Measurement of emission angle anisotropy via long-range angular correlations with high $p_T$ hadrons in $d$$+$Au and $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV

We present measurements of two-particle angular correlations between high-transverse-momentum ($2<p_T<11$ GeV/$c$) $\pi^0$ observed at midrapidity ($|\eta|<0.35$) and particles produced either at forward ($3.1<\eta<3.9$) or backward ($-3.7<\eta<-3.1$) rapidity in $d$$+$Au and $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The azimuthal angle correlations for particle pairs with this large rapidity gap in the Au-going direction exhibit a ridge-like structure that persists up to $p_T{\approx}6$ GeV/$c$ and which strongly depends on collision centrality, which is a similar characteristic to the hydrodynamical particle flow in A+A collisions. The ridge-like structure is absent in the $d$-going direction as well as in $p$$+$$p$ collisions, in the transverse-momentum range studied. The results indicate that the ridge-like structure is shifted in the Au-going direction toward more central collisions, similar to the charged-particle pseudorapidity distributions.

We present measurements of two-particle angular correlations between high-transverse-momentum (2 < pT < 11 GeV/c) π 0 observed at midrapidity (|η| < 0.35) and particles produced either at forward (3.1 < η < 3.9) or backward (−3.7 < η < −3.1) rapidity in d+Au and p+p collisions at √ s N N = 200 GeV. The azimuthal angle correlations for particle pairs with this large rapidity gap in the Au-going direction exhibit a characteristic structure that persists up to pT ≈6 GeV/c and which strongly depends on collision centrality, which is a similar characteristic to the hydrodynamical particle flow in A+A collisions. The structure is absent in the d-going direction as well as in p+p collisions, in the transverse-momentum range studied. The results indicate that the structure is shifted in the Au-going direction toward more central collisions, similar to the charged-particle pseudorapidity distributions.

