Measurement of charged jet suppression in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV

A measurement of the transverse momentum spectra of jets in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV is reported. Jets are reconstructed from charged particles using the anti-$k_{\rm T}$ jet algorithm with jet resolution parameters $R$ of $0.2$ and $0.3$ in pseudo-rapidity $|\eta|<0.5$. The transverse momentum $p_{\rm T}$ of charged particles is measured down to $0.15$ GeV/$c$ which gives access to the low $p_{\rm T}$ fragments of the jet. Jets found in heavy-ion collisions are corrected event-by-event for average background density and on an inclusive basis (via unfolding) for residual background fluctuations and detector effects. A strong suppression of jet production in central events with respect to peripheral events is observed. The suppression is found to be similar to the suppression of charged hadrons, which suggests that substantial energy is radiated at angles larger than the jet resolution parameter $R=0.3$ considered in the analysis. The fragmentation bias introduced by selecting jets with a high $p_{\rm T}$ leading particle, which rejects jets with a soft fragmentation pattern, has a similar effect on the jet yield for central and peripheral events. The ratio of jet spectra with $R=0.2$ and $R=0.3$ is found to be similar in Pb-Pb and simulated PYTHIA pp events, indicating no strong broadening of the radial jet structure in the reconstructed jets with $R<0.3$.


Introduction
Discrete formulations of Quantum Chromodynamics (lattice QCD) predict a phase transition to a new state of matter, the Quark-Gluon Plasma (QGP), at an energy density above a critical value of about 1 GeV/fm 3 and temperatures beyond T C ≈ 160 MeV [1,2].In this state, the elementary constituents of hadronic matter, quarks and gluons, are deconfined and chiral symmetry is expected to be restored.The conditions to create a QGP are expected to be reached for a short time (few fm/c) in the overlap region of heavy nuclei colliding at high energy.
One of the tools to study the properties of the QGP is provided by hard (large momentum transfer Q 2 ) scattering processes of the partonic constituents of the colliding nucleons.These hard scatterings occur early in the collision (≪ 1 fm/c) and the outgoing partons propagate through the expanding hot and dense medium and fragment into jets of hadrons.Jet fragmentation in heavy-ion collisions is expected to be modified (relative to the parton fragmentation in the vacuum) due to parton-medium interactions, e.g.radiative and collisional parton energy loss (jet quenching) [3,4].The initial hard parton production cross sections are calculable using perturbative QCD (pQCD) and the non-perturbative vacuum fragmentation process can be well calibrated via jet measurements in elementary collisions.Jet quenching has been observed at RHIC [5][6][7][8][9][10] and at the LHC [11][12][13][14][15][16][17] via the measurement of high-p T inclusive hadron and jet production, di-hadron angular correlations and the energy imbalance of reconstructed dijets, which are observed to be strongly suppressed and modified, respectively, in central AA collisions compared to a pp (vacuum) reference.Single particle measurements provide limited information on the initial parton energy and its radiation.Jet reconstruction allows more direct access to the parton energies, which can be calculated using pQCD, by integrating over the hadronic degrees of freedom in a collinear and infrared safe way.Jets are reconstructed by grouping the detected particles within a given angular region, e.g. a cone with radius R. The interaction with the medium can result in a broadening of the jet profile with respect to vacuum fragmentation.In this case, for a given jet resolution parameter R and a fixed initial parton energy, the energy of the jet reconstructed in heavy-ion collisions will be smaller than in vacuum.In the case where the gluons are radiated inside the cone, the jet is expected to have a softer fragmentation and a modified density profile compared to jets in vacuum.
Jet measurements in heavy-ion collisions employ various approaches to correct for background energy not associated with jet production and to suppress the combinatorial, false jet yield induced by fluctuations of this background, e.g.via energy or momentum thresholds for particles that are used in the jet finding process.Every approach represents a compromise between potential fragmentation biases in the jet reconstruction and a better separation of the jet signal from the background.
In this article a measurement of the inclusive jet p T spectrum in Pb-Pb collisions at √ s NN = 2.76 TeV is reported in four centrality intervals in the most central 80% of the total hadronic cross-section.Jets are clustered from charged tracks measured with the central barrel detectors in ALICE down to momenta of 0.15 GeV/c, which provides unique access to low p T jet fragments at mid-rapidity at the LHC.Jets are measured with resolution parameters R = 0.2 and R = 0.3 in the pseudo-rapidity interval −0.5 < η < 0.5.The underlying event is subtracted event-by-event for each measured jet.The jet spectrum is corrected for background fluctuations and detector effects affecting the jet energy resolution and scale through an unfolding procedure.
The jet reconstruction strategy and the correction procedure for background from the underlying event is discussed in detail in Section 2. The results are presented in Section 3 and discussed in Section 4.
bias events, which are selected online by requiring a signal in at least two out of the following three detectors: the forward VZERO counters (V0A and V0C) and the Silicon Pixel Detector (SPD) [19].The VZERO counters are forward scintillator detectors covering a pseudo-rapidity range of 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C); the SPD is part of the Inner Tracking System (ITS) described below.The minimum-bias trigger is fully efficient in selecting hadronic events in Pb-Pb collisions.In addition, an offline selection is applied in which the online trigger is validated and remaining background events from beam-gas and electromagnetic interactions are rejected.To ensure a high tracking efficiency for all considered events, the primary vertex was required to be within 10 cm from the center of the detector along the beam axis and within 1 cm in the transverse plane.
The number of Pb-Pb events used in this analysis after event selection is 12.8 million in a centrality range between 0 and 80% most central of the total hadronic cross section, corresponding to a total integrated luminosity of 2 µb −1 .The event sample is divided in four centrality intervals (0-10%, 10-30%, 30-50%, and 50-80%) based on the sum of VZERO amplitudes.A Glauber model is used to calculate the number of participating nucleons N part in the collisions, the number of binary collisions N coll , and the nuclear overlap function T AA [19].The resulting values and their uncertainties for the considered centrality intervals are given in Table 1.

