Underlying event measurements in $p$+$p$ collisions at $\sqrt{s}= 200 $ GeV at RHIC

Particle production sensitive to non-factorizable and non-perturbative processes that contribute to the underlying event associated with a high transverse momentum ($p_{T}$) jet in proton+proton collisions at $\sqrt{s}$=200 GeV is studied with the STAR detector. Each event is divided into three regions based on the azimuthal angle with respect to the highest-$p_{T}$ jet direction: in the leading jet direction ("Toward"), opposite to the leading jet ("Away"), and perpendicular to the leading jet ("Transverse"). In the Transverse region, the average charged particle density is found to be between 0.4 and 0.6 and the mean transverse momentum, $\langle p_{T}\rangle$, between 0.5-0.7 GeV/$c$ for particles with $p_{T}$$>$0.2 GeV/$c$ at mid-pseudorapidity ($|\eta|$$<$1) and jet $p_{T}$$>$15 GeV/$c$. Both average particle density and $\langle p_{T}\rangle$ depend weakly on the leading jet $p_{T}$. Closer inspection of the Transverse region hints that contributions to the underlying event from initial- and final-state radiation are significantly smaller in these collisions than at the higher energies, up to 13 TeV, recorded at the LHC. Underlying event measurements associated with a high-$p_{T}$ jet will contribute to our understanding of QCD processes at hard and soft scales at RHIC energies, as well as provide constraints to modeling of underlying event dynamics.

Particle production sensitive to non-factorizable and non-perturbative processes that contribute to the underlying event associated with a high transverse momentum (pT ) jet in proton+proton collisions at √ s=200 GeV is studied with the STAR detector. Each event is divided into three regions based on the azimuthal angle with respect to the highest-pT jet direction: in the leading jet direction ("Toward"), opposite to the leading jet ("Away"), and perpendicular to the leading jet ("Transverse"). In the Transverse region, the average charged particle density is found to be between 0.4 and 0.6 and the mean transverse momentum, pT , between 0.5-0.7 GeV/c for particles with pT >0.2 GeV/c at mid-pseudorapidity (|η|<1) and jet pT >15 GeV/c. Both average particle density and pT depend weakly on the leading jet pT . Closer inspection of the Transverse region hints that contributions to the underlying event from initial-and final-state radiation are significantly smaller in these collisions than at the higher energies, up to 13 TeV, recorded at the LHC. Underlying event measurements associated with a high-pT jet will contribute to our understanding of QCD processes at hard and soft scales at RHIC energies, as well as provide constraints to modeling of underlying event dynamics. Understanding the underlying physics of hadronic collisions requires detailed characterization of the particle production processes. Proton+proton (p+p) collisions include elastic and inelastic scatterings, with inelastic p+p scatterings consisting of single diffractive, double diffractive and non-diffractive processes. In nondiffractive events, when a hard scattering occurs with large momentum transfer (p T ≥2 GeV/c) from the longitudinal to the transverse plane, other processes could occur in addition to the production of a high energy dijet. These additional processes include softer secondary hard scatterings or multiple parton interactions (MPI), gluon radiation or quark-antiquark splittings from the initial-or final-state partons of the primary hard scattering (ISR/FSR), and color reconnections with the beamremnant partons (BR). Cumulatively, these result in what is referred to, in experiments, as the underlying event. The partons produced in these processes reduce their virtuality and finally fragment mainly into lowenergy particles. The properties of the dijet produced in the initial hard scattering can be calculated by perturbative QCD, with good agreement between experimental measurements and theoretical calculations after careful correction for the underlying event activity [1][2][3]. Modeling the soft physics, which dominates the underlying event activity, is challenging since it does not factorize and requires non-perturbative calculations [4,5]. Experimental studies of the underlying event activity, spanning non-perturbative and perturbative QCD and including sensitivities to multi-scale physics, can help us to improve theoretical modeling and understand the QCD processes. Underlying event activity is often experimentally accessed through topological structure observables, such as particle production away from the primary hard scattering reference direction. The CDF collaboration used the highest-p T charged particle, leading jet, or Drell-Yan pair in each proton+antiproton event to define the hard scattering reference [6,7]. At LHC energies, the ALICE, ATLAS, and CMS collaborations have used the highestp T charged particle, charged jet, jet with both charged and neutral particles, or Z boson as the hard scattering references [8][9][10][11][12]. In this analysis, we use the highest-p T jet as our hard scattering reference.
