Measurement of twoparticle correlations with respect to second and thirdorder event planes in AuAu collisions at GeV
Abstract
We present measurements of azimuthal correlations of charged hadron pairs in GeV AuAu collisions after subtracting an underlying event using a model that includes higherorder azimuthal anisotropy , , and . After subtraction, the awayside ( of the highest transversemomentum trigger ( GeV/) correlations is suppressed compared to that of correlations measured in collisions. At the lowest associated particle , the awayside shape and yield are modified. These observations are consistent with the scenario of radiativejet energy loss. For the lowest trigger correlations, an awayside yield exists and we explore the dependence of the shape of the awayside within the context of an underlyingevent model. Correlations are also studied differentially versus eventplane angle . The angular correlations show an asymmetry when selecting the sign of the triggerparticle azimuthal angle with respect to the event plane. This asymmetry and the measured suppression of the pair yield out of plane is consistent with a pathlengthdependent energy loss. No dependence can be resolved within experimental uncertainties.
PHENIX Collaboration
I Introduction
Energy loss of hardscattered partons (jet quenching Wang and Gyulassy (1992)) resulting from the interaction of a colored parton in the quark gluon plasma (QGP) formed in relativistic heavy ion collisions Arsene et al. (2005); Back et al. (2005); Adams et al. (2005a); Adcox et al. (2005) has been observed in several different ways. Suppression of singleparticle and singlejet invariant yields in central A+A collisions Adler et al. (2003a, 2004); Adams et al. (2003); Chatrchyan et al. (2012a); Aad et al. (2015a, 2013) provide a baseline measurement of jet quenching. Measurements of correlations between two particles and/or jets give more detailed spatial information of the jet quenching process inside the medium Renk (2013); Qin and Wang (2015). The first jet suppression effect observed in these correlations was an attenuation of the awayside yields in hightransverse momenta () correlations in the most central AuAu collisions at 200 GeV Adler et al. (2003b). The centrality dependence of high hadron correlations Adare et al. (2011a) shows a monotonic attenuation of the awayside yields with increasing propagation length of partons through the medium. In addition to awayside yield suppression, direct photonhadron correlations Abelev et al. (2010a); Chatrchyan et al. (2013); Adamczyk et al. (2016), twoparticle correlations Adare et al. (2013); Agakishiev et al. (2012); Nattrass et al. (2016), and jethadron correlations Adamczyk et al. (2014a); Aad et al. (2014a); Chatrchyan et al. (2014a); Khachatryan et al. () show that lowmomentum particles correlated with high jets are enhanced in yield, especially at large angles with respect to the jet axis. This may be attributable to the radiation from the parent parton or other lost energy recovered by the nearby medium. Thus, twoparticle angular correlations have provided much of the experimental information we have about jet energy loss Aamodt et al. (2012); Adare et al. (2010a, 2011a); Adams et al. (2006); Abelev et al. (2010b); Agakishiev et al. (2011).
It is important to understand the interactions of partons with the QGP at all scales from the hardscattering scale to the thermal scale. Below 10 GeV, full jet reconstruction is much more difficult due the underlying event subtraction. Twoparticle correlations are important because they can probe lower energies. However, observations of many of the energy loss effects mentioned above, especially for lower jet and particle momenta in dijet twoparticle correlations, have been obscured due to the much larger contribution from the underlying event at these momenta.
The underlying event modulations are attributed to hydrodynamic collective flow patterns where the importance of higherorder terms was established more recently Alver and Roland (2010); Xu and Ko (2011); Aad et al. (2012); Adare et al. (2011b); Aamodt et al. (2011); Chatrchyan et al. (2014b). These patterns are thought to result from the hydrodynamic response of the QGP to fluctuating initial geometrical shapes of the interacting portions of the colliding nuclei. Many hydrodynamic models have been developed which capture these effects Shen et al. (2016); Lin et al. (2005); Romatschke (2015), but to date, important details of these models are still under development, and their full implementation requires involved calculations. This motivates the use of a simpler datadriven model, which will be explored in this work.
