Study of jet quenching with isolated-photon + jet correlations in PbPb and pp collisions at

Measurements of azimuthal angle and transverse momentum ( p T ) correlations of isolated photons and associated jets are reported for pp and PbPb collisions at √ s NN = 5 . 02 TeV. The data were recorded with the CMS detector at the CERN LHC. For events containing a leading isolated photon with p γ T > 40 GeV / c and an associated jet with p jetT > 30 GeV / c , the photon + jet azimuthal correlation and p T imbalance in PbPb collisions are studied as functions of collision centrality and p γ T . The results are compared to pp reference data collected at the same collision energy and to predictions from several theoretical models for parton energy loss. No evidence of broadening of the photon + jet azimuthal correlations is observed, while the ratio p jetT / p γ T decreases signiﬁcantly for PbPb data relative to the pp reference. All models considered agree within uncertainties with the data. The number of associated jets per photon with p γ T > 80 GeV / c is observed to be shifted towards lower p jetT values in central PbPb collisions compared to pp collisions.

Since electroweak bosons do not interact strongly with the QGP [23][24][25][26], measurements of jets produced in the same hard scattering in conjunction with these bosons have, in contrast to dijet measurements, a controlled configuration of the initial hard scattering [27][28][29]. The electroweak boson p T reflects, on average, the initial energy of the associated parton that fragments into the jet, before any medium-induced energy loss has occurred [30,31].
At LHC energies, the production of jets with p T > 30 GeV/c that are associated with electroweak bosons is dominated by quark E-mail address: cms -publication -committee -chair @cern .ch. fragmentation [32]. Hence, the study of correlations in boson-jet events, such as the azimuthal angle (φ) difference and p T ratio between the boson and the associated jets, opens the possibility for in-depth studies of the parton energy loss mechanisms utilizing theoretically well-controlled initial production processes. These studies also facilitate the extraction of QGP properties via comparisons with theoretical models [31, [33][34][35][36][37]. Measurements of this kind were first performed in PbPb collisions at a nucleon-nucleon center-of-mass energy √ s NN = 2.76 TeV with isolated-photon+jet events [38] and at 5.02 TeV with Z-jet events [39] by the CMS Collaboration at the CERN LHC. The precision of these previous measurements was limited by the available number of boson-jet pairs. In the results reported in this paper, the electroweak boson is an isolated photon, which is selected experimentally by using an isolation requirement, namely that the additional energy in a cone of fixed radius around the direction of the reconstructed photon is less than a specified value [23,24]. This restriction suppresses the background contributions from photons originating from decays of neutral mesons ("decay photons"), and gives a sample containing mostly prompt photons. Prompt photons are photons produced directly in the hard scattering process, or emitted in the fragmentation of a high-p T parton ("fragmentation photons"). This Letter reports the measurement of correlations of isolated photons and associated jets in PbPb and pp collisions at PbPb and pp data samples were collected by the CMS experiment in 2015 and correspond to integrated luminosities of 404 μb −1 and 27.4 pb −1 , respectively. The measurement characterizes parton energy loss through the φ and p T correlations between isolated photons and the associated jets. The azimuthal angle difference φ jγ = |φ jet − φ γ |, the p T ratio x jγ = p jet T /p γ T and its average x jγ , the average number of associated jets per photon, R jγ , and the ratio of the yield of associated jets in PbPb data to pp data, I jet AA , are presented. The results from PbPb collisions are compared to those from pp collisions, with the pp data serving as a reference to extract information about the modifications due to the presence of the QGP.

The CMS detector
The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the solenoid volume are a silicon pixel and strip tracker which measures charged particles within the pseudorapidity range |η| < 2.5, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections.
The barrel and endcap calorimeters provide |η| coverage out to 3.
Photon candidates used in this analysis are reconstructed using the energy deposited in the barrel region of the ECAL, which covers a range of |η| < 1.48. Hadron forward (HF) calorimeters extend the |η| coverage of the HCAL to |η| = 5.2. In PbPb collisions, the HF calorimeters are used to determine the centrality of the collisions, which is related to the impact parameter of the two colliding Pb nuclei [16], and the azimuthal angle of maximum particle density (the event plane) [40]. Muons are detected in gas-ionization chambers embedded in the steel flux-return yoke outside the solenoid. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [41].