I. INTRODUCTION
Azimuthal anisotropy in the multiparticle production from high-energy nucleus-nucleus collisions has been the subject of a great deal of study. These final-state momentum anisotropies are believed to be the result of both spatial anisotropies in the initial geometry and hydrodynamic-like behavior in the subsequent evolution * Deceased † PHENIX Spokesperson: akiba@rcf.rhic.bnl.gov of the medium. The final-state patterns that can be modeled this way are thus often referred to as flow-like correlations, for which a central characteristic is that the majority of produced light-flavor hadrons will exhibit correlations with the initial collision geometry. The measurement of azimuthal correlations of particles with a large rapidity gap (e.g. |∆η| > 3) is particularly useful to extract the signal of the true flow contribution. The near-side enhancement of the long-range correlation function is often called a "ridge" structure, where the large relative pseudorapidity cut suppresses other sources of angular correlations, such as resonance decays or jet fragmentation, that are usually confined within |∆η| ≈ 3.
Analysis of flow-like correlations with hydrodynamical models has provided strong evidence for the creation of the quark-gluon plasma (QGP) state in the highenergy collisions of large nuclei, such as Au+Au and Cu+Cu at the Relativistic Heavy Ion Collider (RHIC), and Pb+Pb at the Large Hadron Collider (LHC) [1,2]. Great interest was sparked when flow-like behavior was first observed in small collision systems, including highmultiplicity p+p and p+Pb at the LHC [3][4][5][6][7][8] and d+Au at RHIC [9][10][11]. Previously, these systems had been regarded as control systems where only nonQGP effects would be present. Since then, similar flow-like observations have also been made in other small systems, including p+Au and 3 He+Au. The debate continues over whether the QGP is actually being created in this class of collisions [12,13], and even at lower √ s N N [14,15]. Possible explanations of these observations include hydrodynamics [16][17][18][19] and Color-Glass-Condensate (CGC) models [20]. The hydrodynamic models include both initial and final state effects, while the CGC-motivated models are based mainly on physics present in the initial state. Interestingly, the kinetic transport model ampt [21] also reproduces the observed flow structure fairly well [13][14][15].
Similarly to hydrodynamics, ampt can translate the initial geometry into final-state momentum anisotropy, but via a very different mechanism, namely the anisotropic probability of partons to escape the partonic scattering stage [22]. The PHENIX experiment has previously measured azimuthal correlations in d+Au and p+p between charged particles produced at midrapidity (pseudorapidity |η| ≈ 0) and energy deposits in a forward calorimeter (|η| ≈ 3.5) [10]. In those analyses, the reach in charged particle p T was statistically limited to p T < 3.5 GeV/c. Measurements of azimuthal anisotropy at low p T are useful to study the collective behavior of the QGP medium. However, at high p T , azimuthal anisotropy signals can no longer be attributed to the collective expansion of the bulk. Measurements in p+Pb at the LHC [7,23] have shown that v 2 decreases sharply between 4 < ∼ p T < ∼ 8 GeV/c, reaching a small near-constant value above that point. It has been suggested that this high-p T behavior might originate from jet quenching. Therefore, the present paper extends the measurements of twoparticle correlations at RHIC to this kinematic region where nonhydrodynamic effects dominate. We use the PHENIX high-energy photon trigger in the midrapidity region, and explore mid-forward(backward) correlations in d+Au and p+p up to p T = 11 GeV/c with identified π 0 at midrapidity.
In large collision systems, the appearance of a nearside enhancement in azimuthal two-particle correlations is considered a hallmark signature of QGP collectivity. Thus, early searches for collectivity in small collision systems focused on observing near-side enhancement. However, unlike in A+A collisions, elementary processes cannot be neglected when analyzing small systems. Thus, even if collectivity exists, it may not be necessarily ob-served as a near-side enhancement because the ratio of quadrupole to dipole contributions is decreasing with multiplicity. This is particularly true for p+p and peripheral d+Au collisions, as the "smallest" of the small systems considered in the present analysis. In light of this, the paper presents a wealth of data and attempts to characterize the shape of the two-particle correlation functions by investigating the behavior of the coefficients of the Fourier series fit, in relation to the appearance of a near-side enhancement.
In addition to measuring flow by the correlation of individual particles to the reaction plane, it is also possible to measure flow by the correlation of two-particles to each other. The advantage of this method is that one does not have to determine the reaction plane. If we write the azimuthal angle distribution of two particles A and B, which are correlated to a reaction plane as: then the azimuthal angle distributions for the two particle correlations can be written as: Instead of measuring v n , this paper presents measurements of c n , the coefficient of the Fourier fit to the correlation functions, because the factorization c n = v A n v B n holds only at low p T , where the two particles are correlated with the same event plane [24]. This relation breaks down when considering high p T particles that are coming from the nonflow contributions such as jet fragmentation.

II. EXPERIMENT AND DATASET
A detailed description of the PHENIX detector system can be found elsewhere [25]. The principal detectors used in this analysis are the beam-beam counters (BBC), the muon-piston calorimeter (MPC) and the electromagnetic calorimeter (EMCal). The BBCs are located north (BBCN, 3.1< η <3.9, d-going) and south (BBCS, -3.9< η <-3.1, Au-going) of the interaction point, covering the full azimuth and are sensitive to charged particles. In d+Au collisions, the Au ions are accelerated in the Au-going direction. The MPCs, which are high resolution electromagnetic calorimeters, are also located north (MPCN, 3.1< η <3.9) and south (MPCS, -3.7< η <-3.1) of the interaction point, in front of the BBCs, and cover the full azimuth. The south (north) MPC comprise 192 (220) PbWO 4 crystal towers with 20.2 X 0 or 0.89 λ I [26]. The EMCal is located in the central (CNT) arms with pseudorapidity range |η| <0.35 and covering two π/2 segments of the full azimuth. Figure 1 shows the acceptance of each relevant PHENIX detector subsystem in φ-η coordinates.
The d+Au and p+p collision data used in this analysis were recorded in 2008 at RHIC. The events triggered by a high energy deposit in a 4x4 tower region of the EMCal in coincidence with the minimum bias (MB) requirement were selected in both the p+p and d+Au data sets. The MB trigger was defined as the coincidence of at least one hit in the BBCS and BBCN. A z-vertex cut of |z| < 30 cm is applied, using the vertex calculated from the BBC timing information. The energy threshold of the 4x4 towers is set to be 2.8 GeV, however, due to the energy smearing effect, the towers also sample hits with lower energies but with lower efficiency. The number of recorded events was 2.85×10 8 (9.64×10 10 MB equivalent) for the p+p and 6.51×10 8 (1.40×10 11 MB equivalent) for the d+Au collisions, which made it possible to measure the π 0 -triggered long-range correlations up to p T =11 GeV/c. In the case of d+Au collisions, centrality was defined by the total charge deposited in BBCS (Augoing direction). Seven partially overlapping centrality bins have been considered, from the most central (0%-5%) to the most peripheral (60-88 %) collisions [27].