The shape of the collective flow in the transverse plane is parameterized Voloshin and Zhang (1996); Ollitrault (1992); Poskanzer and Voloshin (1998); Adare et al. (2010b) by a Fourier expansion with
(1) 
where is the order component of singleparticle correlation due to flow, is the azimuthal angle of emitted particles, and is the event plane angle defined by the harmonic number. For the first decade of the Relativistic Heavy Ion Collider (RHIC), only the even harmonics and frequently only the term, were considered. The shapes of twoparticle correlations after subtraction of the only background motivated the introduction of the other harmonics, most importantly Sorensen (2010); Alver and Roland (2010); Adare et al. (2011b); Aad et al. (2012); Aamodt et al. (2011). Under the twosource (flow + jet) model assumption Adler et al. (2006a), this underlying event is directly subtracted to obtain the jet contributions. In our previous measurements and most RHIC results, the subtracted flow modulations of the underlying event were limited to contributions of and the fourthorder harmonic component with respect to the secondorder event plane Adler et al. (2003b); Abelev et al. (2009a); Adare et al. (2008a); Adler et al. (2006a); Adare et al. (2008b); Adamczyk et al. (2014a); Adare et al. (2011a, 2010a, 2007, 2013). Only the recent STAR measurement Agakishiev et al. (2014) took into account contributions from and the fourthorder harmonic component uncorrelated to the secondorder eventplane .
At low to intermediate in twoparticle correlations, intricate features appear such as the nearside longrange rapidity correlations called the “ridge” Abelev et al. (2009a); Alver et al. (2010) and the awayside “doublehumped” structures Adler et al. (2006a); Adare et al. (2007, 2008b); Abelev et al. (2009b); Adare et al. (2008a); Aggarwal et al. (2010); Adare et al. (2010a); Agakishiev et al. (2014). Across the large rapidity ranges available at the Large Hadron Collider, the rapidityindependence and hence the likely geometrical origin of most of these structures have been established. Experiments have shown that the ridge and the doublehump structures in the twoparticle azimuthal correlations for for ALICE and for ATLAS and CMS measured in , Pb, and PbPb collisions at and TeV Aamodt et al. (2011); Aad et al. (2012); Chatrchyan et al. (2012b) are the same in shape and size at much larger rapidity differences. Both the ridge and hump are successfully explained by the higherorder harmonics. Despite this conclusion, how the jet correlations combine with the flow correlations, especially at small , to yield the total twoparticle correlation has not been quantified. In particular, the correlations left after subtracting a flowbased model at small have not been analyzed in detail.
In this work, we assume a twosource model where the total pair yield is a sum of a jetlike component and an underlyingevent component. The underlyingevent components is modeled using the flow harmonics , event plane resolutions, and the most important event plane correlations between and . We assume that the measured through the event plane method are the the same as those in the correlation functions. Eventbyevent fluctuations Aad et al. (), correlations between different order Aad et al. (2015b), and rapidity dependent event plane decorrelations Khachatryan et al. (2015) are not considered in this background model. Measurements of using the event plane method Adams et al. (2005b); Back et al. (2006); Abelev et al. (2008); Adamczyk et al. (2014b) generally yield at integrated over all . Finite values of differential measurements of Abelev et al. (2008) include momentum conservation and jet (minijet) effects which are considered signal in twoparticle correlations. We therefore excluded contributions from and event plane correlations involving from the background model. For the inclusive trigger correlations, we estimated a potential impact of modulation using an empirical relation found in ATLAS measurements Aad et al. (2012).
After subtracting the underlying event with the model, we study the structures observed at high where the flow backgrounds are negligible. Because the jet signaltoflow background is significantly reduced in the low to intermediate region, studying the correlations there provides a more stringent test of such a background model. Any features left in the residuals can be used to reveal jet energyloss effects at low and intermediate . However, because of our simple model, only substantially significant correlations can be attributable to the medium effect on jets (i.e. broadening or suppression) or the medium response (i.e. yields at large angles from the jet).