Event selection
Events containing high-p T photon candidates are selected by the CMS trigger system, which consists of a level-1 (L1) and a highlevel trigger (HLT) [42]. Events are first selected by requiring an ECAL transverse energy deposit larger than 21 (20) GeV during the PbPb (pp) data-taking period. Photon candidates are then reconstructed at the HLT using the "island" clustering algorithm [24,43], which is applied to energy deposits in the ECAL. The HLT selection efficiency was determined in data and was found to be greater than 98% for events containing a photon with p γ T > 40 GeV/c and |η γ | < 1.44 reconstructed offline. The η γ interval of the photons used in this analysis is restricted to the barrel region of the ECAL, which has the best performance in terms of photon reconstruction and triggering and has the lowest rate of misreconstructed tracks.
A pure sample of inelastic hadronic pp and PbPb collisions is obtained with further offline selection criteria applied to the triggered events [16,44]. Notable among these, a reconstructed event vertex and at least three (one) calorimeter towers in the HF on each side of the interaction point with energy >3 GeV are (is) required in the PbPb (pp) analysis. Events with spurious energy depositions in the HCAL (i.e., sporadic uncharacteristic noise and signals from malfunctioning calorimeter channels) are rejected by established algorithms that flag such events, to remove possible contamination of the jet sample [45]. Events with multiple collisions have a negligible effect on the measurement since the aver-age number of collisions per bunch crossing is around 0.9 for pp collisions, and less than 0.01 for PbPb collisions.
In PbPb collisions, the centrality measurement is based on percentiles of the distribution of the total energy measured in both HF calorimeters. The event centrality observable corresponds to the fraction of the total inelastic hadronic cross section, starting at 0% for the most central collisions, i.e., those with the smallest impact parameter and the largest nuclear overlap [16].

Jet reconstruction
Offline jet reconstruction is performed using the CMS particleflow (PF) algorithm [46]. By combining information from all subdetector systems, the PF algorithm identifies final-state particles in an event, classifying them as electrons, muons, photons, charged hadrons, or neutral hadrons. To form jets, these PF objects are clustered using the anti-k T sequential recombination algorithm provided in the FastJet framework [47,48]. A small jet radius parameter of R = 0.3 is chosen to minimize the effects of heavy ion background fluctuations (∼ 10 GeV in central PbPb collisions) and for consistency with the previous measurement at 2.76 TeV [38].
For the PbPb data, the underlying background from soft collisions (i.e., the underlying event, UE) is subtracted during jet reconstruction by employing the iterative algorithm described in Ref.
[49], using the same implementation as in the PbPb analysis of Ref. [16]. In pp collisions, jets are reconstructed without UE subtraction. For pp and PbPb samples, the reconstructed jet energies are corrected to the energies of final-state particle jets using a factorized multistep approach [50]. The corrections are derived using simulated dijet and photon+jet events generated with the pythia 8.212 [51] (CUETP8M1 tune [52]) Monte Carlo (MC) event generator which, for the case of PbPb corrections, are embedded into a simulated underlying background event from hydjet 1.9 [53]. The background simulation is tuned to reproduce the observed charged-particle multiplicity and p T spectrum in PbPb data.
Reconstructed jets are required to have |η jet | < 1.6 and corrected p jet T > 30 GeV/c, to ensure that the jet reconstruction efficiency and energy resolution (JER) are well understood, i.e., results from data are in agreement with expectations from MC.