At TeV collision energy scales, the average mid-pseudorapidity charged multiplicity density and mean transverse momentum, both sensitive to the underlying event activity, were observed to be positively correlated with observables sensitive to the hard scattering energy [7][8][9][10][11][12]. These positive correlations are understood as resulting from increasing contributions from wide angle ISR/FSR, as the transferred momentum scale, Q 2 , of the hard scattering increases. However, at forward rapidity, CMS found that the relationship between underlying event particle production and leading jet p T depends on collision energy [13]: at √ s = 0.9 TeV, the underlying event particle production activity and leading jet p T were negatively correlated, while at 7 TeV they were mostly positively correlated for leading charged jets with 1<p T <15 GeV/c. The negative correlations reported at the lower collision energy could be due to energy conservation constraining the underlying event production. For these reasons, it is worth exploring the underlying event at RHIC with even lower energies to search for its relationship with the leading jet energy at mid-pseudorapidity.

II. EXPERIMENT AND DATA ANALYSIS
In this paper, we report measurements of underlying event activity in p+p collisions at √ s = 200 GeV by the STAR experiment at RHIC. The data used in this analysis were collected in 2012 with an integrated luminosity of ∼23 pb −1 . The major subsystems used for the analysis were the Time Projection Chamber (TPC) [14], and the Barrel Electromagnetic Calorimeter (BEMC) [15]. The TPC provides charged particle tracking with good momentum resolution, while the 4800 isolated towers of the BEMC record the energy deposited by photons, electrons, π 0 , and η mesons. Both cover mid-pseudorapidity (|η|<1) with full azimuthal angle (φ) coverage.
This analysis used both a minimum bias and a calorimeter-triggered dataset. The minimum bias data required a coincidence of signals from the Vertex Position Detectors [16], which measure photons from π 0 decays at forward and backward pseudorapidity, 4.2≤|η|≤5.1. The calorimeter jet-patch triggered data required a minimum transverse energy (E T ) in a ∆η × ∆φ region of ≈ 1 × 1 of the BEMC. In this analysis, three E T trigger thresholds were used: 3.5, 5.4, and 7.3 GeV. Jets reconstructed from the calorimeter-triggered dataset are therefore biased towards higher neutral energy fractions [17]. Corrections for this electromagnetic calorimetertrigger bias are determined via a data-driven technique using the minimum bias data, and only the corrected calorimeter-triggered data are reported in the final results. Event-level and particle-level selections were applied to the recorded data. The events were required to have a reconstructed primary event vertex, z vtx , within 30 cm of the center of the TPC along the beam axis (z) in order to ensure nearly uniform detector acceptance. Events containing a charged particle with p T >20 GeV/c were discarded to avoid events with low tracking momentum reconstruction resolution. Events with deposited energy in a single BEMC tower of E T >20 GeV were also discarded for symmetry. The charged particle tracks reconstructed in the TPC were required to satisfy the following conditions: 0.2<p T <20 GeV/c for high tracking efficiency; a distance of closest approach (dca) to the event vertex of |dca|<1 cm to ensure particles are from the primary collision vertex; a number of fit points along the track greater than 20 out of a maximum of 45; and a ratio of the number of fit points to the maximum number of possible fit points larger than 0.52 for good primary track reconstruction [14,18]. The neutral energy deposits in each BEMC tower were required to have 0.2<E T <20 GeV. For the particles used in this paper, the pseudorapidity region was restricted to |η|<1.
The simulation sample used for detector response and background correction in this analysis was generated using PYTHIA 6.4.28 [19] with the CTEQ6L1 PDF [20] and the Perugia 2012 tune [4] with the PARP(90) parameter changed to 0.213, which is, throughout this article, referred to as PYTHIA 6 (STAR) [3]. PYTHIA 6 (STAR) is tuned with STAR published minimum bias identified particle spectra [21,22] resulting in agreement with the inclusive identified charged pion cross-sections at the 10% level [23]. The PYTHIA parameter PARP(90) is related to the energy scaling of the minimum bias and underlying event phenomena [4]. PYTHIA 6 (STAR) generated events are processed through the STAR GEANT3 [24] detector simulation with π 0 , η, and Σ 0 decays and weak decays handled by GEANT and set as stable in PYTHIA . The simulated GEANT output events were further embedded into zero bias (randomly triggered) experimental data. This embedding procedure simulates a similar background, such as pile-up, beam-gas interactions and cosmic rays, as exists for the experimental measurements [17]. The default PYTHIA 6.4.28 Perugia 2012 tune with the CTEQ6L1 PDF, and the default PYTHIA 8.215 Monash 2013 tune [25] simulations were also used for comparison with corrected data, later referred to as PYTHIA 6 and PYTHIA 8, respectively.
