UKnowledge Jet-Like Correlations with Direct-Photon and Neutral-Pion Triggers at √ S NN = 200 GeV

Azimuthal correlations of charged hadrons with direct-photon ( γ dir ) and neutral-pion ( π 0 ) trigger par- ticles are analyzed in central Au + Au and minimum-bias p + p collisions at √ s NN = 200 GeV in the STAR experiment. The charged-hadron per-trigger yields at mid-rapidity from central Au + Au collisions are compared with p + p collisions to quantify the suppression in Au + Au collisions. The suppression of the away-side associated-particle yields per γ dir trigger is independent of the transverse momentum of the trigger particle ( p trig T ), whereas the suppression is smaller at low transverse momentum of the associated charged hadrons ( p assoc T ). Within uncertainty, similar levels of suppression are observed for γ dir and π 0 triggers as a function of z T ( ≡ p assoc T / p trig T ). The results are compared with energy-loss- inspired theoretical model predictions. Our studies support previous conclusions that the lost energy reappears predominantly at low transverse momentum, regardless of the trigger energy.


Introduction
Over the past decade, experiments at the Relativistic Heavy Ion Collider (RHIC) at BNL have studied the hot and dense medium created in heavy-ion collisions. The suppression of high-transverse momentum (p T ) inclusive hadrons [1][2][3], indicative of jet quenching, corroborates the conclusion that the medium created is opaque to colored energetic partons [4][5][6][7]. This phenomenon can be understood as a result of the medium-induced radiative energy loss of a hard-scattered parton as it traverses the Quark Gluon Plasma (QGP) created in heavy-ion collisions [8,9]. The angular correlation of charged hadrons with respect to a direct-photon (γ dir ) trigger was proposed as a promising probe to study the mechanisms of parton energy loss [10]. The presence of a "trigger" particle, having p T greater than some selected value, serves as part of the selection criteria to analyze the event for a hard scattering. Direct photons are produced during the early stage of the collision, through leading-order pQCD processes such as quark-gluon Compton scattering (qg → qγ ) and quark-antiquark pair annihilation (qq → gγ ). In these processes the transverse energy of the trigger photon approximates the initial p T of the outgoing recoil parton, before the recoiling ("away-side") parton likely loses energy while traversing the medium and fragments into a jet. The jet-like yields associated with a trigger particle are estimated by integrating the correlated yields of charged hadrons over azimuthal distance from the trigger particle ( φ). Any suppression of the charged-hadron per-trigger yields in the away-side jets in central Au+Au collisions is then quantified by contrasting to the per-trigger yields measured in p + p collisions, via the ratio of integrated yields, I A A [11,12] (defined in Eq. (8)). When requiring a hadron trigger (such as a π 0 ), the p T of the recoiling parton (and hence the away-side jet) is not as well approximated by the transverse energy of the trigger. For example, the PYTHIA Monte Carlo simulator [13] shows that, in p + p collisions at √ s N N = 200 GeV, a π 0 trigger with p T > 12 GeV/c carries, on average, only 80 ± 5% of the original scattered parton's p T . This percentage from PYTHIA is consistent with the values extracted from this analysis, as described below. Despite this complication, it is compelling to compare the suppression for γ dir triggers with that for π 0 triggers because of the expected differences in geometrical biases at RHIC energies [14].
