Measurement of cold nuclear matter effects for inclusive $J/\psi$ in $p$+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 200 GeV

Measurement by the STAR experiment at RHIC of the cold nuclear matter (CNM) effects experienced by inclusive $J/\psi$ at mid-rapidity in 0-100\% $p$+Au collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 200 GeV is presented. Such effects are quantified utilizing the nuclear modification factor, $R_{p\mathrm{Au}}$, obtained by taking a ratio of $J/\psi$ yield in $p$+Au collisions to that in $p$+$p$ collisions scaled by the number of binary nucleon-nucleon collisions. The differential $J/\psi$ yield in both $p$+$p$ and $p$+Au collisions is measured through the dimuon decay channel, taking advantage of the trigger capability provided by the Muon Telescope Detector in the RHIC 2015 run. Consequently, the $J/\psi$ $R_{p\mathrm{Au}}$ is derived within the transverse momentum ($p_{\mathrm{T}}$) range of 0 to 10 GeV/$c$. A suppression of approximately 30% is observed for $p_{\mathrm{T}}<2$ GeV/$c$, while $J/\psi$ $R_{p\mathrm{Au}}$ becomes compatible with unity for $p_{\mathrm{T}}$ greater than 3 GeV/$c$, indicating the $J/\psi$ yield is minimally affected by the CNM effects at high $p_{\mathrm{T}}$. Comparison to a similar measurement from 0-20% central Au+Au collisions reveals that the observed strong $J/\psi$ suppression above 3 Gev/$c$ is mostly due to the hot medium effects, providing strong evidence for the formation of the quark-gluon plasma in these collisions. Several model calculations show qualitative agreement with the measured $J/\psi$ $R_{p\mathrm{Au}}$, while their agreement with the $J/\psi$ yields in $p$+$p$ and $p$+Au collisions is worse.


Introduction
In ultra-relativistic heavy-ion collisions, a new state of matter, referred to as gluons and quarks, if the medium temperature exceeds the melting temperature of the quarkonium states [1,2]. Therefore, observations of quarkonium suppression in heavy-ion collisions have been considered strong evidence for QGP formation and important probes of the medium temperature, a fundamental property of the QGP. However, there are other effects that could modify the observed quarkonium yield in heavy-ion collisions, including the main contributions which are recombination and Cold Nuclear Matter (CNM) effects. The former refers to the quarkonium production mechanism arising from combination of deconfined heavy quarks and anti-heavy quarks in the medium, while the latter is due to the participation of nuclei in the collisions, but not as a result of the creation of the QGP.
As the most abundantly produced quarkonium state that is experimentally accessible, the J/ψ meson suppression in heavy-ion collisions has been extensively measured at Super Proton Synchrotron, RHIC and the LHC [3,4,5,6,7,8,9,10,11,12,13,14,15]. At high transverse momentum (p T > 5 GeV/c), J/ψ mesons are strongly suppressed in central heavy-ion collisions, which is mainly attributed to the dissociation effect. In order to substantiate this conclusion, precise measurements of the CNM effects are needed to understand their potential contribution to the high-p T J/ψ suppression observed in heavy-ion collisions.
The CNM effects have been measured through collisions of a nucleus with a proton/deuteron at RHIC and with a proton at the LHC, in which the QGP is not expected to be produced [16,17,18,19,20,21,22]; or even if produced in such small system collisions, it is not expected to have a substantial effect. A general feature in these measurements is that a sizable suppression of the J/ψ yield, relative to that in p+p collisions, is seen at low p T , which gradually diminishes with increasing p T . A hint of a mild enhancement is seen above 10 GeV/c at the LHC energies [20,21]. Different physics mechanisms could contribute to the experimental observation. The nuclear parton distribution function (nPDF) is believed to be modified compared to the PDF of a free nucleon, e.g. a suppression (shadowing) at small Bjorken x and an enhancement (anti-shadowing) at intermediate x [23,24]. Such a small-x effect, as well as the higher twist contribution [25], can be accounted for alternatively within the framework of the Color Glass Condensate (CGC) effective theory [26]. Before forming a bound state, the color-octet cc pairs could undergo energy loss within the cold nuclear matter of a nucleus [27]. After being formed, the bound-state J/ψ meson can break up through interactions with the nucleons in the nucleus [28] or due to interactions with co-moving particles produced in the same collisions [29]. It could also be possible that a small droplet of the QGP is formed in p/d+A collisions, leading to J/ψ dissociation [30,31].