We also study twoparticle correlations measured differentially with respect to and event planes as depicted in Fig. 1. Such differential correlations probe the pathlength and geometrical dependence of energy loss with more eventbyevent sensitivity and also extend similar studies of high correlations Adare et al. (2011a) down to lower. We also use a new method of distinguishing “left/right” asymmetry in the correlations, which can be employed to provide more information on the background dominated low and intermediate regions.
In this article: Section II describes the detector setup of the PHENIX Experiment. Sections III.1, III.2, and III.3 describe the analysis methodology of particle selections, higherorder flow harmonics, and twoparticle correlations, respectively. Section IV presents analysis results and discusses their interpretations. This section first starts with the highest trigger selections, GeV/, and makes connections to known energyloss effects. Next, lower trigger correlations down to 1 GeV/ are presented. Finally the eventplane dependence of the intermediate selections are investigated. Section V summarizes this article.
Ii Phenix Detector
The PHENIX detector Adcox et al. (2003) was designed to measure charged hadrons, leptons, and photons to study the nature of the QGP formed in ultrarelativistic heavy ion collisions. Figure 2 shows the beam view and side view of the PHENIX detector including all subsystems for this data taking period.
The global detectors, which include the beambeam counters (BBC), the zerodegree calorimeters (ZDC), and the reactionplane detector (RXN), were used to determine event characterizing parameters such as the collision vertex, collision centrality, and eventplane directions. They are located on both the south and north side of the PHENIX detectors. The BBC is located at 144 cm () from the beam interaction point and surrounds the beam pipe with full azimuthal acceptance. Each BBC module comprises 64 quartz Čerenkov radiators equipped with a photomultiplier tube (PMT) and measures the total charge (which is proportional to the number of particles) deposited in its acceptance. The BBC determines the beam collision time, beam collision position along the beam axis direction, and collision centrality. The ZDCs Adler et al. (2001), located at 18 m away from the nominal interaction point, detect the energy deposited by spectator neutrons of the two colliding nuclei. The PHENIX minimumbias trigger is provided by the combination of hit information in the ZDC and BBC, which requires at least one hit in both the ZDC modules and two hits in the BBC modules.
The orientation of higherorder event planes is determined by the BBC and the RXN Richardson et al. (2011), which have different acceptance. The RXNs are located at 38 cm from the beam interaction point and have two rings in each module; RXNinner and RXNouter are installed to cover and , respectively. Each ring has 12 scintillators in its azimuthal angle acceptance .
Charged hadron tracks are reconstructed in the PHENIX central arm spectrometer (CNT), which is comprised of two separate arms, east and west. Each arm covers and .
The PHENIX tracking system is composed of the drift chamber (DC) in addition to two layers of pad chambers (PC1 and PC3) in the east arm and three layers of pad chambers (PC1, PC2, and PC3) in the west arm. Momentum is determined by measuring the track curvature through the magnetic field by means of a Hough transform with hit information from the DC and PC1 with a momentum resolution of Adare et al. (2012). Additional track position information is provided by the outer layers of the pad chambers and the electromagnetic calorimeter (EMCal).
The ring imaging Čerenkov counter (RICH) and the EMCal identify and exclude electron tracks from the analysis. The RICH produces a light yield for electrons with 30 MeV and for pions with 5 GeV, meaning that a signal in the RICH can be used to separate electrons and pions below 5 GeV. Above 5 GeV where this is no longer possible, the energy deposited in the EMCal can be used for this separation. Electrons will deposit much more of their total energy than pions will, so that the ratio of deposited energy to track momentum is significantly higher for electrons than for pions.
Iii Analysis Methodology
The results presented are based on an analysis of 4.38 billion minimumbias events for AuAu collisions at 200 GeV recorded by the PHENIX detector at RHIC in 2007.