Photon reconstruction
Photon candidates are reconstructed from clusters of energy deposited in the ECAL. The "hybrid" algorithm used for the analysis in pp collisions is detailed in Ref. [43], while the description of the island clustering algorithm optimized for high-multiplicity PbPb collisions can be found in Ref. [24].
In order to reduce electron contamination, photon candidates are discarded if the differences in pseudorapidity and azimuthal angle between the photon candidate and any electron candidate track with p T > 10 GeV/c are less than 0.02 and 0.15 radians, respectively [24]. These matching windows are conservative choices based on the detector angular resolution. The relatively large azimuthal angle window allows for the curvature of the electron trajectories. Anomalous signals caused by the interaction of highly ionizing particles directly with the silicon avalanche photodiodes used for the ECAL barrel readout are removed using the prescription given in Ref. [24]. The energy of the reconstructed photons is corrected to account for the effects of the material in front of the ECAL and for the incomplete containment of the shower energy. For PbPb data, an additional correction is applied to account for energy contamination from the UE. The magnitude of the combined energy correction for isolated photons varies from 0 to 10%, depending on the centrality of the collision and p γ T . The cor- Similar to Ref.
[54], a generator-level photon candidate is considered isolated if the p T sum of final-state generated particles, excluding neutrinos, in a cone of radius R = ( η) 2 + ( φ) 2 = 0.4 around the direction of the candidate, SumIso, is less than 5 GeV/c. For a reconstructed photon candidate, the corresponding isolation variable, SumIso UE−sub , is calculated with respect to the centroid of the cluster, not including the p T of the cluster and after correcting for the UE (only in PbPb collisions), and is required to be less than 1 GeV/c. The isolation criterion for reconstructed photons is tighter than for generated photons to minimize the impact of UE fluctuations in PbPb collisions, where a downward fluctuation in the UE could inadvertently allow a nonisolated photon candidate to pass the isolation criteria. A systematic uncertainty is assigned to account for the effect of this difference on the final observables, as detailed in Section 3.5.
Imposing the isolation requirement suppresses the background contributions from fragmentation and decay photons, resulting in a sample enriched in isolated prompt photons. The dominant remaining backgrounds for isolated photon candidates are ECAL showers initiated by isolated hadrons, and real photons that are decay products of isolated neutral mesons, e.g., π 0 , η, and ω. The hadron-induced showers are rejected using the ratio of HCAL over ECAL energy inside a cone of radius R = 0.15 around the photon candidate, H/E. Only photon candidates with H/E < 0.1 are selected for this analysis. The decay photons can be significantly reduced using a cut on the shower shape, a measure of how energy deposited in the ECAL is distributed in φ and η [54], as discussed in Section 3.4. The efficiencies of these criteria in selecting photons are extracted from simulations as a function of p γ T and corrected for in collision data.