In this letter, the first measurement of the CNM effects experienced by inclusive J/ψ at mid-rapidity in p+Au collisions at √ s NN = 200 GeV with the Solenoidal Tracker At RHIC (STAR) experiment [32] is presented. They are quantified using the nuclear modification factor (R pAu ): where ( d 2 σ J/ψ dpTdy ) p+p is the J/ψ cross section in p+p collisions and ( d 2 N J/ψ dpTdy ) p+Au is the invariant yield per inelastic p+Au collision. The nuclear thickness function NN is calculated using a Glauber model [33], where σ inel NN = 42 mb [34] is the inelastic cross section of nucleon-nucleon collisions at 200 GeV, and N coll = 4.7 ± 0.3 is the average number of binary nucleon-nucleon collisions for 0-100% p+Au collisions [17]. The inclusive J/ψ sample used in this analysis includes both directly produced J/ψ as well as those from decays of excited charmonium states (approximately 40% [35]) and b-hadrons. Compared to previous measurements of R dAu at RHIC [16,18], the new R pAu measurement has better precision over the entire kinematic range, especially for p T larger than 3 GeV/c. This precision is partially achieved as the reference J/ψ cross section from p+p collisions was recorded the same year with the same trigger set-up and detector configuration as for the p+Au collisions, which allows for the partial cancelation of systematic uncertainties

Experiment, data set
Both the p+p and p+Au data samples used in this analysis were taken in 2015 by the STAR experiment at RHIC with the "dimuon" trigger. This trigger is dedicated to quarkonium measurements, and requires a coincidence signal in the east and west Vertex Position Detectors (VPD) [36] as well as two muon candidates in the Muon Telescope Detector (MTD) [37]. The VPD, made of plastic scintillators, covers full azimuth within the pseudorapidity (η) range of 4.24 < |η| < 5.1, while the azimuthal coverage of the MTD, consisting of multigap resistive plate chambers, is about 45% within |η| < 0.5. A hit in the MTD is classified as a muon candidate online if the difference between its arrival time measured by the MTD and the collision start time measured by the VPD falls within a pre-defined window, which is chosen to maximize the trigger efficiency (close to 100%) while maintaining a reasonable trigger rate.
The sampled luminosities online are 122 pb −1 and 410 nb −1 for the p+p and p+Au data sets, respectively.
The Time Projection Chamber (TPC) [38], encompassed in a uniform magnetic field of 0.5 T along the beam direction, is a gaseous detector for reconstructing a charged particle's trajectory, determining its momentum and measuring its specific energy loss (dE/dx) for particle identification (PID). It covers full azimuth within |η| < 1.0. Due to the high luminosity environment, most of reconstructed vertices using TPC tracks are from out-of-time collisions from different bunch crossings than the triggered collision. The primary vertex is chosen such that its coordinate along the beam direction (v TPC  where 1/f prescale is the fraction of MB triggered events randomly selected to be written on tape given the limited STAR data acquisition bandwidth. Tracks are further extrapolated radially to the middle of MTD modules, located at varying distances between 392.8 cm and 418.9 cm from the center of STAR, and matched to the closest MTD hits. If more than one track is matched to the same hit, the closest track is chosen. Once a track-hit association is established, the track is identified as a muon candidate when the following two criteria are satisfied: i) the associated MTD hit contributes to the dimuon trigger; ii) the pair survives the cut on a Likelihood Ratio (R) [41]. The R variable is defined as the following: where i stands for the five discriminating variables used, i.e., DCA, nσ π , ∆z/σ ∆z , ∆y × q/σ ∆y×q , ∆t tof , and pdf sig i , and pdf bkg i are the probability distribution functions of each variable for signal muons and background particles. The normalized energy loss is defined as nσ π = . Here (dE/dx) measured is the measured energy loss in the TPC, (dE/dx) π theory is the expected energy loss for a pion based on the Bichsel formalism [42], and σ(ln(dE/dx)) is the resolution of the ln(dE/dx) measurement. The shape of the nσ π distribution is expected to be independent of track p T . ∆z and ∆y are the position differences between the projected track trajectories on the MTD and the associ- range, and is shown as the vertical dashed line in Fig. 1. The optimal cut is determined to be R > −0.01 for the p+Au analysis.
