Measurement of the Azimuthal Angle Dependence of Inclusive Jet Yields in Pb+Pb Collisions at sqrt(s(NN))= 2.76 TeV with the ATLAS detector

Measurements of the variation of inclusive jet suppression as a function of relative azimuthal angle, Delta phi, with respect to the elliptic event plane provide insight into the path-length dependence of jet quenching. ATLAS has measured the Delta phi dependence of jet yields in 0.14 nb^-1 of sqrt(s(NN))= 2.76 TeV Pb+Pb collisions at the LHC for jet transverse momenta p_T>45 GeV in different collision centrality bins using an underlying event subtraction procedure that accounts for elliptic flow. The variation of the jet yield with Delta phi was characterized by the parameter, v_2^jet, and the ratio of out-of-plane (Delta phi ~ pi/2) to in-plane (Delta phi ~ 0) yields. Non-zero v_2^jet values were measured in all centrality bins for p_T<160 GeV. The jet yields are observed to vary by as much as 20% between in-plane and out-of-plane directions.


Measurement of the Azimuthal Angle Dependence of Inclusive Jet Yields in Pb+Pb
Collisions at √ s NN = 2.76 TeV with the ATLAS detector

ATLAS Collaboration
Measurements of the variation of inclusive jet suppression as a function of relative azimuthal angle, ∆φ, with respect to the elliptic event plane provide insight into the path-length dependence of jet quenching. ATLAS has measured the ∆φ dependence of jet yields in 0.14 nb −1 of √ sNN = 2.76 TeV Pb+Pb collisions at the LHC for jet transverse momenta pT > 45 GeV in different collision centrality bins using an underlying event subtraction procedure that accounts for elliptic flow. The variation of the jet yield with ∆φ was characterized by the parameter, v jet 2 , and the ratio of out-of-plane (∆φ ∼ π/2) to in-plane (∆φ ∼ 0) yields. Non-zero v jet 2 values were measured in all centrality bins for pT < 160 GeV. The jet yields are observed to vary by as much as 20% between in-plane and out-of-plane directions.
PACS numbers: 25.75.-q Studies of jet production in Pb+Pb collisions at the LHC [1,2] show behavior consistent with "jet quenching," a general term for the modification of parton showers in the hot dense medium created in ultra-relativistic nuclear collisions. For example, the inclusive yield of jets was observed to be suppressed by a factor of approximately two in central Pb+Pb collisions relative to peripheral collisions [3], consistent with a mediuminduced reduction in the jet energies. Perturbative or weak-coupling calculations model jet energy loss, dE/dx, through a combination of collisional and radiative energy loss of the constituents of the parton shower. The radiative contributions are subject to coherence effects [4] that explicitly depend on the path length of the shower in the medium. Strong-coupling calculations suggest a different path-length dependence [5,6]. Measurements of the jet yield as a function of quantities providing indirect control over the jet path lengths may provide insight into the physical mechanisms responsible for jet quenching [7,8]. Such quantities include the Pb+Pb collision centrality and the azimuthal angle of the jet with respect to the elliptic event plane.
Elliptic flow refers to a cos 2φ modulation of the azimuthal angle (φ) distribution of particles produced in ultra-relativistic nuclear collisions [9]. This modulation is understood to arise from an approximately elliptic anisotropy of the initial-state transverse energy density profile that is imprinted on the azimuthal angle distribution of final-state particles [10] by the strong collective evolution of the medium. The resulting azimuthal angle distribution is often parameterized by the form: where the elliptic event plane angle, Ψ 2 , specifies the orientation of the initial density profile in the transverse plane, and the parameter v 2 quantifies the magnitude of the modulation. Jets measured at different azimuthal angles relative to the event plane, ∆φ ≡ φ jet − Ψ 2 , result from parton showers that traverse, on average, dif-ferent path lengths and density profiles in the medium. Thus, a measurement of the variation of the jet yield as a function of ∆φ should provide a direct constraint on theoretical models of the path-length dependence of the energy loss. This measurement is not directly sensitive to the contribution to jet suppression from higher order flow harmonics, which may arise from the fluctuating initial geometry [11][12][13].