Photon+jet pair selection
To form photon+jet pairs, the highest p T isolated photon candidate that passes the selection criteria is paired with all jets in the same event. The combinatorial background in PbPb collisions, which includes misidentified jets that arise from UE fluctuations, as well as jets from multiple hard parton-parton scatterings in the same collision, needs to be subtracted in order to study the energy loss effects on the jets produced in the same hard scattering as the photon. This background subtraction is performed by correlating each leading isolated photon candidate with reconstructed jets found in 40 different events, randomly selected from minimum bias PbPb data such that the event centrality, the interaction vertex position along the beam axis, and the event plane, are within 5%, 5 cm, and π/10, respectively, of those from the signal event. The values were optimized such that the statistical uncertainty due to the subtraction is negligible compared to the statistical uncertainty of the photon sample.
The background contribution from pairs of decay photons and jets is subtracted with a procedure based on collision data, using a two-component template fit of the electromagnetic shower shape variable σ ηη , which is defined as a modified second moment of the ECAL energy cluster distribution around its mean η position [54, 55]: where E i and η i are the energy deposit and η of the ith ECAL crystal within a 5×5 crystal array centered around the electromagnetic cluster, and E 5×5 and η 5×5 are the total energy and mean η of the 5×5 crystal matrix, respectively. The shape of the signal distribution is obtained from pythia+hydjet simulations of isolated prompt photon+jet processes, while the background templates are obtained from a nonisolated sideband region in data, 10 < SumIso UE−sub < 20 GeV/c. The purity of the photon sample (fraction of prompt photons within the remaining collection of candidates) is determined from the fit. Examples of the template fits are shown in Fig. 1 for the lowest p γ T photons and the four centrality intervals used in this analysis. The purity decreases in more central collisions, reflecting an increase in the backgrounds.
The yields and kinematic characteristics of the background arising from pairs of decay photons and jets are estimated by analyzing events with a larger photon shower width (0.011 < σ ηη < 0.017), which are dominated by decay photons. The background contribution fraction is then subtracted from the yield for the signal events, which have a smaller photon shower width (σ ηη < 0.01), according to the purity obtained from the template fits.
The detector response for low-p T jets can exhibit significant nonlinearity and biases because of the background subtraction procedure of the current jet algorithm, as well as the high magnetic field of the CMS detector. This is neither well-modeled nor well-understood. Hence, the distributions are not unfolded for the detector resolution, but the approach instead is to smear, i.e., convolve with a Gaussian resolution adjustment term, the jet energy in pp events to match the JER in each of the PbPb centrality classes in which the comparison is made. This is done in every figure ex- is the generator-level jet p T without any contributions from a PbPb UE. For PbPb (pp) collisions, the JER is calculated from pythia+hydjet (pythia) events that are Table 1 Jet resolution parameters for pp and PbPb collisions. A global uncertainty of 7% is assigned to the smearing parameters, evaluated as described in text. hydjet with Geant4 simulation has been compared to data by observing the energy collected inside randomly oriented cones with the same radius as the distance parameter of the jet algorithm. The MC simulation is found to be in good agreement with the experimental results. The JER is parametrized using the expression The stochastic term S describes the p T dependence of the jet energy resolution, the constant term C represents the high-p T limit of the resolution, and the noise term N reflects the effect of UE fluctuations on the energy resolution. All parameters for σ (p gen T ) are determined using pythia and pythia+hydjet samples with their numerical values provided in Table 1. Following the smearing to 0-30% PbPb data, the energy resolutions of jets with p jet T = 30(60) GeV/c measured in pp data changes from 18%(14%) to 35%(22%) respectively. Compared to the JER, the jet φ resolution has a negligible effect.