iii.1 Particle Selection
Charged hadrons are selected from candidate tracks using cuts similar to previous correlation analyses Adare et al. (2013). One important cut to reject fake tracks, especially decays in the central magnetic field before the drift chamber, is an association cut to outer CNT detectors. The track trajectories are projected onto outer CNT detectors. The nearest hits in the PC3 and the EMCal from the projections are identified as hits for the track. The distributions of the distance in the azimuthal () and beam () directions between the hits in the PC3 and the EMCal and the extrapolated line are fitted with a doubleGaussian. One Gaussian arises from background and the other from the signal. Hadron tracks are required to be within of the signal Gaussian mean in both the and directions in both the PC3 and the EMCal. To veto conversion electrons, tracks with 5 GeV/ having one or more Čerenkov photons in the RICH are excluded from this analysis. For 5 GeV/, we require c GeV Adler et al. (2006b); Adare et al. (2008b), where is the cluster energy associated with the track.
iii.2 HigherOrder Flow Harmonics
Eventplane and Resolution
Each event plane is determined eventbyevent for different harmonic numbers using the RXN and BBC detectors. The RXN detectors are used to measure the nominal values of while the BBC detectors provide systematic checks to the extracted values. The observed eventplane is reconstructed as
(2) 
Here and are the flow vectors
(3)  
(4) 
where is the azimuthal angle of the th segment in the eventplane detector and is the weight proportional to multiplicity in the th segment.
The thorder resolution of thorder event plane is defined as and can be expressed as Poskanzer and Voloshin (1998)
(5)  
where , is the multiplicity used to determine the eventplane , and is the modified Bessel function of the first kind.
Because the north (N) and south (S) modules of a given eventplane detector have the same pseudorapidity coverage and see the same multiplicity and energy for symmetric nucleusnucleus collisions, the north and south modules should have identical resolution. We obtain the eventplane resolution of an eventplane detector using the two subevent method Poskanzer and Voloshin (1998).
(6)  
The north+south combined eventplane resolution is determined from Eq. (5) with = . The factor of accounts for twice the multiplicity in north+south compared to north or south. Figure 3 shows the the north+south combined eventplane resolution for both RXN and BBC.
measurements
Higherorder flow harmonics Voloshin and Zhang (1996); Poskanzer and Voloshin (1998); Alver and Roland (2010) are measured by the eventplane method Poskanzer and Voloshin (1998). Charged hadron tracks with azimuthal angle are measured with respect to the event plane angle . The flow coefficients are measured as an eventaverage and trackaverage and correcting by the event plane resolution.
(7) 
Four different event planes are studied: , , , and . The flow harmonics are measured by the nine possible combinations of RXN modules: southinner, southouter, southinner+outer, northinner, northouter, northinner+outer, south+northinner, south+northouter, and south+northinner+outer. The reported is an average over the nine different possible RXN combinations, , where is the flow harmonic in one of the nine RXN module combinations.
Systematic uncertainties and results
The systematic uncertainties in measurements are from the following sources:

systematic differences among RXN modules,

matching cut width for CNT hadron tracks,

rapidityseparation dependence between eventplanes and CNT tracks.
The systematic uncertainties in the RXN detector are defined by the standard deviation of
(8) 
As an example, in 20%–30% central collisions measured by different RXN eventplanes are shown in Fig. 4 (a, d, g, j). The (blue) band indicates .
To evaluate the systematic uncertainty due to track matching, the matching cut was varied by from the nominal window. We calculated the uncertainty as the average deviation between the with the nominal cut and the varied cut.
(9) 
The variation due to the track matching cut is illustrated in Fig. 4 (b, e, h, k) by showing the in 20%–30% central collisions measured with tracks having a matching cut of 1.5, 2 and 2.5. The differences between the nominal and both and are also shown and scatter around zero indicating the size of .
The systematic uncertainties associated with the rapidity gap between particles and the eventplane are defined by the absolute difference between determined by the RXN average and determined by the BBC.
(10) 
The measured with the RXN, the BBC, and their difference are shown in Fig. 4 (c, f, i, l). Except in the case of , this systematic uncertainty is much less than the uncertainty due to the RXN module variation. The small uncertainty in the rapidity gap supports the claim that, even though the rapidity gap between the central arm and the RXN is less than one unit of pseudorapidity, the contamination from nonflow correlations does not dominate the uncertainty on the extraction of .
The total systematic uncertainties are the quadrature sum of these individual systematic uncertainties.