While the π 0 trigger is likely to have been produced near the surface of the medium, the γ dir trigger does not suffer the same bias, since the photon mean free path is much larger than the size of the medium. Comparing γ dir -and π 0 -triggered yields offers further opportunities to explore the geometric biases and their interplay with parton energy loss. A next-to-leading order perturbative QCD calculation [15] suggests that production of hadrons at different z T is also affected by different geometric biases, where are transverse momenta of associated and triggered particles, respectively) represents the ratio of the transverse momentum carried by a charged hadron in the recoil jet to that of the trigger particle. The high-z T hadrons in a jet recoiling from a γ dir preferentially originate from a parton scattering near the away-side surface of the medium, since scatterings deeper in the medium will result in a stronger degradation of the high-momentum components of the jet. The high-z T hadrons in a jet recoiling from a π 0 preferentially emerge from scatterings tangential to the surface from the already biased surface-dominated trigger jets (which is consistent with observations in [16]). These two mechanisms turn out to lead to the same level of suppression [15]. Only at low z T does the full sampling of the volume by γ dir triggers show a predicted difference from that of the surfacedominated π 0 triggers. An additional effect at low z T may be the redistribution of the parton's lost energy within the low-momentum jet fragments [17], which is not included in the calculation [15] described above. This was studied by the PHENIX Collaboration, which found an enhancement at low z T and large angles, for direct photon triggers with p trig T in the range of 5-9 GeV/c at √ s N N = 200 GeV in the most central Au+Au collisions [11]. Enhancements due to this mechanism would be expected in hadrons recoiling from other triggers as well, such as π 0 or jets. A previous STAR measurement of hadrons associated with a reconstructed jet has shown an enhancement for p T < 2 GeV/c, for two classes of jets with broadly separated energy scales, in which the enhancement at low p T balances the suppression at high p T [18]. Furthermore, leading order di-jet production comes from both quark and gluon jets. Recent calculations show that pions with high p T relative to the total jet p T are predominantly from quark jets [19,20], so, for the jet energies probed in this paper, the away- side mainly comes from gluon jets [21]. This is in contrast to the away-side of a γ dir trigger, which mainly comes from quark jets, since at leading order a photon does not couple with a gluon. Thus it is expected that, on average, the away-side parton associated with a π 0 suffers more energy loss than that of a γ dir due to the additional color factor from gluons. By comparing the suppression of away-side associated hadrons for γ dir triggers to that for π 0 triggers, one can gain information about both the path-length and the color-factor dependence of parton energy loss.
This manuscript is organized as follows. The detector setup of the STAR experiment is discussed in Sec. 2. The transverse showershape analysis used to discriminate between π 0 and γ dir , and the procedures to extract the charged-hadron spectra, associated with π 0 and γ dir triggers, are discussed in Sec. 3. The per-trigger charged-hadron yields are presented as a function of z T , in Sec. 4. The dependences of the suppression of these yields in central Au+Au collisions relative to those in minimum-bias p + p collisions on both the trigger energy and the associated transverse momentum are discussed, with comparisons to theoretical model predictions. Finally, in Sec. 5, our observations are summarized. Calorimeter (BEMC) [22] to select events containing a high-p T γ or π 0 , the STAR experiment collected an integrated luminosity of 2.8 nb −1 of Au+Au collisions and 23 pb −1 of p + p collisions. STAR provides 2π azimuthal coverage and wide pseudo-rapidity (η) coverage. The Time Projection Chamber (TPC) is the main chargedparticle tracking detector [23], providing track information for the charged hadrons with |η| < 1.0. The centrality selection is determined from the charged-particle multiplicity in the TPC within |η| < 0.5. The BEMC is a sampling calorimeter, and each calorimeter module consists of a lead-scintillator structure and an embedded wire chamber, the Barrel Shower Maximum Detector (BSMD). The BSMD is situated approximately five radiation lengths from the front face of the BEMC. BEMC towers (each covering 0.05 units in η and φ) provide a measurement of the energy of electromagnetic clusters, whereas the BSMD, due to its high granularity (0.007 units in η and φ), provides high spatial resolution for the center of a cluster and the transverse development of the shower. Electromagnetic clusters are constructed from the response of one or two towers, depending on the location of the centroid as determined by the BSMD. The transverse extent of the shower is used to distinguish between γ dir showers and decay photons from π 0 . Details of the π 0 /γ discrimination are discussed in the next section.

Analysis details
Events having a transverse energy in a BEMC cluster E T > 8 GeV, with |η| ≤ 0.9, are selected for this analysis. In order to distinguish a π 0 , which at high p T predominately decays to two photons with a small opening angle, from a single-photon cluster, a transverse shower-shape analysis is performed. In this method, the overall BEMC cluster energy (E cluster ), the individual BSMD strip energies (e i ), and the distances of the strips (r i ) from the center of the cluster are used to construct the "Transverse Shower Profile" (TSP). The TSP is defined as, TSP = E cluster / i e i r 1.5 i [12,24].
The π 0 rich (nearly pure sample of π 0 ) and γ rich (enhanced fraction of γ dir ) samples are selected by requiring TSP < 0.08 and 0.2 < TSP < 0.6, respectively, in both p + p and Au+Au collisions. The π 0 rich sample is estimated to be ∼ 95% pure π 0 , determined from studies of simulated π 0 and γ dir embedded into real data. The φ azimuthal correlations are constructed with chargedhadron tracks within 1.2 GeV/c < p assoc |η| < 0.9. There is an additional requirement that no track with momentum greater than 3 GeV/c is pointing to the trigger tower. This track-rejection cut prevents significant contamination of the measured BEMC energy of the trigger particle. The p T threshold of the track-rejection cut was varied between 1 and 4 GeV/c, as a part of the systematic studies, and the variations showed no significant difference in the away-side charged-hadron yields.
