the BEMC measures electromagnetic energy deposition.
3. J/ψ production cross section J/ψ candidates are reconstructed through the J/ψ → e + e − channel, where electrons are identified using the specific energy loss in TPC, dE/dx, the velocity (β) calculated from the path length and time of flight between the collision where The nσ e value is required to be within (-1.9, 3) for all electron candidates. |1/β − 1| < 0.03 is required for TOF associated electron tracks, and 0.3 < pc/E < 1.5 for BEMC-associated candidates with p T > 1 GeV/c. Both daughters of J/ψ candidates are required to pass the nσ e requirement, and either the β or pc/E requirement. For HT-triggered events, at least one daughter of J/ψ candidates must pass the pc/E requirement and have an energy deposition in the BEMC that is higher than the corresponding HT trigger threshold. The invariant mass spectra of the reconstructed J/ψ candidates from different triggered samples are shown in Fig. 1. The J/ψ raw yields are extracted by subtracting the invariant mass spectra of like-sign electron pairs (M e ± e ± ) from the unlike-sign ones (M e ± e ∓ ). The remaining distribution is fit by a two-component function, composed of a J/ψ signal distribution, the shape of which is obtained from STAR detector simulation [23] with the Crystal-Ball function [24], together with a residual background distribution parameterized by a 1 st -order polynomial function. The J/ψ signal to the residual background ratios in the mass range of 2.9 < M ee < 3.2 GeV/c 2 are 18, 36, and 42 for the VPD MB, HT0 and HT2 data, respectively, and have negligible dependence on n ch . The large values of this ratio reflect that the residual background is small and can be neglected for the measurement of the n ch -dependence of J/ψ relative yields.
The J/ψ production cross sections are obtained by correcting the J/ψ raw yields for the detector geometric acceptance and efficiency. The vertex finding, track reconstruction, BEMC electron identification, VPD, BBC and HT trigger efficiencies are estimated from detector simulation, while the electron identification efficiencies by TPC dE/dx and TOF 1/β requirements are estimated from data. The cross sections from the VPD MB, HT0 and HT2 data are consistent with each other in the overlapping p T regions, and are used for 0 < p T < 1.5, 1.5 < p T < 4.0 and 4.0 < p T < 14 GeV/c, respectively. Here unpolarized J/ψ is used in simulation when calculating the J/ψ acceptance and efficiency, which is around 20% for the VPD MB data, 0.6-12% for the HT0 data, and 1.5-30% for the HT2 data, respectively. The latter two increase as a function of J/ψ p T due to the increasing HT trigger efficiency.
The total systematic uncertainty for the measured cross section is obtained from the square root of the quadratic sum of the individual systematic uncertainties listed in Table 1, which generally depend on the J/ψ signal significance in each p T bin. The uncertainty in the raw J/ψ yield extraction, estimated by varying the fitted mass range and by comparing the fit result to the bin counts in 2.9 < M ee < 3.2 GeV/c 2 corrected for the residual background and for the invariant mass cut efficiency, is between 1-14%. The uncertainties in the track reconstruction and electron identification efficiencies, estimated by varying the corresponding cuts in data and simulation, are 3-15% and 4-14%, respectively. Since the TOF efficiency is calculated from tracks matched with BEMC hits, there is a correction applied to the TOF efficiency by the ratio of true TOF efficiency to that calculated with BEMC-matched tracks. This correction causes an uncertainty of 1-7%. The HT trigger efficiency uncertainty, estimated by varying the trigger requirement in data and simulation, is 4-13%. An 8% normalization uncertainty due to the luminosity determination is applied for both the MB and HT results. An additional 6% (3%) normalization uncertainty for the VPD MB (HT) result is added for the VPD (BBC) trigger and vertex reconstruction efficiency, making the total normalization uncertainty 10% (8.5%).  Figure 2 shows the measured J/ψ production cross section times the J/ψ → e + e − branching ratio (B ee ) as a function of J/ψ p T . The new result is consistent with the published STAR [16] result, but has better statistical precision for p T < 10 GeV/c and includes systematic uncertainties that were not considered previously. It is also consistent with the published PHENIX [17] result, but has better precision for p T > 2 GeV/c. The total J/ψ production cross section times the branching ratio per rapidity unit is estimated to be Also shown in Fig. 2 are theoretical model calculations. The green band represents the result from CEM calculations for 0 < p T < 14 GeV/c and |y| < 0.35 [2], the orange band shows that from Next-to-Leading Order (NLO) NRQCD calculations for 4 < p T < 14 GeV/c and |y| < 1 [3], and the blue band depicts the result from NRQCD calculations for 0 < p T < 5 GeV/c and |y| < 1 which incorporates a Color-Glass Condensate (CGC) effective theory framework for small-x resummation [25]. The CEM and NLO NRQCD calculations describe the data reasonably well for the applicable p T ranges. The CGC+NRQCD calculations are consistent with the data within uncertainties, however, the data are close to the lower uncertainty boundary of the theoretical calculation. We note that the feeddown contribution from bottom hadron decays is included in the experimental data but not included in any of these calculations, which is predicted to be approximately 10-25% in the range of 4 < p T < 14 GeV/c [26,27]. As can be seen, except for the two bins at the highest p T , the uncertainties in the experimental results are smaller than those in the theoretical calculations. Therefore, the new STAR result can be used to constrain theoretical model calculations.