(11) 
These total systematic uncertainties are applied symmetrically for a conservative estimate of the systematic uncertainties in the correlation measurements. In nearly all and centrality selections, the RXN systematic uncertainty dominates the total uncertainty.
The results are shown in Fig. 5 and compared with previous PHENIX measurements Ref. Adare et al. (2011b). They are consistent within uncertainties where they overlap. For the twoparticle correlations, we use larger bins (four bin selections) as indicated in Table 1, which lists the results. A test of scaling between higherorder flow harmonics and the secondorder flow harmonics is in Table 2 similar to that done in Ref. Aad et al. (2012). These ratios are constant as a function of within systematic uncertainties, which are dominant over the statistical uncertainties in 0%–50% central collisions. A possible interpretation of this relation is the acoustic scaling described in Ref. Lacey et al. (2011).
Centrality  GeV/  

0%–10%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
10%–20%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
20%–30%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
30%–40%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
40%–50%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10 
Centrality  GeV/  

0%–10%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
10%–20%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
20%–30%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
30%–40%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10  
40%–50%  0.5–1.0  
1.0–2.0  
2.0–4.0  
4.0–10 
iii.3 TwoParticle Correlations
Pair Selections
Tracks that pass the singleparticle cuts are paired for correlations. In real events two tracks cannot come arbitrarily close together. The tracking algorithm would split or merge the tracks. Therefore, there is an acceptance difference in real and mixed events. These effects are estimated by calculating the distances (rad) and (cm) between hits in the PC1 and the PC3, where (rad) is the relative azimuthal angle and (cm) is the relative length between two track hits in both real and mixed events. The ratios of these distributions are shown in Fig. 6. The ratio is normalized to one where the detectors work well to reconstruct hadrons, and inefficient and overefficient regions deviate from unity. The dashed lines indicate the cuts used to remove the inefficient regions:
(12)  
Inclusive Trigger Correlations
Twoparticle correlations are calculated as
(13) 
where is the relative azimuthal angle between trigger and associated hadrons and and are pair distributions in the real and mixed events, respectively. reflects the physical correlation among trigger and associated hadrons from jets and from the underlying event as well as the dihadron detector acceptance effects. is obtained by pairing trigger and associated hadrons from randomly selected pairs of events that have similar collision vertices and centralities so that it reflects only the dihadron acceptance effects. Taking the ratio between the real and mixed distributions corrects for the nonuniform azimuthal acceptance for dihadrons so that contains only physical effects. The correlation function is normalized so that the underlying event modulates approximately around unity.
Within the twosource model Adler et al. (2006a), the correlation function is composed of a jetlike term and an underlyingevent term that includes modulations from flow . We use the following model for the underlying event Poskanzer and Voloshin (1998)
(14) 
The jetlike correlation is then obtained by subtracting from as
(15) 
The scaling factor is determined with the zero yield at minimum (ZYAM) method Ajitanand et al. (2005); Adams et al. (2005c); Adler et al. (2006a). In the ZYAM assumption, is scaled such that has a minimum of exactly zero. This therefore gives the lower boundary of possible jetlike correlations. The ZYAM scaling factor is determined by fitting the correlation function with Fourier series for and identifying the single point where this fit and have the minimum contact point. The statistical uncertainty of the bin containing the ZYAM point is used to scale to estimate the systematic uncertainty due to ZYAM
(16) 
An example ZYAM identification is shown in Fig. 7.
The jetlike correlations are scaled to the pertrigger yield
(17) 
where is the number of trigger hadrons, is the number pairs, and is the singlehadron tracking efficiency in the associated hadron range. The efficiency is estimated via detector simulations for acceptance and occupancy effects as discussed in Ref. Adler et al. (2004); Adare et al. (2008b, 2010a, 2011a). The tracking efficiency of a trigger particle is canceled by the ratio of .
Event PlaneDependent Correlations
Event planedependent twoparticle correlations are defined as
(18)  
where and and are the event planedependent pair distributions in real and mixed events, respectively.