Jet reconstruction
Jets were reconstructed using charged tracks detected in the Time Projection Chamber (TPC) [20] and the Inner Tracking System (ITS) [21] which cover the full azimuth and pseudo-rapidity |η| < 0.9.For each track traversing the TPC, up to 159 independent space points are measured at radial distances from 85 cm to 247 cm.
The ITS consists of six cylindrical silicon layers with high granularity for precision tracking, with the inner layer at 3.9 cm from the center of the detector and the outer layer at 43 cm.The measured space points in the ITS and the TPC are combined to reconstruct the tracks of charged particles.The transverse momentum is calculated from the measured track curvature in the magnetic field of B = 0.5 T.
The main track selection criteria are a minimum number of points in the TPC, a χ 2 cut on the fit, and a cut on the difference between the parameters of the track fit using all the space points in ITS and TPC, and using only the TPC space points with the primary vertex position as an additional constraint.Tracks for which the total change in the track parameters is more than 6σ (χ 2 > 36) are rejected from the sample resulting in a tracking efficiency loss of 8% for low p T tracks (p track T < 1 GeV/c) and a few percent (1-2%) for higher momentum tracks.For a large fraction (79%) of the tracks used in the analysis, at least one point was found in one of the two inner pixel tracking layers (SPD) of the ITS.To improve the azimuthal uniformity of the selected tracks, tracks without SPD points were also used in the analysis.For those tracks the momentum was determined from a track fit constrained to the primary vertex, to guarantee good momentum resolution.
The p T resolution for tracks is estimated from the track residuals of the momentum fit and does not vary significantly with centrality.All track types have a relative transverse momentum resolution of σ (p T )/p T ≃ 1% at 1 GeV/c.The resolution at p T = 50 GeV/c is σ (p T )/p T ≃ 10% for tracks that have at least three out of six reconstructed space points in the ITS.For the remaining tracks (6% of the track sample) the resolution is σ (p T )/p T ≃ 20% at 50 GeV/c.The track p T resolution is verified by cosmic muon events and the width of of the invariant mass peaks of K 0 S , Λ and Λ [22].The track finding efficiency at p T = 0.15 GeV/c is 60% increasing to ∼ 90% for p T ≃ 1.5 GeV/c and then decreases to ∼ 86% for p T ≥ 2.5 GeV/c.In peripheral events the track finding efficiency is ∼ 2% larger than in central collisions due to the lower track multiplicity.
Jets are reconstructed with the anti-k T algorithm using the FastJet package [23,24] with resolution parameters R = 0.2 and R = 0.3.Charged tracks with |η| < 0.9 and p T > 0.15 GeV/c are used as input for the jet algorithm.The transverse momentum of the jets, p raw T,ch jet , is calculated with the boost-invariant p T recombination scheme.The area, A, for each jet is determined using the active area method as implemented in FastJet [25].So-called 'ghost particles' with very small momentum (∼ 10 −100 GeV/c) are added to the event and the number of ghost particles in a jet measures the area.Ghost particles are uniformly generated over the tracking acceptance (0 < ϕ < 2π and |η| < 0.9), with 200 ghost particles per unit area.Jets used in the analysis are required to have an area larger than 0.07 for R = 0.2 jets and 0.2 for R = 0.3 jets.This selection mostly removes low momentum jets with p raw T,ch jet < 20 GeV/c.Jets are selected to have |η| < 0.5, so that they are fully contained in the tracking acceptance.In addition, jets containing a track with a reconstructed p T > 100 GeV/c are rejected from the analysis, to avoid possible contributions from tracks with poor momentum resolution (the momentum resolution is 20% for tracks with p T = 100 GeV/c).This selection has negligible effect in the reported range of jet momenta.

Background subtraction
In Pb-Pb events, the large background consisting of particles from soft scattering processes as well as fragments from other jets, is subtracted using the procedure proposed in [26,27].The background is measured on an event-by-event basis by clustering all particles using the k T -algorithm and determining the median of the transverse momentum density ρ i ch = p i T,ch jet /A i of all clusters i in the event, excluding the two leading clusters to limit the impact of the hard jet signal on the background estimate.The signal anti-k T jets are then corrected for the average background contribution using the median ρ ch : with p T,ch jet the background subtracted jet p T , p raw T,ch jet the uncorrected measured jet p T and A the area of the anti-k T signal jet.The inclusive jet distribution is then corrected via unfolding to account for background fluctuations and detector effects.
As demonstrated in [28] the measured background density ρ ch is directly related to the multiplicity and average transverse momentum of the reconstructed charged particles.Since it is based on the same collection of input particles used for the signal jets, the quantity ρ ch used in the analysis intrinsically includes all detector effects, such as tracking efficiency and momentum resolution.To enable comparisons with other experiments and generator studies, the corrected background momentum density is obtained using the Hit-Backspace-Once-More (HBOM) method proposed in [29], i.e. by repeatedly applying the parameterized detector response to the measured heavy-ion events and extrapolating the measured ρ to an ideal detector.The advantage of the method lies in the data-driven approach where only the detector response is taken from simulation.This is of particular importance when studying observables that are sensitive to the a-priori unknown structure of the heavy-ion event and the correlation between different regions in the event.This procedure yields a corrected transverse momentum density of ρ p T >0.15 ch = 155.8± 3.7 GeV/c for the 10% most central events, with a spread σ (ρ p T >0.15 ch ) = 20.5±0.4 GeV/c with no significant dependence on the distance parameter R employed in the ρ calculation.
Measurement of charged jet suppression in Pb-Pb collisions at √ s NN = 2.76 TeV 5