III. ANALYSIS
The long-range two-particle correlation functions are constructed by pairing a high p T π 0 ("trigger" particle) found in the PHENIX EMCal with the energy deposit E dep in each tower of one of the MPCs ("associated" hit). In the following sections we describe (i) the π 0 identification, (ii) construction of the initial azimuthal correlation functions, (iii) correction for combinatoric background in the π 0 sample, and (iv) fitting the corrected correlation functions with a harmonic expansion. Throughout this paper the results for central-MPC south (CNT-MPCS) and central-MPC north (CNT-MPCN) correlations are shown separately.
A. π 0 selection Each trigger π 0 was measured in the EMCal via the π 0 → γγ decay channel using photon showers reconstructed using the standard PHENIX method [28][29][30]. The photon showers were identified using a shower-shape cut [31]. A cut on the energy asymmetry of the photon pair α = |E 1 − E 2 |/(E 1 + E 2 ) < 0.7 has been applied to reduce the combinatoric background. A sample γγ invariant mass plot is shown in Fig. 2 for pairs with pair p T > 3 GeV/c. The π 0 mass region was defined as 0.12 < m γγ < 0.16 GeV/c 2 , and every measured pair in this range was used in compiling the initial correlation shaded "Net π 0 " peak is clearly visible above a small [yellow] shaded "Estimated combinatoric background" in the same mass window 0.12 < mγγ < 0.16 GeV/c 2 (note the semilog scale). We estimate the combinatoric background by interpolating linearly between two points outside the peak, as shown by the [blue] line, which is obtained by fitting around the peak with a combined Gaussian and linear function. The purely combinatoric pairs in the shaded [green] "Sideband" region are used to correct the correlation functions for the effects of background pairs in the peak region (see Section III C).
functions, binned according to pair p T . As shown in Fig. 2 the π 0 peak is quite prominent in the pair mass spectrum, on top of a small background continuum due primarily to combinatoric pairs. We estimated the level of this background in terms of the signal/background ratio S/B within the chosen π 0 mass window as shown in Fig. 3. The ratio was used for subtracting the combinatoric background contribution in the correlation functions as explained in the section III C.

B. Initial correlation functions
The procedure used to construct the initial π 0 -MPC correlation functions is essentially the same as was used in our earlier analysis of central-arm charged track -MPC correlations in d+Au and p+p collisions [10]. Over a selected event sample and π 0 p T bin, we compile the relative azimuthal angle distribution, S(∆φ, p T ), between γγ pairs in a given mass window and MPC towers in the same event where ∆φ = φ γγ − φ tower is the azimuthal opening angle between the γγ pair-sum momentum direction and a line to the center of the MPC tower. We choose the weighting for each tower to be the transverse energy w tower = E dep sin (θ tower ), where E dep is the energy deposit in that tower, and θ tower is the angular position of the tower with respect to the beam line. The w tower introduces a p T spectrum weight on the hit frequency in the MPC. The MPC towers with deposited energy E dep > 0.3 GeV were selected to avoid the background from noncollision noise sources (≈75 MeV) and to cut out the deposits by minimum ionizing particles (≈245 MeV).
To maximize statistics the energy is lowered compared to the one used in a previous publication [10].
In addition to physical pair correlations from the collisions, the shape of the same-event distribution S(∆φ, p T ) will reflect the effects of detector acceptance, detector inefficiencies, and kinematic cuts. We estimated these instrumental effects by constructing a mixed-event distribution M (∆φ, p T ) [Eq. 5], but using γγ pairs from one event and MPC towers from a different event in the same event class (centrality and π 0 p T ). We then correct for instrumental effects by constructing the correlation function C X (∆φ, p T ), for any particular choice X of γγ pair selection criterion Both the same-event numerator and the mixed-event denominator have been normalized by their respective integrals.