The correlation functions represent the number of associated charged hadrons (N assoc ) per trigger particle, (1/N trig )(dN assoc / d φ), as a function of φ, where N trig is the number of trigger particles. The yield is integrated over η = 2, with no correction applied for the particle-pair acceptance in η. In Fig. 1, a sample of the azimuthal correlation functions for γ rich -and π 0 rich -triggered associated charged hadrons, for different p assoc T ranges, is shown for the 12% most central Au+Au and minimum-bias p + p collisions. In the lower p assoc T bins, the uncorrelated background (shown in Fig. 1 as dashed curves) is higher than that in higher p assoc T bins, especially in Au+Au collisions, whereas in p + p collisions, this uncorrelated background is small in all p assoc T bins.
On the near-side ( φ ∼ 0) the π 0 rich -triggered correlated yields are larger than those for γ rich triggers, as expected. The non-zero near-side γ rich -triggered yields are due to the background in the γ rich trigger sample and are used to determine the amount of background, as further discussed below. In the higher p assoc T range, it is also observed that the away-side ( φ ∼ π ) γ rich -triggered yields are smaller than those of the π 0 rich triggers, which can be understood since the π 0 triggers originate from the fragmentation of partons generally having a higher energy than the corresponding direct-photon triggers.
The background subtraction and the pair-acceptance correction The v trig 2 ( v assoc 2 ) is the average value of the second-order flow coefficient [26] of the trigger (associated) particle at the mean The trigger-associated charged-hadron yields are determined from the azimuthal correlation functions, per trigger particle (π 0 rich and γ rich samples), per φ, both on the near side ( φ ∼ 0) and the away side ( φ ∼ π ). In this analysis, the near-side and away-side yields are extracted by integrating the correlation functions, for given z T bins, over | φ| ≤ 1.4 and | φ − π| ≤ 1.4, respectively. The raw near-side and away-side associated chargedhadron yields are corrected for the associated-particle efficiencies determined by embedding simulated charged hadrons into real events. The average tracking efficiencies for charged hadrons (with p assoc T > 1.2 GeV/c) are determined via detector simulations to be around 70% and 90% for central Au+Au and minimum-bias p + p collisions, respectively. The π 0 -triggered yields are calculated from the π 0 rich -triggered correlation functions, with no further correction for the contamination in the trigger sample, because of the high purity in the π 0 rich sample.
Away-side charged-hadron yields for γ dir triggers are determined by assuming zero near-side yield for γ dir triggers, and using the following expression Here Y away γ rich +h (Y away π 0 rich +h ) represents the away-side yield of γ rich (π 0 rich ), and R is given by the ratio of the near-side yield in the γ rich -triggered correlation function to the near-side yield in the π 0 rich -triggered correlation function. This means where N γ dir (N γ rich ) is the number of γ dir (γ rich ) triggers. The values of 1 − R, representing the fractions of signal in the γ rich trigger sample, are found to be 40% and 70% for p + p and the central Au+Au collisions, respectively. Using this technique, almost all sources of background (including photons from asymmetric hadron decays and fragmentation photons) can be removed, assuming that their correlations are similar to those for π 0 triggers. This assumption was tested using PYTHIA simulations, with decay photons as the trigger particles, and it was found to be valid to within at least 15% (the statistical precision of the PYTHIA study).
Systematic uncertainties include the effects of track-quality selection criteria, neutral-cluster selection criteria, π 0 /γ discrimination (TSP) cuts for the π 0 rich and γ rich samples, the size of the ZYA1 normalization region, the v 2 uncertainty range, and the yieldintegration windows. All of these sources of uncertainty are evaluated for each data point individually. For groups of sources that are not independent, such as different yield-extraction conditions, the maximum deviation among the different conditions is taken as the contribution to the systematic error. The systematic uncertainties from sources that are considered to be independent are added in quadrature. The π 0 /γ discrimination uncertainty dominates in most z T bins, varying between 10 and 25%. The track-quality selection criteria typically contributes a 5-10% uncertainty. In the lowest z T bin in Au+Au collisions for π 0 triggers, the yield extraction uncertainty dominates with as much as 50% uncertainty in the near-side yield. The variation of the p T threshold for the track-rejection cut for the neutral-tower trigger selection typically has a negligible effect.

