Event-shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at s NN =2.76 TeV

We report on results obtained with the event-shape engineering technique applied to Pb-Pb collisions at √ s NN = 2 . 76 TeV. By selecting events in the same centrality interval, but with very different average ﬂow, different initial-state conditions can be studied. We ﬁnd the effect of the event-shape selection on the elliptic ﬂow coefﬁcient v 2 to be almost independent of transverse momentum p T , which is as expected if this effect is attributable to ﬂuctuations in the initial geometry of the system. Charged-hadron, -pion, -kaon, and -proton transverse momentum distributions are found to be harder in events with higher-than-average elliptic ﬂow, indicating an interplay between radial and elliptic ﬂow.


I. INTRODUCTION
Results from lattice quantum chromodynamics [1,2] predict the existence of a plasma of deconfined quarks and gluons, known as the "quark gluon plasma" (QGP). This state of matter can be produced in the laboratory by colliding heavy nuclei at relativistic energies [3][4][5]. The QGP was found to behave as a nearly perfect liquid and its properties can be described using relativistic hydrodynamics (for a recent review, see Ref. [6]). The current experimental heavy-ion programs at Brookhaven's Relativistic Heavy Ion Collider and at CERN's Large Hadron Collider (LHC) are aimed at a precise characterization of the QGP, in particular of its transport properties.
The system created in a heavy-ion collision expands and hence cools down, ultimately undergoing a phase transition to a hadron gas, which then decouples to the free-streaming particles detected in the experiments [6]. A precision study of the QGP properties requires a detailed understanding of this expansion process. If the initial geometry of the interaction region is not azimuthally symmetric, a hydrodynamic evolution of a nearly ideal liquid (i.e., with a small value of the shear viscosity over entropy ratio η/s) gives rise to an azimuthally anisotropic distribution in momentum space for the produced particles. This anisotropy can be characterized in terms of the Fourier coefficients v n of the particle azimuthal distribution [7]. The shape of the azimuthal distribution, and hence the values of these Fourier coefficients, depend on the initial conditions and on the expansion dynamics. The geometry of the initial state fluctuates event by event and measurements of the resulting v n fluctuations pose stringent constraints on initial-state models. A quantitative understanding of the initial geometry of the produced system is therefore of primary importance [6]. A number of different experimental measurements and techniques have been proposed to * Full author list given at the end of the article. disentangle the effects of the initial conditions from QGP transport, including measurements of correlations of different harmonics [8], event-by-event flow fluctuations [9][10][11][12], and studies in ultracentral collisions [13,14]. Recent results from pp and p-Pb collisions at the LHC, moreover, suggest that hydrodynamic models may be also applicable to small systems [15][16][17][18][19]. This further highlights the importance of studying Pb-Pb collisions with more differential probes, to investigate the interplay between the initial conditions and the evolution, in the system where the hydrodynamic models are expected to be most applicable.
One of the new tools for the study of the dynamics of heavyion collisions is the "event shape engineering" (ESE) [20]. This technique is based on the observation that the event-byevent variation of the anisotropic flow coefficient (v n ) at fixed centrality is very large [12]. Hydrodynamic calculations show that the response of the system to the initial spatial anisotropy is essentially linear for the second and third harmonic, meaning that the final state v 2 (and v 3 ) are very well correlated with the second (and third) order eccentricities in the initial state for small values of η/s [7,21,22]. These observations suggest a possibility to select events in heavy-ion collisions based on the initial (geometrical) shape, providing new opportunities to study the dynamics of the system evolution and the role of the initial conditions.
The ESE technique is proposed to study ensemble-averaged observables (such as v 2 and inclusive particle spectra) in a class of events corresponding to the same collision centrality, but different v n values. In this paper events are selected based on the magnitude of the second-order reduced flow vector q 2 (see Sec. III A). The technique was recently applied to study correlations between different flow harmonics in the ATLAS experiment [23]. In this paper we present the results on elliptic flow and charged-particle spectra in Pb-Pb collisions at √ s NN = 2.76 TeV obtained with the ESE technique. The events selected with the ESE technique are characterized by the measurement of v 2 to quantify the effect of the selection on the global properties of the event. To search for a connection between elliptic and radial flow the effect of the ESE selection on the inclusive transverse momentum distribution of charged hadrons, pions, kaons, and protons is then studied. The results are presented for primary charged particles, defined as all prompt particles produced in the collision including all decay products, except those from weak decays of light flavor hadrons and of muons. The differential measurement described in this work could provide important constraints to identify the correct model for initial conditions and for the determination of transport properties. The development of flow in hydrodynamical models is driven by the pressure gradients and anisotropy in the initial state. A correlation between anisotropic and radial flow may stem from the specific fluctuation pattern in the initial state and/or can be produced in the final state depending on the bulk and shear viscosity of the system [7]. A few important caveats, which can affect the selectivity of the ESE technique, have to be kept in mind in this study. First, the discriminating power of the q 2 selection depends on the multiplicity and v 2 value in the pseudorapidity, η, region where it is computed and on the intrinsic resolution of the detector used for the measurement. Second, nonflow effects (such as resonance decays, jets, etc. [22]) could bias the q 2 measurement. In this work we discuss both aspects in detail, making use of different detectors with different intrinsic resolution and different η coverage.
The paper is organized as follows. In Sec. II a brief review of the ALICE detector and of the data sample is presented. In Sec. III the analysis technique, with an emphasis on the event selection and the particle identification strategy, is discussed. The results are presented in Sec. IV. Their implication for the hydrodynamic interpretation is discussed in Sec. V. Finally, we come to our conclusions in Sec. VI.