C. Combinatoric sideband correction
The initial correlation function is constructed using all pairs in the π 0 mass window, which necessarily includes an admixture of both true π 0 pairs and background pairs. Therefore, it will not reflect simply the true π 0 -MPC correlation but rather a weighted average of the correlations of true π 0 pairs and those of background pairs. Though the background is typically a small fraction of the signal, as shown in Fig. 3, we carried out the following correction to remove any influence from the background pairs.
We denote the initial correlation function constructed using all photon pairs in the π 0 mass peak region as C S+B (∆φ, p T ), because it contains correlations from both signal and background pairs. We then approximate the correlation function C B (∆φ, p T ) that would result from using the background pairs only, by constructing a correlation function according to Eq. 6, but with pairs chosen from the "sideband" mass region 0.20 < m γγ < 0.25 GeV/c 2 [see Fig. 2]. We then derive the true π 0 -MPC correlation function C(∆φ, p T ), which would result from including only the true π 0 decay pairs, by inverting the weighted average via where B/S is the background-to-signal ratio in the peak region, which is the reciprocal of the number shown in Fig. 3. In practice, this correction for background pairs is very small; it does not change the harmonic amplitudes of the correlation function (see Section III D) by more than a few percent of their value in the lowest S/B cases and becomes negligible as S/B increases toward higher p T .

D. Harmonic expansion fitting
Our objective in this analysis is to examine the shapes of the π 0 -MPC correlation functions across π 0 p T and collision system centrality classes. We quantify each correlation function by fitting them to an expansion in Fourier terms over ∆φ up to fourth order via The fits were optimized using only the statistical errors in the final correlation functions. The fit for each p T and event class combination has five parameters: the four c n and an overall normalization. Each correlation function was compiled in 20 bins of ∆φ, leaving 15 degrees of freedom (NDF) for each fit. The C(∆φ, p T ) with fit functions are shown in section IV and in the Appendix. The χ 2 /NDF goodness-of-fit values are compiled and shown in Fig. 4. There is no particular structure seen with π 0 p T or event class, and the distribution agrees with what would be expected for a χ 2 estimator.
When we fit the correlation functions with c 2 fixed to zero, the χ 2 /NDF's are found to be as high as ≈40 around p T =3 GeV/c, and don't reach χ 2 /NDF≈4 before p T ≈6 GeV/c, for both 0%-5% central d+Au and p+p collisions. This shows that the correlation functions have a significant second-order component.