Background fluctuations
All particles created in a collision are clustered into jets, but not all of them originate from hard processes.The distinction between jets originating from a hard parton and soft clusters containing mostly background particles (combinatorial jets) is to some extent arbitrary and requires a pragmatic definition.At very high p T , it is clear that all jets originate from parton fragmentation processes, while at low and intermediate p T , clusters can be formed by including fragments from multiple, independent parton scatterings or even from the soft hadronization.
Jet clusters which originate from a hard scattering will contain a large amount of uncorrelated, mostly soft, background particles.The background subtraction procedure described in Section 2.3, removes the background energy on average, but the background has large region-to-region fluctuations in the event, both due to statistical fluctuations of the particle number and momentum, and collective phenomena like elliptic flow.
Combinatorial jets and background fluctuations are intimately related: low energy jets, for example with a momentum below 5 GeV/c, are also subject to background fluctuations and appear at relatively high p T (well above 20 GeV/c).Such jets are mostly background energy, and thus background fluctuations give rise to combinatorial jets.
For the results reported in the next sections an unfolding procedure is used to correct for background fluctuations.In this procedure, the combinatorial jets will emerge at low p T , while the spectrum is only reported above a certain p T cut-off, thus effectively removing the combinatorial jets from the result.To illustrate the impact of combinatorial jets, Fig. 1 shows uncorrected jet spectra after event-by-event subtraction of the background following Eq. 1.The black solid circles show the result without further selection of the jets, which shows a broad peak around p T,ch jet = 0 GeV/c.A large fraction of the combinatorial jets can be removed by selecting jets with a leading charged particle above a certain threshold [30].The crosses and squares in Fig. 1 show the jet spectra with a leading charged particle above 5 and 10 GeV/c.It can be seen clearly that selecting jets by a leading high p T particle reduces the background contribution for p T,ch jet < 40 GeV/c.However, this selection does not only reject combinatorial jets, but also introduces a bias towards harder fragmentation.
In the following, unbiased and leading track biased jet spectra are reported.The systematic uncertainty arising from the combinatorial jet correction by unfolding is smaller for the biased spectra (for details, see Section 2.7).
Fluctuations of the background are quantified by placing cones with R = 0.2 and R = 0.3 at random locations within the acceptance of the measured Pb-Pb events (0 < ϕ < 2π and |η RC | < 0.5).The transverse momentum of charged particles in the Randomly positioned Cone (RC) is summed and the difference δ p ch T = ∑ RC i p T,i − ρ ch A is calculated, which represents the statistical (region-to-region) fluctuations of the background.An alternative method to quantify the background fluctuations is also used in which high p T probes are embedded into the Pb-Pb events [28].The events with embedded probes are clustered with the anti-k T jet finder and the transverse momentum p T,ch jet containing the embedded probe in the heavy-ion environment is compared to the embedded transverse momentum p The left panel of Fig. 2 shows the δ p ch T distribution from the 10% most central events for the two jet resolution parameters used in this analysis.The standard deviation of the background fluctuations, σ (δ p ch T ), is 4.47 GeV/c for R = 0.2 jets and 7.15 GeV/c for R = 0.3 jets (the statistical uncertainties are less than 4 MeV/c due to the large sample of random cones).The right panel of Fig. 2 shows the evolution of σ (δ p ch T ) with centrality for the two jet resolution parameters extracted with the random cones technique.The upper edge of the shaded boxes indicates the σ (δ p ch T ) obtained with track embedding, where single tracks with 20 < p track T < 110 GeV/c were embedded in the heavy-ion events.The small increase in the standard deviation for more central events is due to the finite jet area resolution in the embedding [28].
Due to the asymmetry of the δ p ch T distribution, fluctuations that increase the jet energy are more probable than fluctuations to lower jet energy.More importantly, the steeply falling p T -spectrum favours low-p T jets with upward fluctuations over downward fluctuations of high-p T jets at a given p T .
Fluctuations of the background depend strongly on the multiplicity, jet area (or radius), and minimum p T of the measured particles [28].The analysis presented here is limited to R = 0.2 and R = 0.3 to avoid instabilities in the correction which are present for larger radii, see also Section 2.6.
The measured (uncorrected) δ p ch T distributions are used directly to correct the jet spectrum for back-ground fluctuations.In addition, the magnitude of background fluctuations also provides a potentially important characteristic of the properties of the heavy-ion event and the region-to-region variation of the transverse momentum density.For this purpose, the measured values were corrected using the HBOM iterative procedure in the same way as for the background density ρ, i.e. applying the parameterized detector effects multiple times and extrapolating the fluctuations to an ideal detector [29].Since the correction is based on the properties of the measured heavy-ion event, it takes into account all correlations in the event.The corrected width of the δ p ch T distribution is given in Table 2 for central collisions and various cone radii.The FastJet package provides a measure of fluctuations, σ FJ , which is defined from the distribution of individual jet momentum densities p i T,ch jet /A i such that 15.9% of all clusters within an event satisfy p i T,ch jet /A i < ρ − σ FJ √ A [31].This measure corrects to first order the area dependence of fluctuations (σ ∝ √ A), but is not sensitive to the tail of the distribution.The σ FJ obtained with different radius parameters for the k T jet finder and extrapolated to an ideal detector for charged particles above p T > 0.15 GeV/c is also reported in Table 2.It is multiplied by √ πR 2 to re-introduce part of the area dependence, present in σ (δ p ch T ).The FastJet fluctuation measures are reported to enable the comparison of fluctuations in heavy ion reactions by standard jet reconstruction tools in models and data.