Similar to inclusive correlations, event planedependent jetlike correlations are obtained by subtracting the event planedependent flow background term from with a ZYAM scale factor as
(19) 
We use the same as determined from the inclusive correlations from the same trigger, associated and centrality selection. An analytical formula for including the event plane dependence exists Bielcikova et al. (2004), however, it is not easily applied with finite correlations between the and event planes. For this reason, a Monte Carlo simulation is employed to estimate . This is described in Sec. III.3.4 below.
The event planedependent jetlike correlations are converted into event planedependent pertrigger yield as
(20)  
where is the number of trigger hadrons and is the number of pairs in the trigger eventplane bin.
Flow Background Model Including Event Plane Dependence
With the assumption that the measured from the event plane method are purely from collective dynamics of the medium, flowlike azimuthal distributions of single hadrons can be generated by performing a Monte Carlo simulation inputting the experimentally measured , the resolution of the event planes, and the strength of correlation among different order event planes. The singlehadron azimuthal distributions due to collective flow can be described by a superposition of as
(21) 
where is the azimuthal angle of the emitted hadrons and is a true thorder event plane defined over . Separate distributions using for each ranges of trigger and associated particles are used in the simulation. The trigger and associated distributions in real events share a common , while those in mixed events do not.
The experimental event plane resolution is introduced through a dispersion term where . We calculate as
(22) 
where and is the error function Ollitrault (); Poskanzer and Voloshin (1998). This equation can be solved for by using the experimentallydetermined from the measured event plane resolutions using Eq. (5).
Because a weak correlation between and exists Adare et al. (2011b), the directions of and are generated independently. The direction of is generated assuming a correlation with , . We estimate assuming the correlation between the two event planes follow similar functional forms as the dispersion of event planes due to the resolution. That is, we assume,
(23) 
where . The parameter is assumed to be similar to Eq. (5)
(24)  
where Yan and Ollitrault (2015). The functional shape of Eq. (23) is verified by event plane correlation studies using the BBCs and the RXNs following the method described in Ref. Aad et al. (2014b). The correlation strength between and , , is measured to be consistent with zero within large statistical uncertainties. Potential impacts of to the event plane dependent correlations are estimated using the value of reported in Ref. Aad et al. (2014b) by the ATLAS Experiment. The impact of is within the systematic uncertainties described later.
We use the averaged value between GeV/ and GeV/ for event planedependent correlations of ( (), ( (), and ( () GeV/ because would contain autocorrelations from jets at high .
The event planedependent background shapes are determined by generated particles in this simulation using Eq. (18). Figure 9 shows event planedependent correlations and backgrounds with a selection of the absolute trigger azimuthal angle relative to the eventplanes . The backgrounds agree with the experimental correlations except at where contributions from jets are expected. Figure 9 shows event planedependent correlations and backgrounds with a selection of trigger azimuthal angle relative to event planes . Agreement between the experimental correlations and the background except at is also observed here. Other eventplane dependent correlations and backgrounds with a selection of trigger azimuthal angle relative to eventplanes for different collision centralities and selections are shown in the Appendix.
iii.4 Unfolding of Event PlaneDependent Correlations
In this analysis, is divided into 8 bins. The width of the bins is and when correlating with and , respectively. The event planedependent pertrigger yields are smeared across neighboring event plane bins due to limited experimental resolution of the event planes. We unfold the smearing to obtain the true eventplane dependence of the correlations. Two different methods are used to check the unfolding procedure: (I) iterative Bayesian unfolding, , and (II) correcting the event planedependence of the pertrigger yield based on a Fourier analysis, .
Iterative Bayesian Unfolding
The Iterative Bayesian Unfolding Method presented in Ref. D’Agostini (1995); Adye (2011) is applied to this analysis with the following formulation
(25)  
(26) 
where is the unfolded distribution, is the experimentally observed distribution, is the prior distribution, is the conditional probability matrix where is measured to be , and is the efficiency. In the iterative calculation, also serves as the prior distribution of the next loop. We perform this unfolding separately for every bin.
We define the experimentally observed distribution as using the measured event planedependent pertrigger yield. The offset is to prevent a divergence in the iteration due to small yields near the ZYAM point. In the initial loop of the iteration, we define the prior distribution as