E. Estimation of systematic errors
The systematic uncertainties of the measurement have been estimated as follows. The width of the π 0 extraction window as well as the location and width of the sideband have been varied in five different combinations as listed in Table I. Note that the case-0 corresponds to the standard windows in this analysis.  In the sixth case the original windows were kept as case-0 but the asymmetry cut was changed to α < 0.5. Following the exact same procedure for obtaining the true π 0 -MPC correlation functions as described in the previous sections, the correlation functions for the six cases were obtained and the values of c 2 and −c 2 /c 1 were recalculated. The deviations for the case-0 values, with respect to the standard result, were calculated and averaged over the six cases. The averaged deviations are the systematic uncertainties. The resulting uncertainties on c 2 are 2% for p+p (all p T ), and for the 0%-5% d+Au (worst case) they are 8% at 2 GeV/c and 3% at 6 GeV/c for CNT-MPCS (Au-going). The uncertainty for the −c 2 /c 1 is very similar to that of c 2 owing to a smaller uncertainty of c 1 . This study was also performed for CNT-MPCN (d-going) correlations, obtaining 4% (2 GeV/c) and 2% (6 GeV/c) for p+p and 12% (2 GeV/c) and 3 % (6 GeV/c) for the 0%-5 % d+Au. Both CNT-MPCS and CNT-MPCN show consistent systematic uncertainties given the large statistical uncertainties in the CNT-MPCN correlations. Considering the better statistical precision for the CNT-MPCS correlations, we quoted the errors for them as the systematic uncertainties for the final results. There is a possible systematic uncertainty associated with the mixed event distributions M (∆φ, p T ). This uncertainties are effectively folded during the procedure of the systematic uncertainty estimate described above.  The correlation functions are largely dominated by a dipole component (n = 1), and higher components (n > 1) contribute to form a near-side enhancement structure in the near-side (∆φ ≈ 0) of the functions. The dipole component is usually attributed to the backto-back dijet contribution and momentum conservation in the system. With the large psuedorapidity gap employed (|∆η| > 3), the near-side particles of the dijet triggered by π 0 (|η| < 0.35) will not form a peak at ∆φ ≈ 0 in the MPCs (3.1 < |η| < 3.9). Therefore, the near-side enhancement is formed by other sources, possibly a quadrupole flow from a bulk medium. The characteristic structure is clearly visible for CNT-MPCS (Au-going), but not for CNT-MPCN (d-going). In addition, the structure is more prominent in the more central collisions (e.g. see the first plot in the Appendix), and it gradually disappears with both decreasing centrality and increasing p T . The trend in the CNT-MPCS correlation hints that the characteristic structure has a similar characteristic as the hydrodynamical particle flow in A+A collisions. Looking at the evolution of the individual Fourier-components c i with centrality and p T provides a richer and more quantitative picture. As seen in Figs. 5 and 6, the c 3 and c 4 are both very small, and are found to be consistent with zero within uncertainties. Therefore, we discuss here only the centrality-and p T -dependence of the dipole (c 1 ) and quadrupole (c 2 ) coefficients.