Dependence of J/ψ production on n ch
The BBC has a much higher trigger efficiency than the VPD for low multiplicity p+p collisions. Therefore, the BBC-triggered MB data are used to characterize the n ch distribution at mid-pseudorapidity (|η| < 1) in MB p+p collisions. The n ch distribution for p+p collisions producing J/ψ is obtained by subtracting the n ch distribution of events containing like-sign electron pairs with 2.9 < M ee < 3.2 GeV/c 2 from that of unlike-sign pairs, both of which are reweighted by the inverse of the J/ψ reconstruction efficiency. Here the raw n ch for each event is obtained from the number of tracks reconstructed in the TPC with a matched hit in the TOF. Unlike the TPC, which is susceptible to pile-up tracks from out-of-time collisions, the TOF only records signals from particles produced from the triggered collision. About 1% of tracks from pile-up collisions may randomly match a TOF hit and the effect of these pile-up tracks is considered as a systematic uncertainty. The raw n ch distributions are corrected for the vertex finding efficiency, which is important for low multiplicity p+p collisions, and for the TPC and TOF acceptances and efficiencies  [16]; triangles are the published results for |y| < 0.35 from PHENIX [17]. Bars and boxes are statistical and systematic uncertainties, respectively. The curves are NRQCD and CEM theoretical calculations for |y| < 1 and |y| < 0.35, respectively. Bottom: ratios of these results with respect to the central value from this analysis.
through an iterative Bayesian unfolding method [28]. The response matrix used for unfolding is obtained from MC samples generated with PYTHIA8.183 [11] and convoluted with the detector acceptances and efficiencies. Here the true n ch in the response matrix is defined as the number of charged particles produced promptly from the primary vertex, including pion, kaon, proton, electron, and muon with |η| < 1, p T > 0 GeV/c, and not from K 0 or Λ decays. In addition, J/ψ events require that the J/ψ-decay electrons are within |η| < 1 and included in the n ch calculations. Figure 3 shows the corrected n ch distributions, together with a negative binomial distribution (NBD) function fitted to the distribution in MB p+p collisions. The average charged-particle multiplicity per pseudo-rapidity unit obtained from the fit, dN MB ch /dη = 2.9 ± 0.3(stat.) ± 0.2(model) ± 0.4(syst.), is consistent with the previous STAR published result [23]. The model uncertainty is estimated from the difference between the average value of the n ch distribution and the NBD fit result. As can be seen, the average n ch for p+p collisions producing J/ψ increases with increasing J/ψ p T and is higher than that for MB collisions.