Detector effects
The jet response in the ALICE detector is evaluated using simulations with the PYTHIA6 [32] event generator and GEANT3 [33] for detector response, using the same reconstruction software settings that are used for the reconstruction of Pb-Pb events.The effect of the high track density in Pb-Pb events on the tracking efficiency was studied using HIJING [34] events with the GEANT3 detector simulation.It is found that the tracking efficiency is ∼2% lower in central Pb-Pb collisions than in peripheral collisions and pp collisions.This additional centrality-dependent inefficiency was introduced to the PYTHIA events by a random rejection of tracks.
The jet response is determined on a jet-by-jet basis by comparing jets before (particle level jets) and after detector simulation (detector level jets), that are geometrically matched.Particle level jets are clustered from primary charged particles produced by the event generator.Primary charged particles include all prompt charged particles produced in the collision, including the products of strong and electromagnetic decays, but excluding weak decays of strange hadrons.In this analysis the detector to particle level correction is based on the Perugia-0 tune [35] of PYTHIA6.It was verified that the simulated detector response for jets is largely independent of the generator tune by comparing to the jet response obtained with the Perugia-2010 and 2011 tune [36,37].The contribution from weak decay products to the track sample is small due to the track selection requirements and low material budget (11.5% ± 0.5% X 0 in the central tracking systems [38]).The remaining contamination is included in the response matrix.No correction for hadronization effects was applied since the relation between parton level jet and particle level jet in heavy-ion collisions is not well-defined.
The detector effects that influence the jet energy scale and resolution are the charged particle tracking efficiency and the transverse momentum resolution, with the tracking efficiency being the dominant contributor.The finite p T resolution of reconstructed charged tracks has a small effect on the jet energy resolution since the majority of the constituents of a jet are of moderate p T where the tracking momentum resolution is good.In addition, since the transverse momentum of the jet is the sum of the transverse momentum of independently measured tracks, the relative momentum resolution is in general better than that of individual tracks.The distributions correspond to the 10% most central events.Events were generated using PYTHIA with the standard ALICE detector response simulation using GEANT3 and the data reconstruction algorithms and settings used for Pb-Pb events.The dominant systematic uncertainty is the uncertainty on tracking efficiency.
Figure 3 shows the probability distribution of the relative transverse momentum difference between the detector and particle level jets with resolution parameters R = 0.2 and R = 0.3 in three different intervals of the transverse momentum of the particle level jet p part T,ch jet .The most probable detector level p det T,ch jet is very close to the particle level jet p part T,ch jet in all cases.The average momentum of the detector level jet is lower than the particle level momentum, because of the average inefficiency of 10-20% in the charged particle reconstruction.Momentum resolution effects and under-subtraction of the background (back reaction) can cause a detector level jet to have a higher momentum.The momentum difference distribution is highly asymmetric and cannot be described by a Gaussian distribution.
To characterize the detector response, the mean of the relative difference between p det T,ch jet and p part T,ch jet as a function of the jet momentum at particle level is shown in Fig. 4. For unbiased jets the reconstructed jet momentum is on average 14-19% lower than the generated momentum, in the range p part T,ch jet = 20 − 100 GeV/c, with a weak p T -dependence.The mean of the jet response is also shown for leading track biased jets with p leading track T > 5 and 10 GeV/c.Those jets whose leading track is not reconstructed in the detector are rejected from the sample.This results in an improved jet energy resolution at low jet p T while the jet finding efficiency is decreased, as shown in Fig. 5.
To give more details on the detector response to jets, the most probable value of the relative difference between p part T,ch jet and p det T,ch jet is shown as a function of p part T,ch jet in the right panel of Fig. 4. The most probable value is determined as the mean of a Gaussian function fitted to the peak region, −0.03 < The jet-finding efficiency is obtained by taking the ratio between the spectra of the particle level jets which have a detector level partner, and all particle level jets.In case of jets biased by a high p T con-stituent, the numerator consists of jets fulfilling the high p T track requirement on detector level and the denominator are all particle level jets with a high p T generated particle.Figure 5 shows the jet-finding efficiency for the unbiased sample, which is unity at high p T and reduces to 95% at p part T,ch jet = 20 GeV/c due to migration of the jet axis outside the η acceptance.The jet-finding efficiency for jets with radii of R = 0.2 and R = 0.3 differs by a few per cent at low p T and is the same at high p T .In general the jet-finding efficiency is ∼1% higher in pp compared to Pb-Pb without a p T dependence for p > 10 GeV/c, which is consistent with the charged particle tracking efficiency.

Unfolding
Both background fluctuations and detector effects lead to smearing of the measured jet momentum in heavy ion collisions.These effects can be corrected for using deconvolution, or unfolding procedures [39][40][41].The background fluctuations and detector effects partially compensate: an upward energy shift is more likely due to background fluctuations while detector effects mainly induce a shift to lower p T .
The relation between the measured spectrum M m and the 'true' jet spectrum T t is where R det d,t is the response matrix for detector effects (including efficiencies), R The response for background fluctuations is extracted with the data-driven method described in Section 2.4 and the response for detector effects is obtained from detector simulations as described in Section 2.5.The response matrices are combined into an overall response matrix R tot m,t .It was verified that correcting for detector effects and background fluctuations in two separate unfolding steps yields the same unfolded jet spectrum.Figure 6 shows the width of the combined response σ (p det T,ch jet )/p part T,ch jet as a function of p part T,ch jet .It can be observed that the dominant correction at low momenta originates from the background fluctuations while at high p T the detector effects dominate.
Inverting Eq. 2 to obtain the true spectrum from the measured spectrum requires some care: calculating the inverse of the response matrix leads to solutions for the true jet spectrum that has large unphysical bin-to-bin-fluctuations.To suppress these fluctuations, unfolding algorithms implement regularisation procedures, which impose a smoothness criterion on the final result.There is some freedom in the choice of regularisation procedure, which leads to an additional systematic uncertainty on the unfolded spectrum for the final result.
Three unfolding algorithms with different regularisation procedures were tested: the χ 2 method with a log-log-regularisation (see Appendix A), the (generalized) Singular Value Decomposition (SVD) method as implemented in RooUnfold, and the Bayesian method [40,[42][43][44][45].It was found in a closure test with a thermal background model that the Bayesian method does not converge properly for this case, while the other two methods give similar results.The covariance matrix cov(x, y) for the unfolded result is calculated by propagating the measurement errors in the unfolding and/or using Monte Carlo variations of the input spectra [45].The quality of the unfolded result is evaluated by inspecting the Pearson coefficients ρ(x, y) = cov(x,y) σ x σ y .A large (anti-)correlation between neighboring bins indicates that the regularisation is too strong or too weak.The statistical uncertainties on the unfolded data points are the square root of the diagonal elements of the covariance matrix of the unfolded spectrum.