The invariant mass distributions for unlike-sign muon candidate pairs, integrated over p T , are shown in Fig. 2 as filled circles for p+p (left) and p+Au (right) events. For each unlike-sign pair, one of the muon candidates should have a p T above 1.5 GeV/c, while the other above 1.3 GeV/c. The pair rapidity is within |y| < 0.5. The combinatorial background is estimated using like-sign TPC track pairs without matching to the MTD, which are scaled to the invariant mass distributions of like-sign muon candidate pairs and corrected for the MTD acceptance difference for like-sign and unlike-sign pairs. Such an acceptance difference is evaluated using the ratio of unlike-sign to like-sign muon candidate pairs from mixed events, i.e. the two muons in a pair are taken from different events, using 200 GeV Au+Au collisions recorded in 2014 [7].
To extract the raw J/ψ yield, the unlike-sign invariant mass distribution, with the combinatorial background subtracted, is fit with the sum of a Student's t function representing the J/ψ signal and a first-order polynomial function describing the residual background, using the minimum χ 2 method. The normality parameter in the Student's t function, which determines to what extent its tail

Efficiency and acceptance correction
The TPC tracking efficiency and acceptance are evaluated through an embedding procedure. Simulated J/ψ → µ + µ − processes are propagated through the STAR detector simulation using the GEANT3 package [43]. They are then mixed with randomly sampled dimuon triggered real events, and reconstructed the same way as real data. The embedded J/ψ is assumed to have zero polar-ization [44]. The TPC tracking efficiency is 86% (85.5%) independent of muon p T above 1.3 GeV/c for p+p (p+Au) data. An additional inefficiency observed in the data for one of the TPC sectors is applied to the embedding sample. The MTD trigger efficiency consists of three components: trigger electronics efficiency, trigger timing window cut efficiency and trigger patch configuration efficiency. The first two components are evaluated using MB triggered event samples for which only the coincidence signal in east and west VPD is required.
The probability for a muon candidate to generate a correct signal in the trigger electronics and pass the trigger timing window cut is found to be close to 100% for both p+p and p+Au data. The third component arises from the fact that the dimuon trigger requires signals from distinct trigger patches [7] while the muon daughters from high-p T J/ψ decays are highly boosted and could hit the same MTD trigger patch. Since this component is driven by the MTD geometry and the J/ψ decay kinematics, the embedding sample is utilized. The resulting efficiency is mostly 100% until J/ψ p T of 5 GeV/c, and decreases to about 95% at 8-10 GeV/c.
The muon PID efficiency associated with the cut on R is estimated using a tag-and-probe method based on real data. For each unlike-sign pair of TPC tracks matched to the MTD, one muon is randomly selected as the tag muon while the other the probe muon. For the tag muon, a strict cut of R > 0.25 is applied to increase the signal-to-background ratio. For the probe muon, two cases are tried, i.e., no cut on R and the default cut on R. The J/ψ counts in each probe muon p T bin are extracted for the two cases, and the ratio is parametrized as the muon PID efficiency. In the p+p analysis, the muon PID efficiency increases from 90% at 1.3 GeV/c to 98% above 5 GeV/c, while it increases from 69% at 1.3 GeV/c to 96% above 5 GeV/c for p+Au analysis due to the tighter cut applied.
The VPD trigger and vertex finding efficiencies are obtained by embedding PYTHIA [45,46] (HIJING [47]) events, after passing through the GEANT simulation of the STAR detector, into zero-bias p+p (p+Au) events. The zero-bias events were taken without any trigger requirement at random times. For the p+p analysis, both the MB PYTHIA events and PYTHIA events containing a J/ψ within |y| < 0.5 are used for embedding. The former is needed for calculating the equivalent number of MB events corresponding to the analyzed dimuon triggered events. Two different PYTHIA configurations: i) PYTHIA 6.4.28 [45] plus the Perugia2012 tune [48]; ii) PYTHIA 8.1.62 [46] with the STAR heavy flavor tune as detailed in the appendix, are used as they bracket the measured multiplicity distribution of J/ψ events [49]. To account for the apparent differences between data and PYTHIA, event multiplicity distributions for both MB [50] and J/ψ events [49] are then used to weight the embedding samples. The VPD efficiency for events containing a J/ψ decreases with increasing J/ψ p T , due to the decreased amount of energy available for producing particles in the VPD acceptance in these events. The average efficiencies of the two PYTHIA configurations are taken as the central values, while half the difference of the two is taken as a source of systematic uncertainties. For the p+Au analysis, a similar procedure is used except that the HIJING event generator [47] is employed.