The corrected n ch distributions are divided into five intervals: 0-5, 6-10, 11-15, 16-21 and 22-31. The J/ψ relative yield N J/ψ / N J/ψ and relative charged-particle multiplicity (dN MB ch /dη)/ dN MB ch /dη are estimated for each interval, where N J/ψ is the number of J/ψ produced per MB collision in a multiplicity interval, and N J/ψ the average value over the whole multiplicity range. The last bin in MB events is excluded due to the large statistical uncertainty. The systematic uncertainties for (dN MB ch /dη)/ dN MB ch /dη and N J/ψ / N J/ψ are summarized in Table 2. The vertex finding efficiency correction has 3% uncertainty, estimated by the difference between the default PYTHIA8 tune and the STAR heavy flavor tune [29]. The track reconstruction efficiency correction is obtained from detector simulation. It depends on n ch and has 4-5 % uncertainty for MB events and 4-23 % uncertainty for J/ψ events. The unfolding process uncertainty is studied by changing the number of Bayesian unfolding iterations and the PYTHIA tune, and by reweighting PYTHIA n ch distribution to match with the unfolded n ch distribution from data. This uncertainty is found to be 2-7 % and 1-30 % for MB and J/ψ events, respectively. The effect of pile-up track contributions is estimated by the difference between the NBD fit and the actual n ch distribution in MB p+p collisions, as well as by the difference in the n ch distribution between the lowest and highest Zero-Degree Calorimeter (ZDC) [30] coincidence rate. The ZDC rate ranged between 1-13 kHz and is proportional to the instantaneous luminosity. The uncertainty due to pile-up track contributions is 2% and 1-10% for MB and J/ψ events, respectively. Figure 4 shows the dependence of the J/ψ relative yield on the relative charged-particle multiplicity for J/ψ p T > 0, 1.5 and 4 GeV/c, respectively. A strong increase in J/ψ relative yields with n ch is observed, and the increase is  stronger at higher p T . The result for J/ψ relative yield with p T > 0 GeV/c in p+p collisions at √ s = 200 GeV is compared with that at √ s =7 TeV [6]. The two results follow a similar trend despite more than one order of magnitude difference in √ s, suggesting a weak dependence of the underlying mechanism on √ s. Also shown in Fig. 4 are calculations from different MC generators and the percolation model. PYTHIA8.183 [11] with the color reconnection scenario describes MPI through pQCD, taking into account the dependence on the energy and impact parameter (the distance between the colliding protons in the plane perpendicular to the beam direction) of p+p collisions. It can describe the J/ψ relative yield and predicts stronger increase of the J/ψ relative yield with n ch at higher p T . EPOS3 [12] uses a Gribov-Regge multiple scattering framework to describe initial p+p collisions and thus includes MPI in both hard and soft processes. Furthermore, it incorporates features of hydrodynamical evolution [13] in highmultiplicity p+p collisions, which is suggested to be important for p+p collisions at √ s = 7 TeV [7] but has little effect at √ s = 200 GeV. Because EPOS3 does not implement J/ψ production, we compare our data with the prediction from EPOS3 on the open charm production. The latter for 2 < p T < 4 (4 < p T < 8) GeV/c is found to be in good agreement with the STAR J/ψ result for p T > 1.5 (p T > 4) GeV/c. The Percolation model [14] adapts a framework of color string interactions to describe p+p collisions. In a high-density environment, the coherence among the sources of the color strings leads to a reduction of their effective number. The total charged-particle multiplicity, which originates from soft sources, is more reduced than heavy-particle production for which the sources have a smaller transverse size. The Percolation model prediction is consistent with the data for p T > 0 GeV/c.  Figure 4: (Color online) The multiplicity dependence of J/ψ production in p+p collisions at √ s = 200 GeV. Purple circles, blue squares, and red triangles represent the results for J/ψ with p T greater than 0, 1.5, and 4 GeV/c, respectively. Bars and open boxes are statistical and systematic uncertainties, respectively. The ALICE result [6] is shown in the left panel. The purple, blue and red bands in the middle panel are generated from PYTHIA8 for J/ψ with p T greater than 0, 1.5, and 4 GeV/c, respectively. The blue and red bands in the right panel are from EPOS3 model calculations for D 0 with 2 < p T < 4 and 4 < p T < 8 GeV/c, respectively, while the green curve is from the Percolation model for J/ψ with p T > 0 GeV/c.

Summary
In summary, inclusive J/ψ production at mid-rapidity |y| < 1 in p+p collisions at √ s = 200 GeV is studied through the J/ψ → e + e − channel with the STAR experiment. The measured differential production cross section as a function of J/ψ p T can be described within experimental and theoretical uncertainties by CEM calculations for 0 < p T < 14 GeV/c, NLO NRQCD calculations for 4 < p T < 14 GeV/c, and CGC+NRQCD calculations for 0 < p T < 5 GeV/c. The total J/ψ production cross section per rapidity unit times J/ψ → e + e − branching ratio is 43.2 ± 3.0(stat.) ± 7.5(syst.) nb. The J/ψ relative yield is found to increase with charged-particle multiplicity at midrapidity. The increase is stronger than a linear rise, and depends strongly on J/ψ p T but weakly on the center-of-mass energy of the p+p collisions when compared to the experimental result at √ s = 7 TeV. The increase can be described by PYTHIA8 and EPOS3 MC generators taking into account Multiple-Partonic Interactions, and by the Percolation model.