Unfolding strategy -p T ranges
There are two relevant kinematic ranges in the unfolding strategy applied in this analysis: the p T -range of the measured spectrum and the p T -range of the unfolded spectrum, which may be different.A minimum p T cut-off on the measured jet spectrum is introduced to suppress jet candidates, which are dominated by background fluctuations, including combinatorial jets, while the unfolded spectrum starts at the lowest possible p T , p unfolded T > 0 GeV/c.The minimum p T cut-off (p min,meas T ) on the measured spectrum removes a large fraction of combinatorial jets, which makes the unfolding procedure more stable.Feed-in from true jets with p T < p min,meas T into the region used for unfolding is accounted for by extending the unfolded spectrum to p T,ch jet = 0 GeV/c.The feed-in from low p T true jets is a significant effect since the spectrum falls steeply with p T,ch jet .Combinatorial jets still present in the measurement after applying the kinematical selections are transferred in the unfolding procedure to the region below p min,meas T .Feed-in from jets with p T,ch jet larger than the maximum measured p T,ch jet is also included by extending the reach of the unfolded spectrum to p T,ch jet = 250 GeV/c.The optimal value of the minimum p T cut-off has been studied using the jet background model described in [30] and within simpler set-up in which a jet spectrum is folded with the measured background fluctuations.Stable unfolding is obtained with a minimum p T cut-off of at least five times the width of the δ p ch T -distribution σ (δ p ch T ).For the most central collisions and R = 0.3, this means that the spectrum is reported for p T,ch jet > 40 GeV/c.In addition, the maximum p T cut-off is driven by the available statistics.The present data set allows for a measurement of p T,ch jet < 110 GeV/c in central events and p T,ch jet < 90 GeV/c in peripheral events.In case of leading track biased jets, the unfolding is more stable since the correction for combinatorial jets is reduced.

Systematic uncertainties
The systematic uncertainties on the results were evaluated by varying a number of key assumptions in the correction procedure and by using different unfolding methods.The different tests and the resulting systematic uncertainties are discussed in the following subsections, and summerized in Table 3.

Unfolding and regularisation uncertainties
The uncertainties from the regularisation and the unfolding procedure were evaluated by changing the regularisation strength β in the χ 2 -method and by comparing the results from the χ 2 method and the generalised SVD method.Both variations give an uncertainty on the applied regularisation.Therefore, the uncertainties were taken to be the maximum deviation from both studies.The SVD method also makes use of a prior, which was varied.This has a negligible effect on the result.

Regularisation strength β
The regularisation strength β (see Eq. A.2) is varied from a value where fluctuating solutions dominate to the point where the unfolding becomes over-constrained.The main effect of varying β is that the unfolded jet spectrum changes shape.With increasing regularisation, the unfolded spectrum becomes steeper at low p T and flatter at high p T .The maximum deviation of the yield for each p T bin of the unfolded spectra within the reasonable range of β is used as the systematic uncertainty.The uncertainty is largest for the unbiased jet sample with resolution parameter R = 0.3 in the most central collisions up to 20% at low p T,jet .

Unfolding method
The spectrum obtained with the χ 2 minimization method is compared to results using the Bayesian and SVD unfolding methods.The χ 2 and SVD unfolded spectra agree within ±10% for all centrality classes and jet samples.The Bayesian method is only included in the estimate of the systematic uncertainties for the cases where the combinatorial jets are suppressed by selecting jets with a leading track with p T > 5 or 10 GeV/c.Without this selection, the Bayesian method was found to be unreliable: large deviations up to 50% at low p T,jet are observed in central collisions with a resolution parameter R = 0.3.Such deviations are also seen in the validation studies with a heavy-ion background model where the Bayesian method did not give the correct result, unless the truth was used as the prior.
Prior The unfolding algorithm starts from a QCD inspired shape for the unfolded spectrum, the prior.The measured jet spectrum is used as a standard prior for all unfolding methods and the sensitivity to the choice of prior is evaluated by changing the shape and yield of the prior.When the prior is far from the truth (for example a uniform distribution), the χ 2 unfolding takes more iterations to converge but eventually an unfolded jet spectrum is obtained, which is statistically not significantly different from the unfolded spectrum obtained with the measured spectrum as a prior.The choice of prior has a negligible effect on the final unfolded spectrum.

Combinatorial jets
The effect of combinatorial jets in the sample is evaluated by changing the minimum p T of the unfolded spectrum and the measured range where the unfolding is applied.

Minimum p T of unfolded jet spectrum
In the default analysis the unfolded spectrum starts at p T,ch jet = 0 GeV/c.The sensitivity of the result to very low energy (combinatorial) jets is explored by removing the first bin from the unfolding procedure, i.e. starting the unfolded spectrum at p T,ch jet = 5 or 10 GeV/c instead of p T,ch jet = 0.This removes one parameter from the χ 2 minimization.It results in an increase of the unfolded jet yield by a few percent depending on the centrality bin and jet radius.

Minimum p T of measured jet spectrum
Increasing the minimum measured p T reduces the amount of combinatorial jets in the measured spectrum (see Fig. 1).The remaining combinatorial jets contribute to the jet yield at low p T in the unfolded spectrum.The minimum p T of the measured jet spectrum is varied by 10 GeV/c to a lower and higher value.With the two variations the unfolding is performed again and the resulting difference between the unfolded spectra with the default one assigned as a systematic uncertainty.This systematic uncertainty is largest at low p T in the region where the p min,meas T cut-off is placed.For unbiased jets in most central collisions and resolution parameter R = 0.3 the uncertainty at p T,jet = 40 GeV/c is 25%, while it decreases to a few percent for p T,jet > 60 GeV/c.

Measurement of charged jet suppression in Pb-Pb collisions at
√ s NN = 2.76 TeV 13

Uncertainty on background
Background fluctuation distribution: random cones and high p T probe embedding The δ p ch T distribution obtained from embedding single high p T tracks in measured Pb-Pb events is used as a variation to the δ p ch T distribution from random cones.The width of the background fluctuations obtained from single-track embedding is a few 100 MeV/c larger than for the random cones.The uncertainty is taken as the difference between the unfolded jet spectrum using the δ p ch T response from single-track embedding and the response from random cones.The difference is largest at low p T,jet (< 40 GeV/c), where ∼ 15% deviation in the jet yield for the unbiased R = 0.3 central jet spectrum is observed.