All charged tracks with p T >0.2 GeV/c and all BEMC towers with deposited E T >0.2 GeV, within |η|<1 were used to reconstruct jets.
Jet reconstruction used the anti-k T algorithm [26] with a resolution parameter R anti−k T =0.6 as implemented in the FastJet pack-age [27]. The reconstructed jets were restricted to |η jet |<0.4 to ensure that all tracks/neutral energy deposits of the jets were inside our detector acceptance. The jet neutral energy fraction [17] was required to be less than 90% to minimize non-collision backgrounds such as beam-gas interactions and cosmic rays. Jet axes were further required to be within ∆R = ∆η 2 + ∆φ 2 =0.6 distance from the jet-patch center for calorimeter-triggered data [17]. The reported jet energies include contributions from the underlying event and are corrected for detector effects including pile-up via the unfolding procedure described below.
The analysis followed the CDF topological structure method [6]. For each collision event, the leading, highest p T , jet azimuthal angle (φ jet ) is defined as the reference angle. The reconstructed charged particles are then categorized into different regions by the relative difference of their azimuthal angle (φ i ) to the jet's reference angle, ∆φ ≡ φ i − φ jet . The "Toward" region contains particles with |∆φ|<60 • , while the "Away" region, which is not required to contain a reconstructed jet, is defined as those particles with |∆φ-180 • |<60 • . Finally, the "Transverse" region covers 60 o ≤|∆φ|≤120 • . The activity in each region is integrated over |η|<1, which is inside of the TPC acceptance. The underlying event activity is then accessed through the η integrated Transverse region and reported for charged tracks only. The average charged particle multiplicity density, dN ch dηdφ , and the mean transverse momentum, p T , are studied as a function of the leading jet p T .
Each event has two Transverse regions, 60 • ≤∆φ≤120 • and -120 • ≤∆φ≤-60 • . For each event, the Transverse region with larger charged multiplicity density was defined as "TransMax", and the other as "TransMin". This binning procedure will cause the results to differ, even if the TransMax and TransMin distributions originate from the same parent distribution, due to region-to-region statistical fluctuations. Since the MPI and BR processes are potentially unrelated to the hard scattering jet angle, both processes make comparable contributions to both the TransMax and TransMin regions. However, ISR/FSR may produce a wide angle third jet, the fragmentation particles of which have a high probability of being recorded in only one of the Transverse regions. ISR/FSR can therefore also result in a significant difference in the two regions' multiplicity densities. Comparisons of TransMax and TransMin regions may therefore reveal details of the various processes contributing to the underlying event. The TransMin region is sensitive to particle production from BR and MPI, while the Trans-Max region also contains signal from ISR/FSR.
The measured data were corrected for trigger bias, detector inefficiency, cosmic-ray background, and pile-up effects. The trigger bias was corrected for by weighting calorimeter-triggered data to have the same jet neutral fraction distribution as minimum bias data. The trigger bias corrections were p T dependent and were less than 15% for the multiplicity density results and less than 20% for p T .