Since no quarkonium production is implemented, HIJING events containing a D 0 meson within |y| < 0.5 are used for embedding, which is validated by the good agreement seen between the efficiencies extracted from embedding J/ψ and D 0 PYTHIA events. The event multiplicity as a function of pseudorapidity in HIJING p+Au events is compared to the PHOBOS measurement for d+Au collisions [51] scaled by the difference in N part between p+Au and d+Au collisions. Here N part refers to the number of participating nucleons in a p+Au or d+Au collision. These results agree for both mid-rapidity and the p-going side.
However, on the Au-going side HIJING significantly underpredicts the particle multiplicity, and therefore the VPD efficiency in this side is assumed to be 100% as an upper limit. The average VPD efficiency in the Au-going side (∼ 91%) from the default HIJING and the upper limit is taken as the central value.

Results and discussions
The differential cross section of inclusive J/ψ times the branching ratio within |y| < 0.5 in p+p collisions at √ s = 200 GeV is shown in the top panel of Fig. 3 as a function of p T . The data points are placed at the p T positions whose yields are equal to the average yields of the corresponding bins [52]. For this purpose, the following empirical function is used to fit the differential cross section as a function of p T iteratively: where A, B and C are free parameters. The integrated J/ψ cross section per unity rapidity is: Br µµ dσ J/ψ dy | y=0 = 43.9 ± 0.7(stat.) ± 6.1(syst.) nb (4)  [4], 10% (8.5%) for STAR 2012 result at p T < 1.5 GeV/c (p T > 1.5 GeV/c) [49] and 10% for the PHENIX measurement [35]. Bottom: ratios of current measurement and different model calculations [53,54,55,56,57,58] to the fit. Systematic uncertainties on data points are smaller than the marker size.
To facilitate the comparison of this measurement to previous publications, Eq. 3 is used to fit the differential J/ψ cross section, and the fit result is shown as the dashed line in the top panel of Fig. 3. Ratios of the current and previous results [4,35,49] to the fit function are shown in the middle panel of  [53,54,55,56,57,58] to the fit. Systematic uncertainties on data points are smaller than the marker size.
utilizes the NLO EPS09 nPDF [62], while the CGC+ICEM approach directly calculates the cc production cross section in p+Au collisions based on the CGC formalism. The uncertainties for the former arise from the nPDF uncertainties, while for the latter the main contributions are the variations of the average momentum of soft color exchanges and the scale factor between the saturation scales for proton and Au nucleus. In the Lansberg calculation, the nCTEQ15 nPDF at NLO [23], constrained by the J/ψ measurements at the LHC, is used [55,56,57,58]. The systematic uncertainty band of the Lansberg calculation includes the nPDF uncertainty at 68% confidence level as well as variations on the factorization scale. Very similar results, not shown here, are obtained using the EPPS16 nPDF at NLO [24] within the same framework. The comparison between data and model calculations is similar to that seen for p+p collisions, even though the contribution of b-hadron decayed J/ψ is not included in the model calculations for p+Au collisions. which gradually goes away as p T increases. For p T above 3 GeV/c, the J/ψ R pAu becomes consistent with unity, indicating little CNM effects on the J/ψ production in this kinematic range. The inclusive J/ψ R dAu [18] in d+Au colli- and nCTEQ15 [23] parameterizations, respectively. The TAMU model extends the transport model for heavy-ion collisions to p+Au collisions [30,31]. In this model, the NLO EPS09 nPDF is utilized [62], and the short-lived hot medium modifies the observed J/ψ yields in p+Au collisions through both dissociation and recombination. Uncertainties of this calculation includes nPDF uncertainties, variation of the broadening parameter for incorporating the Cronin effect, and uncertainties in the formation times for both the QGP and J/ψ meson. In another model, shown as the solid line and labeled as "Eloss+Broadening", interactions between fast-moving color-octet cc pairs in the nucleus rest frame and the cold nuclear medium induce both radiative energy loss and p T -broadening [27]. The latter is responsible for the J/ψ enhancement above 2.5 GeV/c. A comover model, introducing breakup of J/ψ mesons through interactions with final state particles traveling along with J/ψ, is shown as the dot-dashed line in the panel [29]. The nPDF effect is also included in the comover model, based on leading-order EPS09 parameterization. All the model calculations are consistent with data within theoretical and experimental uncertainties. It is worth noting that the comover model underpredicts data above 3.5 GeV/c by 2.3σ.