IV. RESULTS AND DISCUSSIONS
The c 1 (dipole) values for CNT-MPCS correlations are summarized in Fig. 7(a). They exhibit a definite ordering with system size: the largest negative values are observed in p+p, the smallest ones in the most central d+Au. Similar ordering, albeit with smaller absolute differences, can be seen for CNT-MPCN in Fig. 8. This trend is similar to the decrease of the absolute value of c 1 with increasing multiplicity that was observed in [11]. If the negative c 1 at large ∆η is indeed a consequence of a dijet fragmentation into the CNT and MPC regions, then we would expect the effect to be diluted as the underlying event multiplicity increases. Because the overall multiplicity on the d-going side is smaller we would also expect a larger magnitude for c 1 there compared with the Augoing direction, as seen in the data. Interestingly, the c 1 coefficients vary with p T and have a maximum magnitude around 4-5 GeV/c. It may be related to the fact that this is the p T region where hard scattering becomes dominant over bulk phenomena that govern particle production at lower p T .
The To gauge the magnitude of characteristic-structure correlations as a measure of a bulk property of the system, we calculated −c 2 /c 1 , the ratio of c 2 (quadrupole) to −c 1 (dipole), for all p+p and d+Au systems, as shown in Fig. 7(c). For the CNT-MPCS correlations [ Fig. 7(a)] the data exhibit a well-defined ordering with system centrality, within errors, from the most central d+Au down to the most peripheral (60%-88%) which is consistent with the p+p. We then see a smooth evolution from the most central collisions observed at lowest p T , where the near-side correlations are most prominent and which would be expected to have the largest contribution from a collective source, to the more peripheral and higher p T limit, where the near-side correlation vanishes and elementary processes are expected to dominate. The trend is very different for CNT-MPCN correlations [ Fig. 8(b)]. Here all the −c 2 /c 1 ratios are consistent for both d+Au and p+p collisions, indicating no additional near-side correlations in d+Au over p+p collisions for any system across the entire π 0 p T range studied here. There is also no visible ordering of −c 2 /c 1 with system centrality for p T > 2.5 GeV/c, in contrast to the CNT-MPCS case, within uncertainties.
The c 1 and c 2 for the symmetric p+p collisions are somewhat different between CNT-MPCS and CNT-MPCN, which results from the difference of psuedorapidity coverage in MPCN (3.1 < η < 3.9) versus MPCS (−3.7 < η < −3.1). The fact that the −c1/c2 are very consistent indicates that the same phenomena is observed in each direction.
Recently, attempts have been made to develop methods that effectively subtract the nonflow contributions present in two-particle correlations, as measured in p/d+A collisions [4,8,32,33]. Despite their differences, all of these methods rely on the assumption that one can identify a class of events (usually p+p or peripheral p/d+A) with low enough multiplicity such that the corresponding correlation function can be attributed entirely to nonflow. However, there is currently no consensus in the field regarding how the subtraction procedure should be carried out. This paper therefore focuses on the shape analysis of the correlation functions, leaving nonflow subtraction outside of the scope. However, we point out that the quantity −c 2 /c 1 encodes some information about the relative strength of nonflow, and its comparison between collision systems can provide useful insight.
Another shape study of the near-side correlations can be performed by examining the second derivative of dN/d(∆φ). If we approximate the n > 2 coefficients as negligible (c 3 ≈ c 4 ≈ 0) then the condition of having a local maximum at ∆φ = 0 corresponds to The observed positive c 2 and negative c 1 lead us to use the threshold of −c 2 /c 1 > 0.25 as the condition indicating that a near-side correlation with a local maximum is present in the correlation function, as also pointed out in the literature [34]. It should be noted that the absence of a local maximum doesn't necessarily imply that the near-side contribution is absent.
We now examine the system and centrality dependence of the correlation functions. Figure 9 shows the c 1 , c 2 , and −c 2 /c 1 as a function of the mean number of collision participants N part [27] for the two selected p T ranges 3-3.5 GeV/c and 5-6 GeV/c.
The values for both CNT-MPCS and CNT-MPCN are shown. The smooth decrease of c 1 with N part is clearly seen for both p T selections, but the decrease of c 1 for the CNT-MPCS is more rapid compared to that of CNT-MPCN. In contrast, the c 2 is flat or exhibits little increase (decrease) as a function of N part for CNT- collisions. This observation clearly shows again that the characteristic structure is clearly seen in Au-going direction, rather than in d-going direction, and ceases at high p T which is a similar characteristic as the hydrodynamical particle flow in A+A collisions.
The centrality dependence of −c 1 /c 2 can be understood in terms of the asymmetry of the charged particle pseudorapidity distributions with respect to η = 0 in d+Au collisions [35]. When going to greater centrality, the results indicate that the characteristic structure is shifted in the Au-going direction, similar to the chargedparticle pseudorapidity distributions. This is consistent with the findings of the STAR experiment [11] in the re-gion where the p T ranges overlap. There is a possible fluctuation of the event plane as a function of psuedorapidity as observed by the CMS experiment at the LHC [36]. Although this may partly explain the centrality-dependent difference between CNT-MPCN and CNT-MPCS, our measurements lack the precision to gauge the effect. These results provide a strong argument for studying long-range correlations in asymmetric systems separately in the forward/backward directions.

V. SUMMARY
We have measured long-range azimuthal correlations between high-transverse-momentum (2 < p T < 11 GeV/c) π 0 observed at midrapidity (|η| < 0.35) and particles produced either at forward (3.1 < η < 3.9) and backward (−3.7 < η < −3.1) rapidity in d+Au and p+p collisions at √ s N N =200 GeV. The centrality and p T -dependent two-particle correlations were fitted with a Fourier-series up to the fourth term. While the 3rd and 4th coefficients (c 3 , c 4 ) were consistent with zero within uncertainties, the c 1 (dipole) values exhibit a definite ordering with the system size both in the Au-going and d-going directions. The c 2 (quadrupole) values exhibit similar magnitudes for both directions. However, −c 2 /c 1 values exhibit well-defined ordering with system centrality and decrease with increasing p T in the Au-going direction, while the values are consistent over all systems and p T in the d-going direction. This implies that the characteristic structure clearly exists in the Au-going direction, rather than in the d-going direction, and ceases at high p T which is a similar characteristic as the hydrodynamical particle flow in A+A collisions. The difference of the behavior in the Au-going and the d-going direction can be understood from the fact that the characteristic structure is shifted in the Au-going direction toward more central collisions, similar to the charged-particle pseudorapidity distributions. This suggests that looking at two directions in asymmetric systems is essential.