Correction for collective flow effects in case of leading track biased jets
Due to the presence of collective effects such as elliptic and triangular flow in heavy-ion collisions the background density differs from region-to-region.Jets with a high p T leading track are preferentially found in regions with larger background density (in-plane).The subtracted background, however, is the average p T density of the event, ρ ch , multiplied by the area of the jet.A correction for the larger background for biased jets is included in the response matrix.This correction is determined by calculating ρ ch on the near, away side and in the region perpendicular to the leading track biased jet in an event.The correction is largest for events in the 10-30% centrality class where for R = 0.3 jets with a 5 GeV/c bias an overall increase of the background of 0.49 GeV/c is present.The correction for flow effects is only applied for leading track biased jet spectra since for the unbiased case, jets are selected regardless of their correlation with the event or participant plane [28].
The uncertainty on the correction for flow effects is calculated by changing the background to the lowest and highest values found in the different azimuthal regions (perpendicular and near-side regions respectively).The uncertainty on ρ ch is 3 GeV/c for the jet sample with a 5 GeV/c leading track selection, and 2 GeV/c for a 10 GeV/c leading track requirement in central events.The systematic uncertainty on the unfolded jet spectrum for R = 0.3 jets with p leading track T > 5 GeV/c in 10% most central collisions is 8% at p T,jet = 40 GeV/c and decreases to 4% at p T,jet = 100 GeV/c.A previous study has shown that the background fluctuations (δ p T -distribution) are almost independent of the orientation with respect to the reaction plane [28]; this effect is negligible compared to the change in the average background.

Uncertainty on the detector response
The detector response has two main components: tracking efficiency and momentum resolution of which the tracking efficiency is the dominant uncertainty.The uncertainty on the tracking efficiency is estimated to be 4%, motivated by detector simulation studies with PYTHIA and HIJING events, and by varying the track selection criteria.To determine the systematic uncertainty on the result, a second response matrix is constructed from a simulation with a 4% lower efficiency and the measured Pb-Pb jet spectrum is unfolded.The difference between the nominal unfolded solution and the unfolded spectra with a modified detector response is ∼ 20% at p T,jet = 50 GeV/c and decreases to ∼ 11% at p T,jet = 100 GeV/c; the full difference is used as the systematic uncertainty, which corresponds to a 3-5% uncertainty on the charged jet p T .

Centrality determination
The relative uncertainty on the fraction of hadronic cross-section used in the Glauber fit to determine the centrality classes is 1% [19].The contribution of this uncertainty on the jet spectrum is estimated by varying the limits of the centrality classes by ±1% (e.g. for the 10-30% centrality class to 9.9-29.7%and 10.1-30.3%).With the shifted limits of the centrality classes the jet spectrum is compared to the nominal jet spectrum.The uncertainty is the same for the jet spectrum with different leading track biases and increases from central to peripheral events.For the 0-10% centrality class the uncertainty is less than 1% and in the peripheral centrality class 50-80% it is ∼ 1.9%.Unfolding method Table 3: Overview of systematic uncertainties for jet spectra with a leading track with p T > 5 GeV/c.Relative uncertainties are given in percentiles for two p T -intervals and two different centrality intervals.

Total systematic uncertainty
The differential production yields are reported with their systematic uncertainties separated into two categories: -Shape uncertainty These are uncertainties that are highly anti-correlated between parts of the spectrum: if the yield is increased in some bins, it decreases in other bins.The uncertainties from the unfolding method and regularisation, and the uncertainty on the background fluctuations (only δ p ch T uncertainty) fall into this category.The contributions are added in quadrature.
-Correlated systematic uncertainty These are uncertainties that result in correlated changes over the entire spectrum.The contributions to this type of uncertainty are the uncertainty on the detector response, the effect of flow in the background, and the influence of the combinatorial jets.The contributions are added in quadrature.

Systematic uncertainty on ratios
The following procedures are used for ratios of jet spectra: -Uncorrelated uncertainties The systematic uncertainties from the unfolding method, which include regularisation and variation of p T -ranges, are not correlated from one unfolded jet spectrum to another.The contributions from these sources are added in quadrature to calculate the uncertainies on ratios.
-Correlated uncertainties The systematic uncertainties from the flow bias, the δ p ch T -distribution, and the detector effects are highly correlated between unfolded spectra from different centrality classes, jet resolution parameters and leading track biases.The uncertainty on the tracking efficiency is similar for all centrality classes.The flow bias depends on the p T of the leading track, jet resolution parameter, and centrality class but is correlated.As a consequence, within a ratio the correlated systematic uncertainties partially cancel.