Variations in jet yield as a function of ∆φ have been observed indirectly through measurements of single hadrons with large transverse momentum (p T ) at RHIC [14][15][16] and the LHC [17][18][19]. The utility of such measurements is limited by the weak relationship between hadron p T and the transverse momentum of the parent parton shower. This Letter presents results of measurements using fully reconstructed jets, which have kinematics properties that are more closely related to those of the parent partons. The ∆φ dependence of the inclusive jet yield was measured in √ s NN = 2.76 TeV Pb+Pb collisions as a function of jet p T and Pb+Pb collision centrality. The measurement was performed with the anti-k t algorithm [20] with distance parameter R = 0.2, chosen to limit the contribution of the underlying event (UE) to the measurement. The ∆φ dependence was characterized by the jet v 2 , v jet 2 , and the ratios of the jet yields in different ∆φ intervals at fixed p T and centrality. Such dependence is expected to be small in either the most central or most peripheral collisions, due to the lack of initial-state anisotropy and the lack of quenching, respectively. For intermediate centralities, measurement of the ∆φ dependence of the jet yields probes the interplay between contributions to quenching from the overall system size and energy density, as well as from the initial state anisotropy.
The measurements presented here were performed with the ATLAS detector [21] using its calorimeter, inner detector, trigger, and data acquisition systems. The calorimeter system consists of a liquid argon (LAr) electromagnetic (EM) calorimeter covering |η| < 3.2, a steel/scintillator sampling hadronic calorimeter covering |η| < 1.7, a LAr hadronic calorimeter covering 1.5 < |η| < 3.2, and a forward calorimeter (FCal) covering 3.2 < |η| < 4.9. Charged-particle tracks were measured over the range |η| < 2.5 using the inner detector [22], which is composed of silicon pixel detectors in the innermost layers, followed by silicon microstrip detectors and a straw-tube transition-radiation tracker (|η| < 2.0), all immersed in a 2 T axial magnetic field. The zerodegree calorimeters (ZDCs) are located symmetrically at z = ±140 m and cover |η| > 8. 3. In Pb+Pb collisions the ZDCs primarily measure non-interacting "spectator" neutrons from the incident nuclei. A ZDC coincidence trigger was defined by requiring a signal consistent with one or more neutrons in each of the calorimeters.
Pb+Pb collisions corresponding to a total integrated luminosity of 0.14 nb −1 were analyzed. The events were recorded using either a minimum-bias trigger, formed from the logical OR of triggers based on a ZDC coincidence or total transverse energy in the event, or a jet trigger implemented using the Pb+Pb jet reconstruction algorithm. The jet trigger selected events having at least one jet with transverse energy E T > 20 GeV. Event selection and background rejection criteria were applied [17] yielding 52 million and 14 million events in the minimum-bias and jet-triggered samples, respectively. For each event, Ψ 2 was computed from the azimuthal distribution of the transverse energy measured in the FCal [17,23], and angles with respect to Ψ 2 were defined over 0 ≤ ∆φ ≤ π/2. The centrality of Pb+Pb collisions was characterized by ΣE FCal T , the total transverse energy measured in the FCal [17]. The results reported here were obtained using the following centrality intervals defined according to successive percentiles of the ΣE FCal T distribution ordered from the most central (highest ΣE FCal T ) to the most peripheral collisions: 5-10%, 10-20%, 20-30%, 30-40%, 40-50%, and 50-60%. The centrality interval 5-60% coincides to the range over which the Ψ 2 resolution is adequate for the measurement. The percentiles were defined after correcting the ΣE FCal T distribution for an estimated 2% minimum-bias trigger inefficiency that is concentrated in the most peripheral intervals, which are not included in this analysis. A Glauber model analysis [24,25] of the ΣE FCal T distribution [17] was used to evaluate the average number of nucleons participating in the collision, N part , in each centrality interval.
The jet reconstruction and underlying event subtraction procedures are the same as those used in Ref. [3], which is summarized in the following. The anti-k t algorithm was applied to calorimeter towers with segmentation ∆η × ∆φ = 0.1 × 0.1. A two-step iterative procedure was used to obtain an event-by-event estimate of the average η-dependent UE energy density while excluding actual jets from that estimate. The jet kinematics were obtained by subtracting the UE energy from the towers within the jet. This subtraction accounts for elliptic flow by modulating the average background density by the magnitude of the elliptic flow measured by the calorimeter, v calo 2 , over the interval |η| < 3.2 and excluding η regions containing jets. Following reconstruction, the jet energies were corrected to account for the calorimeter energy response using an η-and E T -dependent multiplicative factor that was derived from the MC simulation [26].
Separate from the calorimeter jets, "track jets" were reconstructed by applying the anti-k t algorithm with R = 0.4 to charged particles having p T > 4 GeV. The p T of the track jets, p trkjet T , is largely unaffected by the UE due to the p T > 4 GeV requirement. To exclude the contribution to the jet yield from UE fluctuations of soft particles falsely identified as calorimeter jets, the jets used in this analysis were required to be within ∆R = ∆η 2 + ∆φ 2 = 0.2 of a track jet with p trkjet T > 10 GeV or an EM cluster [27] with p T > 9 GeV [28].