Results and discussion
In this measurement, both π 0 and γ dir triggers are required to be within a range of 12 < p trig T < 20 GeV/c, or 8 < p trig T < 20 GeV/c for the study of the p trig T dependence. In contrast to a γ dir trigger, a π 0 trigger carries a fraction of the initial parton energy of the hard-scattered parton. In this case, the z T for a trigger+associated-particle pair is only a loose approximation of the fractional parton energy carried by the jet constituent. The integrated away-side and near-side charged-hadron yields per π 0 trigger, D(z T ), are plotted as a function of z T , both for Au+Au (0-12% centrality) and p + p collisions, in Fig. 2. Yields of the away-side associated charged hadrons are suppressed, in Au+Au relative to p + p, at all z T except in the low z T region. On the other hand, no suppression is observed on the near-side in Au+Au, relative to p + p collisions, due to the surface bias imposed by triggering on a high-p T π 0 . Fig. 3 shows the away-side D(z T ) for γ dir triggers, as extracted from Eq. (1), as a function of z T for central Au+Au and minimumbias p + p collisions. The π 0 -triggered away-side charged-hadron yields cannot be directly compared to those of γ dir triggers, as the π 0 trigger is a fragment of a higher energy parton. One can approximate the fraction of additional energy by integrating z T times a fit to the near-side D(z T ) distribution, measured in p + p collisions, over all z T (z T = 0 → ∞). The value of that fraction is where p jet-charged T is equal to the p trig T plus the total p T carried by the near-side associated charged hadrons. This is consistent with what is obtained when applying the same analysis on π 0 -triggered charged-hadron correlations from a PYTHIA simulation. In PYTHIA, the neutral associated energy can also be accounted for, giving us an estimate of the fractional energy carried by the π 0 trigger, when accounting for all associated particles (charged and neutral), Since z corr T represents the fractional momentum of the jet carried by the associated particles, it is (to the extent that the p γ T is a good approximation of the initial p T of the recoil parton) equivalent to the z T measured when using γ dir triggers. D(z corr T ) is directly compared to the fragmentation function measured via direct-photon triggers in Fig. 4 and shows reasonable agreement.
In order to quantify the medium modification for γ dir -and π 0 -triggered recoil jet production as a function of z T , the ratio, defined as of the per-trigger conditional yields in Au+Au to those in p + p collisions is calculated. In the absence of medium modifications, I A A is expected to be equal to unity. Fig. 5 shows the away-side medium modification factor for π 0 triggers (I π 0 A A ) and γ dir triggers Theoretical model predictions, labeled as Qin [27] and ZOWW [15,28], using the same kinematic coverage for γ dir triggered awayside charged-hadron yields, are compared to the data. In the model by Qin et al., the energy loss mechanism is incorporated into a thermalized medium for Au+Au collisions with impact parameters of 0-2.4 fm by using a full (3+1)-hydrodynamic evolution model description. Although this model also includes jet-medium photons (photons coming from the interaction of hard partons with the medium [29,30]) and fragmentation photons (photons radiating from hard partons [30]), both of these contribute to I γ dir A A mainly at high z T and thus do not affect our comparison at low to mid z T . The vertical lines represent statistical error and the vertical extent of the boxes represents systematic errors. The curves represent theoretical model predictions [15,17,27,28].