Results
Jet spectra are measured with resolution parameters R = 0.2 and 0.3 in four centrality classes: 0-10%, 10-30%, 30-50% and 50-80%.Figure 7 shows the measured Pb-Pb jet spectra reconstructed from charged constituents with p T > 0.15 GeV/c.The jet spectra are unfolded for detector effects and background fluctuations, and corrected for the jet finding efficiency as described in the preceding sections.The upper panels show the inclusive jet spectra while for the center and lower panels the jet spectra with a leading track bias of at least 5 and 10 GeV/c are shown.The markers represent the central values of the unfolded jet spectra.It should be noted that the unfolding procedure leads to correlations between the data points, because the width of the response function is similar to the bin width: neighboring p T -bins tend to fluctuate together (correlated) while bins with some distance tend to be anti-correlated.The vertical error bars represent the statistical uncertainties.The filled and open boxes indicate the corresponding shape and correlated systematic uncertainties discussed previously.
The jet yield is given per event and normalized by the average number of nucleon-nucleon collisions N coll corresponding to the given centrality interval.The markers shown below 20 GeV/c indicate the normalization uncertainty on the extracted values of N coll (see Table 1).The jet yield evolves with centrality: for central collisions fewer jets are observed per N coll than in peripheral collisions.
The left panels in Fig. 8 show the ratio between the unbiased jet spectra and jets with a leading track of at least 5 GeV/c.Although the biased spectrum is a subset of the unbiased spectrum, the statistical uncertainties are added in quadrature since the unfolding procedure introduces a point-to-point correlation between the statistical uncertainties.In the jet p T -range considered here, p T,ch jet > 20 GeV/c, the PYTHIA vacuum expectation from the Perugia-2011 tune [35] is that almost all jets have a constituent of at least 5 GeV/c, resulting in a ratio at unity as indicated by the PYTHIA data points.The ratio between the unbiased and 5 GeV/c biased measured Pb-Pb jet spectra is consistent in peripheral and central collisions with the vacuum expectation.No evidence of the modification of the hard jet core is observed.
The right panels in Fig. 8 show the ratio between the jet spectra with a leading track p T of at least 10 GeV/c and 5 GeV/c as measured in central and peripheral Pb-Pb collisions compared to the same observable at particle level in PYTHIA with the Perugia-2011 tune.By selecting jets with a higher momentum for the leading jet constituent, low p T jets with a soft fragmentation pattern are removed from the sample.The ratio increases with p T reaching unity at p T,ch jet = 50 GeV/c for R = 0.2 jets and at p T,ch jet = 60 GeV/c for R = 0.3 jets in central and peripheral collisions.This rising trend is due to the increased fragmentation bias and is compatible with the fragmentation bias observed in PYTHIA.Jet quenching in most central heavy-ion collisions is quantified by constructing the jet nuclear modification factor R CP , which is the ratio of jet p T spectra in central and peripheral collisions normalized by the nuclear overlap functions T AA as calculated with a Glauber model for each centrality class [19].If the full jet energy is recovered within the cone, and in the absence of initial state effects like parton shadowing [46][47][48], R CP is unity by construction.In that case, jet quenching would manifest itself as redistribution of the energy within the cone as compared to jet fragmentation in the vacuum.The jet suppression factor R CP is shown in Fig. 9, using centrality class 50-80% as the peripheral reference.A strong jet suppression, 0.3 < R CP < 0.5, is observed for 0-10% central events, while more peripheral collisions (30-50%) are less suppressed, R CP ≃ 0.8 at high p T,ch jet .A mild increase of R CP with increasing p T,ch jet is observed at low jet energies while at high p T 50 GeV/c the suppression is consistent with a constant.The R CP does not change significantly with the resolution parameter R for the range studied (R = 0.2 and R = 0.3).  Figure 10 shows the jet R CP at 60 < p T,ch jet < 70 GeV/c as a function of the average number of participant nucleons corresponding to the selected centrality classes (see Table 1).A decreasing trend of the R CP as a function of the number of participants is observed.Figure 10 also compares the suppression of jets with a high p T track selection, and shows no evident dependence on the fragmentation pattern.
The ratio of the jet p T spectra measured at different R can potentially provide information about jet structure modifications due to redistribution of energy caused by jet quenching [49,50].Figure 11

Discussion and Conclusions
Before the first jet measurements in heavy ion collisions were performed, it was expected that medium interactions redistribute the momenta of jet fragments to small or moderate angles, because of kinematic effects (the momentum of the jet is large compared to the typical momenta of partons in the medium) as well as dynamics (the cross section for medium-induced radiation peaks at small angles [51]).At the same time, there were some indications from numerical calculations by Vitev [52] and in the q-PYTHIA event generator [53,54] that large angle radiation is kinematically favoured for large medium density.The first jet measurements in heavy ion collisions at the LHC showed a large energy imbalance for jet pairs [15,16,55], indicating that a significant fraction of jet momentum is transported out of the jet cone by interactions with the medium for recoil jets.Since then, it has been realised that there is a variety of mechanisms that may contribute to large angle radiation, such as jet broadening by medium-induced virtuality (YaJEM) [56,57], reinteractions of the radiated gluons (also called 'frequency collimation of the radiation') [58,59], and quantum (de-)coherence effects [60,61].
The large suppression of charged jet production with R = 0.2 and R = 0.3 in central Pb-Pb collisions shown in Fig. 9, also indicates that momentum transport to large angles is an important effect.
To further explore these effects, Fig. 12 compares the jet measurement reported in this paper to the nuclear modification factor for charged hadrons measured by ALICE [22] and CMS [14] and to the calorimetric jet measurements by ATLAS [17].
Comparing the R CP of jets to charged particles in Fig. 12, one would expect the suppression for jets to be smaller than for hadrons, since jet reconstruction collects multiple jet fragments into the jet cone, thus recovering some of the medium-induced fragmentation.However, it can be seen that the R CP for jets is similar to that observed for single hadrons over a broad momentum range.This indicates that the momentum is redistributed to angles larger than R = 0.3 by interactions with the medium.Such a strong redistribution of momentum might also be expected to lead to a significant broadening of the energy profile within the larger cone radius R = 0.3.The results presented in this paper, however, show that the ratio of yields for jets with R = 0.2 and R = 0.3 is similar in PYTHIA pp simulations and Pb-Pb collisions (see Fig. 11), indicating that the energy profile of the found jets is not significantly modified.In addition, Fig. 8 shows that the effect of selecting jets with a leading hadron with p T > 5 or 10 GeV/c is similar in Pb-Pb collisions and in PYTHIA pp events, which indicates that the longitudinal   ATLAS [17] and to charged particle suppression by ALICE [22] and CMS [14].Note that the underlying parton p T scale is different at the same measured p T for charged particles, charged jets and full jets.momentum distribution of (leading) high p T tracks in jets reconstructed in Pb-Pb collisions remains largely unmodified.This observation is in qualitative agreement with measurements of fragmentation properties by CMS [62,63] and ATLAS [64].
A further impression of the importance of soft radiation can be obtained by comparing the calorimetric jet measurement by ATLAS to the ALICE results in this paper.The ALICE measurement is more sensitive to low-momentum fragments due to the high tracking efficiency and good momentum resolution of charged particle tracks at low p T .The agreement between these two jet measurements in Fig. 12 suggests that the contribution of low momentum fragments to the jet energy is small.A study of PYTHIA events shows that the expected contribution of fragments with p T < 1(2) GeV/c is 4(7)% of the jet energy at p T,ch jet = 40 GeV/c with cone radius R = 0.2(0.3) in pp collisions.The results indicate that this contribution is also limited in Pb-Pb collisions.
The measured ratios of jet cross sections with R = 0.2 and R = 0.3 and with and without leading particle selection show that the transverse and longitudinal fragment distributions of the reconstructed jets are similar in pp (PYTHIA calculations) and Pb-Pb collisions.This 'unmodifed hard core' of the jet may be due to formation time effects (the parton leaves the medium with relatively high momentum and then fragments without further interactions) [56,65], quantum interference effects (a group of partons with small opening angles interacts with the medium as one parton) [66], kinematics (large momentum emissions are kinematically favoured at small angles) [56] and/or selection bias effects [56,67].
First results from the JEWEL event generator show a strong suppression of jets, in agreement with the R CP shown in Fig. 12 [68].However, more extensive comparisons of theoretical models to the different experimental measurements are needed to determine how well they constrain the dynamics of parton energy loss models.
In summary, a measurement of charged jet spectra in Pb-Pb collisions at different centralities was reported, using charged hadrons with p T > 0.15 GeV/c.The analysis was performed for a jet sample with a minimal fragmentation bias by introducing different p T -ranges in the unfolding procedure for the unfolded and measured spectrum.To suppress combinatorial jets from the measured population, jet spectra with a leading track selection of p leading track T > 5 and 10 GeV/c were also reported.The effect of the leading track cut at 5 GeV/c is small for the measured range p T,ch jet > 20 GeV/c, while for p leading track T > 10 GeV/c, the effect is sizeable, but consistent with expectations from jet fragmentation in PYTHIA events, indicating that the high-p T fragmentation is not strongly modified by interactions with the medium.The ratio of jets reconstructed with R = 0.2 and R = 0.3 is found to be similar in central and peripheral Pb-Pb events, and similar to PYTHIA calculations, indicating no strong broadening of the radial jet profile within R = 0.3.The nuclear modification factor R CP for jets is in the range 0.3-0.5, and tends to be lower at low p T,ch jet ≈ 30 GeV/c than at high p T,ch jet ≈ 100 GeV/c.The value of R CP for jets is similar to charged hadrons, which suggests that interactions with the medium redistribute energy and momentum to relatively large angles with respect to the jet axis.collisions at s**(1/2) = 200-GeV and the pseudorapidity dependence of high p(T) suppression," Phys.Rev.Lett. 91 (2003)