The performance of the jet reconstruction was evaluated using the GEANT4-simulated detector response [29,30]  Through this embedding procedure, the MC sample contains a UE contribution that is identical in all respects to the data, including azimuthal modulation of the UE due to harmonic flow. Jets reconstructed in the MC events using the same algorithms as applied to data were compared to generator-level jets reconstructed from finalstate PYTHIA hadrons. Potential variations in the jet energy resolution (JER) and jet energy scale (JES) with ∆φ due to elliptic and higher-order modulation [11][12][13] of the UE were investigated in the MC sample; no significant variation was found.
The dependence of the JES on ∆φ was further constrained by comparing the calorimeter jets to matched track jets in the data. For different values of ∆φ, the mean p T of calorimeter jets was evaluated as a function of the p T of the matched track jet, and no significant variation with ∆φ was observed. This study provides an upper limit on the variation in the JES between jets at ∆φ = 0 and ∆φ = π/2 of 0.1% for p T > 45 GeV.
Double differential jet yields, d 2 N jet /dp T d∆φ, were measured over |η| < 2.1 for each of the centrality ranges described above and in five p T intervals: 45-60 GeV, 60-80 GeV, 80-110 GeV, 110-160 GeV, and 160-210 GeV. The measurement in each p T range was performed using events selected by the jet trigger except for the 45-60 GeV p T range, in which minimum-bias events were used. The ∆φ dependence of the jet yields in the 60-80 GeV p T interval is shown for each centrality range in Fig. 1. A significant ∆φ variation that is consistent with a cos 2∆φ modulation is seen for all centrality intervals.
The measured yields and the resulting v jet 2 | meas values are distorted by the finite resolutions in Ψ 2 and the jet p T . The Ψ 2 resolution was evaluated using a sub-event technique [17,23] in which Ψ 2 was measured separately in the positive and negative η halves of the FCal yielding values Ψ + 2 and Ψ − 2 , respectively. The width of the Ψ + 2 − Ψ − 2 distribution was used [23] to estimate a factor, κ, that was used to correct each measured v 2 value for the finite Ψ 2 resolution according to This factor was evaluated for events containing jets to account for the relevant distribution of events within each centrality interval. The p T dependence, and possibly also the ∆φ dependence, of the measured yields are affected by the JER, which arises from both fluctuations in the UE and the detector response. The MC study shows that for the R = 0.2 jets used in this analysis, the JER-induced migration between jet p T intervals is sufficiently small that a "bin-by-bin" unfolding method, utilizing multiplicative corrections to the jet yields, is appropriate. The binby-bin correction factors are defined to be the number of generator-level jets divided by the number of reconstructed jets in each p T , ∆φ, and centrality interval. The MC studies show no significant ∆φ variation of the JER, JES, and the correction factors, and so these correction factors were taken to be ∆φ-independent. Since the measurements presented here depend only on the ratios of jet yields between different ∆φ intervals for the same p T range, the correction factors do not affect any of the final results; the potential for a ∆φ dependence of the correction factors is included in the estimates of the systematic uncertainty.
Systematic uncertainties on the corrected v 2 values arise due to uncertainties on the two correction procedures described above. Uncertainties on κ were estimated by using the values obtained in previous studies [17] for slightly different centrality intervals and interpolating to obtain values appropriate for the centrality intervals used here. The uncertainties were found to vary between 1% and 4% from central to peripheral collisions. Potential distortions in the measurement of Ψ 2 due to the production of jets in the FCal pseudorapidity range were studied in the MC sample and found to be negligible for the centrality intervals included in this analysis.
Uncertainties on the measurements arising from ∆φdependent systematic uncertainties on the bin-by-bin correction factors were estimated by determining the sensitivity of these correction factors to each systematic variation and then parameterizing that sensitivity with a cos 2∆φ dependence. The sensitivity to the ∆φ dependence of the spectrum was evaluated by varying the p T spectrum of the generator-level jets in each ∆φ interval within a range consistent with the measured v jet 2 values. The JES and JER contributions to the uncertainty were obtained by varying the relationship between generator-level and reconstructed jet p T in the determination of the correction factors. These procedures utilized the JES constraints obtained from track jets and direct measurements of the UE contribution to the JER [3]. Parameterizations of the measured v calo 2 and the average background E T underlying a typical jet measured in the data were used to provide the dependence of variations on centrality. The systematic uncertainties on v jet 2 are less than 0.002 except in the most central and lowest p T intervals where the JER contribution dominates, resulting in uncertainties between 0.005 and 0.01.