Systematic uncertainties
Systematic uncertainties are estimated separately for the pp and PbPb analyses. The uncertainties are determined for each centrality and p γ T interval using similar procedures as described in Ref. [38]. Seven sources of uncertainty are considered: photon purity, isolation definition, photon energy scale, electron contamination, photon efficiency, JER, and jet energy scale (JES). The total systematic uncertainties are calculated by summing in quadrature the uncertainties from all sources.
The uncertainty on the photon purity estimate is evaluated by varying the nonisolated sideband regions used to obtain the background template. The maximum deviation from the nominal values is ±10% (±6%) for central (peripheral) PbPb collisions, and ±5% in pp collisions. The varied purity values are then used to perform the background subtraction, and the maximum difference from the nominal results is quoted as the uncertainty. The uncertainty due to the isolated photon definition is determined by comparing the photon+jet observables when using generator-level and detectorlevel definitions of the isolation variables. The photon energy scale uncertainty is based on the residual data-to-simulation photon energy scale difference after applying the photon energy corrections, amounting to about 1%, independent of p γ T and event centrality. The uncertainty due to electron contamination is evaluated by repeating the analysis without applying electron rejection, and scaling the difference in the final observables to the residual electron contamination after applying electron rejection. The electron rejection efficiency is determined to be 66% from MC studies. The uncertainty on the photon efficiency correction is determined by varying the selection criteria for matching reconstructed photons with generator-level photons. The uncertainty on the JER has two sources. The first source is the difference between the JER in data and simulation, which is around 15% for all centralities in both pp and PbPb collisions. The associated systematic uncertainty is evaluated by propagating the effects of having a JER that differs by 15% relative to the nominal value. The second source (7%) accounts for the uncertainty in the resolution and the modeling of the JER distributions, and was obtained by considering the differences between the extracted JER in each p gen T bin and the parametrization using Eq. (2), and determining the value at one standard deviation of that distribution, assuming that the differences are normally distributed.
Finally, the JES uncertainty arises from three contributions that are added in quadrature for the final value. Two are common to both the pp and PbPb samples: the residual deviation from unity in simulation (i.e., the closure) of the JES after applying all jet energy corrections (2%) and the difference between data and simulation (2%). These two effects are independent of centrality and together amount to 2.8%. The closure of the JES depends on the flavor of the fragmenting parton: simulations show that the energy scale of quark jets is consistently higher than that of gluon jets. For pp collisions, the fragmentation dependence of the JES has been studied and is accounted for in the uncertainty from the difference between data and simulation. However, in PbPb collisions, the ratio of quarks and gluons can be different from pp data because of expected differences in centrality-dependent quenching of jets initiated by quarks or gluons. The subtraction of the UE in PbPb collisions results in the JES having a larger dependence on the fragmentation pattern than found for pp collisions, since one can only distinguish between soft particles from the jet fragmentation and the underlying event on average. Hence, an additional uncertainty, evaluated using collision data and simulation, is applied in PbPb collisions to account for these fragmentation effects on the JES arising from the subtraction algorithm, underlying event, and quenching. The photon-tagged jet fragmentation function in PbPb data is constructed and fit by a two-component model of the jet fragmentation functions for quark and gluon jets that were obtained from MC simulations. For p γ T > 60 GeV/c, the results show that the fraction of jets originating from gluon fragmentation in data can be constrained to between 0% and approximately 26%, which corresponds to the fraction found in pythia+hydjet MC samples. Hence, in this kinematic region, the difference between the JES for a pure quark jet sample and the inclusive sample is used in the uncertainty estimation.
For 40 < p γ T < 60 GeV/c, where the results of the template fit are inconclusive because of the large statistical uncertainties, the full difference in the JES between having 0% and 100% gluon jet fraction is used. This difference is approximately 2-5% (1.5-2.5%) in central (peripheral) collisions. The final systematic uncertainty associated with the unknown quark-gluon ratio in data is taken as the maximum deviation from varying the JES up and down according to the quark-gluon ratio constraints mentioned above for each p γ T interval.
A summary of the systematic uncertainties for R jγ , x jγ , and φ jγ in PbPb collisions is shown in Tables 2 and 3, averaged over multiple p γ T and/or event centrality intervals. The dominant sources of uncertainties in both pp and PbPb collisions are from JES and photon purity estimation. The systematic uncertainties for PbPb and pp collisions are considered uncorrelated.

Photon+jet azimuthal correlation
Possible modification of the back-to-back photon and recoiling jet alignment by the medium can be studied by comparing  the relative azimuthal angle ( φ jγ ) distributions in pp and PbPb collisions [16,17]. The distributions are normalized by the number of photon+jet pairs. The shape of the φ jγ distribution in pp and PbPb collisions is studied in intervals of leading photon p T and two event centrality classes, as shown in Fig. 2. The exponentially falling region ( φ jγ > 2π /3) is fit to a normalized exponential function, as in Ref. [38], and the values of the exponents in PbPb and pp collisions from the fits are compared. Within the quoted statistical and systematic uncertainties, the PbPb results with different photon p T and event centrality selections are consistent with the corresponding smeared pp reference data, i.e., no broadening of the distributions is observed.