The calorimeter-triggered data were then unfolded using a detailed simulation of the trigger to correct for inefficiencies as a function of jet p T . Differences to the previously mentioned bias-corrected result were accounted for as part of the systematic uncertainty estimate. The detector inefficiency, resolution effects, and background corrections were performed using 2-dimensional Bayesian unfolding [28]. The response matrices were constructed from matched generator-level and detector-level observables [29]. The generator-level is from PYTHIA 6 (STAR) and the detector-level is from the embedded sample to include the backgrounds to the signal, such as the pile-up contribution. A jet pair was considered matched if the distance of a leading jet at the detectorlevel to a leading or sub-leading jet at the generator-level was less than the jet resolution parameter, R anti−k T =0.6. When there was a match, the leading jet p T at the generator-level was used to create the response matrices. For the track level observable p T , a matched track pair was also required. The track pair is considered matched when more than ten hits are matched [18]. The embedding sample had the same track and jet quality requirements applied as the experimental data which included requiring the particle p T >0.2 GeV/c, |η|<1 and leading jet |η jet |<0.4. The negative bins represent the probability for no match to be identified for the concerned variable. Although the two figures exhibit a fairly linear correlation between the detector-level and generator-level variables, their correlations are smeared. To ensure closure of the unfolding correction procedure, the simulation data were divided into two subsets, one was used for training and one for the unfolding closure test. This successful closure test also demonstrated that the uncertainty due to the response matrices is negligible. The unfolding method uncertainty was estimated by varying the Bayesian iterations (with 4 as the default), the unfolding prior, and the maximum tower energy cut of 20 GeV. The effects on the unfolded results due to the uncertainty on the TPC tracking efficiency of 4% and the BEMC tower energy calibration uncertainty of 4% were also estimated. For both cases the response matrices were recalculated after varying the simulations by the appropriate uncertainty and the data unfolded with the new matrix. The systematic errors obtained from these variations were added quadratically with the unfolding uncertainty to form the total systematic uncertainty. The total correction uncertainties were found to be less than 15%.  Figure 2 shows the fully corrected average charged particle multiplicity densities for particles with p T >0.2 GeV/c and |η|<1 as a function of the leading jet p T . In this and the following figures, data points are placed at the center of each p T bin. The statistical uncertainties are shown as vertical bars, which are smaller than the data symbols. The box heights are systematic uncertainties, while their widths correspond to the p T bin sizes. The Toward and Away average multiplicity densities, dN ch dηdφ , both show a rise with leading jet p T . For the Transverse region, dN ch dηdφ tends to slightly decrease as the leading jet p T increases. In contrast, at LHC energies the mid-pseudorapidity transverse multiplicity was observed to quickly increase and then saturate or slightly increase with increasing leading jet/track p T [8,9]. PYTHIA 6 (STAR), PYTHIA 6 default Perugia 2012 and PYTHIA 8 default Monash 2013 simulations are also shown as curves with widths from widest to thinnest, respectively. Deviations for all the simulations from data for jet p T >15 GeV/c are observed in the Transverse region, with PYTHIA 6 (STAR), which was tuned with STAR published minimum bias spectra, closest to the measured results. However, while the agreement between data and PYTHIA 6 (STAR) is reasonable, additional improvements to the tuning or modeling itself would still be appropriate at RHIC energies. To allow comparison with results obtained at facilities with higher collision energies, analyses for particle p T > 0.5 GeV/c were also performed. Figure 3 compares the fully corrected dN ch dηdφ in the Transverse region as a function of the leading jet p T for particle p T >0.2 GeV/c and p T >0.5 GeV/c. Similar trends are observed for these two p T cases, with mismatch between data and PYTHIA.

III. RESULTS AND DISCUSSION
The p T was measured to further profile the characteristics of the underlying event. Figure 4 shows the fully corrected charged particle p T as a function of the leading jet p T for the three regions, with particle p T >0.2 GeV/c. The Transverse region p T slightly increases as the leading jet p T increases. Both the Toward and Away regions show linearly increasing trends. PYTHIA simulations, shown as curves, provide a better description of the p T measurements than the average multiplicity density.  Figure 5 shows the fully corrected transverse region charged particle p T as a function of the leading jet p T for p T >0.2 GeV/c and p T >0.5 GeV/c. Similar trends are observed for these two p T cases. Figure 6 shows the uncorrected detector-level Trans-Max and TransMin average charged particle multiplic- ity densities as a function of the leading jet p T . At √ s = 200 GeV, we observe that while the multiplicity densities in the TransMax and TransMin regions have different overall magnitudes, they both exhibit slightly decreasing trends with increasing leading jet p T with the difference in the densities staying roughly constant.