The azimuthal dependence of jet suppression can be characterized by v jet 2 , which was obtained by correcting the v jet 2 | meas values using Eq.(2). Figure 2 shows the resulting v jet 2 values as a function of jet p T for all centrality intervals. Significant, non-zero values are observed over the range 45 < p T < 160 GeV for all centrality intervals. A direct comparison between the v 2 of single high-p T charged particles and v jet 2 is generally not possible; however the fact that both quantities exhibit only a weak p T dependence leads to the expectation that they should be of similar magnitude. In the charged particle measurements, the v 2 values of charged particles with 28 < p T < 48 GeV were found to vary between 0.02 and 0.05 for the 10-50% centrality range [18], which are generally in agreement with v jet 2 values reported here indicating no obvious inconsistencies between the two results. The centrality dependence of v jet 2 is shown in Fig. 3 as a function of N part for different ranges in p T . The variation in jet yields with ∆φ can also be characterized by the ratio of jet yields between the most out-of-plane (3π/8 ≤ ∆φ ≤ π/2) and most in-plane (0 ≤ ∆φ < π/8) bins, R max ∆φ ≡ d 2 N jet /dp T d∆φ out / d 2 N jet /dp T d∆φ in . (3) This quantity is more general than v jet 2 as it does not assume a functional form for the ∆φ dependence of the jet yields. The nuclear modification factor, R AA , is a measure of the effect of quenching on hard scattering rates, and R max ∆φ can be interpreted as the ratio of ∆φdependent R AA factors, R max ∆φ = R AA | out / R AA | in [16]. The yields were corrected for Ψ 2 resolution assuming that the ∆φ variation is dominated by the cos 2∆φ modulation, d 2 N corr jet dp T d∆φ = d 2 N meas jet dp T d∆φ 1 + 2v jet 2 cos 2∆φ 1 + 2v jet 2 | meas cos 2∆φ .
The results, expressed in terms of the quantity f 2 ≡ 1 − R max ∆φ , show as much as a 20% variation between the out-of-plane and in-plane jet yields, but they are reduced slightly from the maximal difference, evaluated at ∆φ = π/2 and ∆φ = 0, by the finite bin size used in the measurement. That reduction was corrected by assuming a 1+2v jet 2 cos 2∆φ variation of the jet yields within the ∆φ bins containing ∆φ = 0 and π/2, and calculating the corresponding yields at those ∆φ values. From these yields, f corr 2 was calculated analogously to f 2 . The magnitude of the correction is typically a few percent. The f corr 2 values are shown in Fig. 3. For a pure cos 2∆φ modulation of the jet yields, f corr 2 would be given by 4v jet 2 /(1+2v jet 2 ). To test for deviations of the ∆φ dependence of the jet yields from a pure cos 2∆φ variation, 4v jet 2 /(1 + 2v jet 2 ) was calculated using the measured v jet 2 values and is shown for each p T and centrality interval in Fig. 3.
Similar variations of v jet 2 , f corr 2 and 4v jet 2 /(1 + 2v jet 2 ) with N part are seen in the 60-80 GeV range, which has the best statistical precision. A reduction in f corr 2 and v jet 2 in both the most central and peripheral collisions is not surprising; for very central collisions, the anisotropy of the initial state is small and the possible ∆φ variation of path lengths in the medium is limited. Although the anisotropy is greater in peripheral collisions, there is little suppression in the jet yields [3]. Therefore large variations in jet yield as a function of ∆φ would be unexpected. The f corr 2 and 4v jet 2 /(1 + 2v jet 2 ) values are generally in agreement within uncertainties, indicating an azimuthal dependence of relative suppression when measured with respect to the elliptic event plane that is dominated by second-harmonic modulation.
This Letter has presented results of ATLAS measure-ments of the variation of R = 0.2 anti-k t jet yields in √ s NN = 2.76 TeV Pb+Pb collisions as a function of ∆φ, the relative azimuthal angle of the jet with respect to the elliptic event plane. A significant ∆φ variation in the jet yield is observed for all centrality intervals and in all p T ranges except for the 160-210 GeV p T interval where the statistical uncertainties are large. The observed azimuthal variation of jet yields amounts to a reduction of 10-20% in the jet yields between in-plane and out-ofplane directions. These results establish a relationship between jet suppression and the initial nuclear geometry that should constrain models of the path-length dependence of the quenching mechanism.
We thank CERN for the very successful operation of the LHC, as well as the support staff from our institutions without whom ATLAS could not be operated efficiently.