The calculation by ZOWW also incorporates the parameterized parton energy loss into a bulk-medium evolution [28]. It does not include fragmentation or jet-medium photons, and also describes the experimental measurement of I γ dir A A as a function of z T for the top central Au+Au collisions. The calculated I π 0 A A (also by ZOWW) shows a somewhat larger suppression than the I γ dir A A at low z T . The difference at low z T between the I γ dir A A and the I π 0 A A (as calculated by ZOWW) is likely due to the color factor effect and the differences in average path lengths between π 0 triggers and γ dir triggers. The calculated difference in the suppression is approximately 50% at z T = 0.1. The data are not sensitive to this difference within the measured uncertainties. These models (Qin and ZOWW) do not include a redistribution of the lost energy to the lower p T jet fragments, in contrast to the YaJEM model [17]. The YaJEM model is also shown in Fig. 5, although for a somewhat lower trigger p T range of 9-12 GeV/c. It predicts I γ dir A A = 1 at z T = 0.2 (corresponding to p assoc T ∼ 1.8 GeV/c) and rising well above 1 in the z T range of 0.1-0.2 [17]. This is calculated with a small integration window of π/5 around φ = π . Although this calculation has a different p trig T cut, such a large rise is not observed in our data. In contrast to the other calculations shown (Qin and ZOWW), the rise in I γ dir A A at low z T in YaJEM is predominantly due to the redistribution of lost energy. In this picture, the inmedium shower is modified by the medium and a suppression at high z T results in an enhancement at lower z T . The authors compare the "medium-modified shower" picture to an "energy loss" picture, where the energy is carried through the medium by a single parton, and the lost energy would only show up at extremely low energies and large angles. In such a picture, they argue that the rise in I γ dir A A at low z T would be more modest and I γ dir A A would remain less than 1.
Because PHENIX has reported an enhancement at low z T (z T < 0.4) in I γ dir A A at large angles [11], it is interesting to compare our results over the full integration window of | φ − π| < 1.4 radians to an I γ dir A A calculated with a smaller window of | φ − π| < 0.6 radians in Fig. 6. Within our uncertainties, an enhancement effect is only seen in the lowest z T bin for π 0 triggers. However, for the PHENIX measurement, z T < 0.4 corresponds to lower p T for the associated hadrons ( 2 GeV/c), since the p γ T was chosen in the range of 5-9 GeV/c. In our analysis, associated hadrons with p T < 2 GeV/c are only present at z T < 0.2. The apparent inconsistency between STAR and PHENIX, when investigating the recovery of the lost energy as a function of z T , indicates that p assoc T may be the more pertinent variable. The conclusion is that the "modified | φ − π | < 1.4 radians over that of | φ − π | < 0.6 radians for γ dir − h ± (left panel) and π 0 − h ± (right panel), are plotted as a function of z T for Au+Au at 0-12% central collisions. The vertical lines represent statistical error bars and boxes represent systematic errors. Since this is a ratio of yields for two overlapping angular windows, much of the uncertainties cancel; and only the surviving uncertainties are shown. fragmentation function" (constructed from the in-medium jet-like yields as a function of z T ) is not universal. In particular, the lost energy is not recovered at a fixed range of z T , but perhaps at a given range of p assoc T . The conclusion that the lost energy is recovered at larger angles only for p T < 2 GeV/c, regardless of the trigger energy, is consistent with the conclusion of the STAR paper on jet-hadron correlations [18].
The earlier measurements [12] at low trigger energy (8 < . Both model predictions shown [15,27], which do not include the redistribution of lost energy, are in agreement with the data.

Summary
In summary, in order to understand the medium modification of partons in the QGP, away-side charged-hadron yields for γ dir and π 0 triggers in central (0-12%) Au+Au collisions are compared with those in minimum-bias p + p collisions. Both I π 0 A A and I γ dir A A show similar levels of suppression, with the expected differences due to the color-factor effect and the path-length dependence not manifesting themselves within experimental uncertainties. At low z T and low p assoc T , the data are consistent with less suppression than at higher p assoc T . The suppression shows little difference for integration windows of ± 0.6 vs. ± 1.4 radians around φ = π , with an enhancement at large angles observed only for z T < 0.2 (p assoc T < 2.4 GeV/c) for π 0 triggers. There is no triggerenergy dependence observed in the suppression of γ dir -triggered yields, suggesting little dependence for energy loss on the initial parton energy, in the range of p trig T = 8-20 GeV/c. The data are consistent with model calculations [15,27,28], in which the suppression is caused by parton energy loss in a thermalized medium. These calculations do not include redistribution of energy within the shower. The very large I γ dir A A at low z T predicted by models of in-medium shower modification (including energy redistribution) [17] is not observed for p trig T > 12 GeV/c. This is in contrast to the PHENIX result [11], where the I γ dir A A exceeds unity, for p trig T 5-9 GeV/c. However, it is not clear that the redistribution of lost energy would scale with the jet energy. In fact, our studies support previous conclusions that the lost energy reappears predominantly at low p T (approximately p T < 2 GeV/c), regardless of the trigger p T . This leads to the important conclusion that the modified fragmentation function is not universal (i.e. it does not have the same z T dependence for all trigger p T ).