Photon+jet transverse momentum imbalance
The asymmetry ratio x jγ = p jet T /p γ T is used to quantify the photon+jet p T imbalance due to in-medium parton energy loss.
In addition to the photon and jet selections used in the φ jγ study, a φ jγ > (7π )/8 selection is applied to select back-to-back photon+jet topologies, suppressing the contributions from background jets as well as photon-multijet events. Fig. 3 shows the x jγ distributions for different centrality and p γ T regions in pp and PbPb collisions, normalized by the number of photons. In 0-30% centrality PbPb collisions, significant modifications (lower mean and smaller integral values) of the x jγ spectra with respect to the smeared pp reference data are observed, while the modifications are smaller in the 30-100% centrality PbPb collisions.
The mean values, x jγ (in effect, a truncated mean because of the p jet T threshold), of the x jγ distributions are shown as a function of p γ T in Fig. 4 (top). The x jγ values in PbPb and smeared pp collisions are consistent with each other within the quoted uncertainties over the whole p γ T interval probed in 30-100% centrality PbPb collisions and in the region p γ T < 60 GeV/c for 0-30%  centrality PbPb collisions. At higher p γ T in the more central PbPb events, the x jγ value is lower than in pp data.
With a jet p T threshold of 30 GeV/c, the x jγ values observed for the selected photon+jet pairs likely underestimates the actual imbalance. Photon+jet pairs for which the momentum of the associated jets falls below the jet p T threshold do not contribute to the x jγ value. To assess how the "missing" jets might affect the x jγ results, the average number of associated jets per photon passing the analysis selections, R jγ , is shown in Fig. 4 (bottom). In the 0-30% most central PbPb collisions, the value of R jγ is found to be lower than in the smeared pp data in all leading photon p T intervals. The absolute difference is approximately constant as a function of p γ T , but the relative difference is larger at lower p γ T , since the R jγ in pp collisions is itself lower in that region.

Centrality dependence
The centrality dependence in PbPb collisions of x jγ spectra for p γ T > 60 GeV/c is shown in Fig. 6. In the most peripheral collisions (50-100% centrality), the x jγ distribution agrees with the smeared pp reference data. As collisions become more central, the PbPb distributions shift towards lower x jγ and the integrals of the x jγ spectra become smaller. This is consistent with the expectation that a larger amount of parton p T is transported out of the jet cone as a consequence of the larger average path length that the parton needs to travel through in more central PbPb collisions [57,58]. Fig. 7 shows x jγ and R jγ in pp and PbPb collisions as a function of event centrality, quantified by N part , which is the mean number of participating nucleons within a given centrality interval. The N part values are estimated from a MC Glauber model [15,59]. In central collisions, a suppression of both x jγ and R jγ is observed in comparison to the smeared pp reference data, con-   sistent with significant in-medium energy loss of the associated jets.

Comparison to theoretical models
The results for PbPb collisions presented in Fig. 2 for φ jγ and  Fig. 10. The jewel model is a dynamical, perturbative framework for jet quenching, which has been extended to simulate boson-jet events [37,60]. The LBT 2017 model [34] uses a linearized Boltzmann transport model for jet propagation through the medium, including the recoiled medium partons in the reconstruction of the partonic jets. The hybrid model [35,36] combines a perturbative description of the weakly coupled physics of jet production and evolution with a gauge/gravity duality description of the strongly coupled dynamics of the medium, and of the soft exchanges between the jet and the medium. The calculations from the jewel and hybrid models have been smeared to the corresponding JER in pp or PbPb collisions.
Predictions from the jewel and hybrid models have previously shown reasonable agreement with measurements of inclusive jet nuclear modification factors [36,61]. For the results reported in this Letter, all models describe well the pp results. They also capture the general features of the 0-30% PbPb data, although the hybrid model appears to better describe the x jγ results. As shown in Fig. 9, the jewel and LBT models appear to underestimate the x jγ spectra in the high x jγ region (x jγ > 0.9) for central PbPb col-   lisions, which suggests that the amount of energy transported out of the jet cone is larger in these models than in data. A similar effect is also hinted at in the 30-100% PbPb data, which can be attributed to the fact that those distributions are dominated by events in the 30-50% centrality interval, where energy loss effects are still significant. The models are also consistent with data in that none of them show a broadening of the observed φ jγ distributions in PbPb compared to pp collisions in the photon and jet kinematic ranges presented, despite their implementing contributions from partonic collisions.

Summary
Correlations of isolated photons with transverse momentum p γ T > 40 GeV/c and pseudorapidity |η γ | < 1. 44  from various theoretical models. The better statistical precision of the new higher energy data provides an opportunity to test theoretical models against data over a wide kinematic range in p γ T and x jγ , and for different event centralities, using a selection of partons with defined flavor (quark/gluon) and initial kinematics.

Acknowledgements
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centers and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.