Meanwhile, experiments at the LHC have reported an increasing difference in the charged particle multiplicities of these regions with increasing leading trigger p T [8,9]. Increasing contributions to the TransMax region from wide angle third-jet production via ISR/FSR is understood as the main physical cause of the LHC results. To further investigate our results, we tested the hypothesis that the TransMax and TransMin charged particle density distributions are drawn, statistically independently, from the same parent probability distribution, f (x). In such a case the probability distribution functions for the measured charged particle multiplicities in the Trans-Max and TransMin regions, f max (x) and f min (x) respectively, can be expressed as f max (x) = 2f (x)F (x) and f min ( The calculated averages of f max (x) and f min (x) as a function of leading jet p T are shown as curves in Fig. 6, when f (x) is taken as the average of the measured Trans-Max and TransMin distributions.
These calculated distributions account for most of the features of the measured data, suggesting any net contribution from additional physical sources is small. Detector-level variables were compared here to avoid the impact of additional fluctuations from the unfolding procedure, with the caveat that any detector response asymmetries could enlarge the TransMax and TransMin difference at the detector-level. This suggests that there are less ISR/FSR contributions to p+p events at RHIC energies than at LHC energies.
Besides the underlying event activity's dependence on the hard scattering reference energy scale, studying the collision energy dependence also contributes to our understanding of how to model these low momentum processes. Detailed underlying event measurements have been reported at a variety of collision energies, which makes it possible to study the energy scaling of the underlying event phenomena, including a possible collision energy dependence of the transverse momentum cut-off between hard and soft scatterings [30]. A world-data comparison with our RHIC measurements is done with jets or charged particles as the hard scattering reference to avoid any possible complexity that different hard references may introduce to the underlying event activity.
Since the underlying event multiplicities at the Tevatron and LHC energies show the same general trend of a rapid rise with reference p T before reaching a plateau [8], comparison points were chosen from the region where the plateau is just reached. An exception is the ATLAS full jet measurement at 7 TeV, where the general trend of the underlying event is not observed due to limited kinematic reach at lower p T . In this case, the lowest p T data point was chosen for comparison [31]. Figure 7 shows the collision energy dependence of the charged particle density extracted for these Transverse regions and Table I details the beam energy, trigger type and p T range, and Transverse region's η coverage for each experiment. Note all the reported results use charged particles with p T >0.5 GeV/c to measure the underlying event (UE) activity and that the LHC and STAR results are from p+p collisions while those of CDF are from p+p events.
A near-linear increase with the log of the collision energy is observed in Fig. 7, despite the different references and pseudorapidity coverage for the various measurements. It has been shown in [4] (for example), that it remains unclear how to model correctly the collision energy scaling of the p+p data; a tension emerges when trying to simulate minimum bias and high multiplicity data with the same tune. This study of the collision energy dependence of the underlying event's average charged particle density provides additional information that may aid in resolving this tension.

IV. SUMMARY
We have reported several observables sensitive to the underlying event activity in p+p collisions at √ s = 200 GeV as recorded by the STAR experiment.
The results used full jets reconstructed at mid-pseudorapidity |η jet |<0.4 with R anti−k T =0.6 and 5<p jet T <45 GeV/c. The charged particles used for the underlying event measurements were required to have |η|<1, 0.2<p T <20 GeV/c, and 60 • ≤|∆φ|≤120 • . The reported observables were corrected to the generator-level to enable direct comparison with theoretical calculations. The detector response corrections were performed via a data-driven trigger correction and embedded PYTHIA 6 (STAR)+GEANT simulations into zero-bias experimental data. The uncertainties from the detector response corrections are included in the systematic uncertainties.
The corrected observables were reported for three topological regions, Toward, Away, and Transverse, based on the azimuthal angle of the particles relative to that of the highest p T jet. The average charged particle multiplicity densities and their mean transverse momenta in these regions were studied as functions of the leading jet p T . These correlations characterize the relationship between the underlying event activity and a hard scattering in p+p collisions. The Transverse charged particle density was observed to slightly decrease with the leading jet p T , while the Transverse p T slightly increases with the leading jet p T . The slight negative correlation of dN ch dηdφ is consistent with energy conservation restricting particle production in the Transverse region as the leading jet becomes more energetic.
The Transverse regions were further split into Trans-Max and TransMin areas. The observation of similar charged particle production in the TransMax and Trans-Min regions at RHIC, which is not observed at the LHC, suggests that ISR/FSR contributes less to the underlying event at √ s = 200 GeV than at TeV collision energies.