Fig. 1 :
Fig.1: Uncorrected jet spectra after background subtraction, with radius parameters R = 0.2 (left) and R = 0.3 (right) in central Pb-Pb events, without leading particle selection (unbiased, black circles) and with at least one particle with p T > 5 (green crosses) or 10 GeV/c (red squares).

Fig. 2 :
Fig. 2: Left: δ p ch T distribution for jets with resolution parameter R = 0.2 and R = 0.3 measured with random cones in central collisions.Right: Width of the background fluctuation δ p ch T distribution as a function of centrality for cone radii R = 0.2 and R = 0.3.The shaded uncertainty bands indicate the difference between the width of the δ p ch T distribution from random cones and high p T probe embedding.

Fig. 3 :
Fig.3: Distributions of relative transverse momentum difference between detector and particle level anti-k T jets with R = 0.2 and R = 0.3 and several ranges of jet transverse momentum at particle level.The distributions correspond to the 10% most central events.Events were generated using PYTHIA with the standard ALICE detector response simulation using GEANT3 and the data reconstruction algorithms and settings used for Pb-Pb events.The dominant systematic uncertainty is the uncertainty on tracking efficiency.

Fig. 4 :Fig. 5 :
Fig.4: Jet detector response for jet finding resolution parameter R = 0.3 for the 10% most central events.Data points extracted from event and full detector simulation.Systematic uncertainty originates from the uncertainty on the tracking efficiency.Left: mean of the jet response for charged jets with R = 0.3.See text for details.Right: Mean, most probably value and quartiles of the jet response as a function of jet momentum.
part T,ch jet > 20 GeV/c.For leading track biased jets, the jet-finding efficiency is reduced and reaches 90% at p part T,ch jet ≈ 25 GeV/c for p leading track T > 5 GeV/c and at p part T,ch jet ≈ 60 GeV/c for p leading track T bkg m,d is the response matrix for background fluctuations, and R tot m,t = R bkg m,d •R det d,t is the total response matrix for the combined effects of background fluctuations and detector effects.The subscripts m, d,t are indices indicating the bin number.

Fig. 6 :
Fig. 6: Combined jet response for charged jets for the two resolution parameters considered, including background fluctuations and detector effects for 0-10% central Pb-Pb events.Left panel: R = 0.2.Right panel: R = 0.3.

Fig. 7 :Fig. 8 :
Fig. 7: Charged jet spectra, corrected for background fluctuations and detector effects, using two cone radius parameters R = 0.2 (left panels) and R = 0.3 (right panels) and different leading track selections: unbiased (top panels), p leading track T > 5 GeV/c (middle panels), and p leading track T > 10 GeV/c (bottom panels).The uncertainty bands at p T,ch jet < 20 GeV/c indicate the normalisation uncertainty due to the scaling with 1/N coll .

Fig. 9 :
Fig. 9: Nuclear modification factor R CP for charged jets with a leading charged particle with p track T > 5 GeV/c, with R = 0.2 (left panels) and R = 0.3 (right panels) and different centrality selections.

Fig. 10 :
Fig. 10: R CP for unbiased and leading track biased jets with 60 < p T,ch jet < 70 GeV/c as a function of the average number of participants in the collision.Left panel: R = 0.2.Right panel: R = 0.3.For visibility the data points for all jets and for jets with p track T > 10 GeV/c are shifted to the left and right respectively.themeasured ratio σ (R = 0.2)/σ (R = 0.3) for central and peripheral collisions.The comparison of the measured ratio to the ratio obtained with PYTHIA (particle level) shows that the transverse jet shape in central and peripheral Pb-Pb collisions are consistent with jet shapes in vacuum.No sign of a modified jet structure is observed between radii of 0.2 and 0.3 within uncertainties.

Fig. 11 :> 5
Fig. 11: Ratio of charged jet p T -spectra with radius parameter R = 0.2 and 0.3 and a leading charged particle p track T > 5 GeV/c in Pb-Pb data and simulated PYTHIA events.

Fig. 12 :
Fig.12: Comparison to jet R CP measured by ATLAS [17] and to charged particle suppression by ALICE[22] and CMS[14].Note that the underlying parton p T scale is different at the same measured p T for charged particles, charged jets and full jets.