II. ALICE DETECTOR AND DATA SAMPLE
The ALICE detector at the CERN LHC was designed to study mainly high-energy Pb-Pb collisions. It is composed of a central barrel (|η| 0.8 for full-length tracks), containing the main tracking and particle identification detectors, complemented by forward detectors for specific purposes (trigger, multiplicity measurement, centrality determination, muon tracking). A detailed description of the apparatus can be found in Ref. [24]. The main detectors used for the analysis presented in this paper are discussed below.
The main tracking devices in the central barrel are the inner tracking system (ITS) and the time projection chamber (TPC). They are immersed in a 0.5-T solenoidal field. The ITS is the detector closest to the interaction point. It is a six-layer silicon tracker with a very low material budget (∼7% of one radiation length X 0 ). The ITS provides information on the primary interaction vertex and is used to track particles close to the interaction point, with the first layer positioned at a radial distance of 3.9 cm from the interaction point and the sixth one at 43 cm. It can measure the transverse impact parameter (DCA xy ) of tracks with a resolution of about 300 (40) μm, for transverse momentum p T = 0.1 (4) GeV/c, allowing the contamination from secondary particles to be significantly reduced. The TPC [25] is a large-volume gas detector (external diameter 5 m) which measures up to 159 space points per track, providing excellent tracking performance and momentum resolution (σ p T /p T ∼ 6% at p T = 10 GeV/c) [26]. It is also used in this work to identify particles through the measurement of the specific energy loss, dE/dx. The dE/dx, computed as a truncated mean utilizing only 60% of the available samples, has a resolution of ∼5% in peripheral and ∼6.5% in central collisions [26]. At a radius of 3.7 m from the beam axis, the time-of-flight (TOF) detector measures the arrival time of particles with a total resolution of about 85 ps in Pb-Pb collisions, allowing a π/K (K/p) 2σ separation up to p T = 3(5) GeV/c. The ALICE reconstruction software performs tracking based either on the information from the TPC alone (TPC-only tracks) or on the combined information from the ITS and TPC (global tracks). The former have the advantage of an essentially flat azimuthal acceptance and are used for v 2 and q 2 measurements. The latter provide better quality tracks (σ p T /p T ∼ 1.5% at p T = 10 GeV/c) [26], rejecting most of the secondary tracks. However, the acceptance and reconstruction efficiency of global tracks are not flat in azimuth and as a function of transverse momentum, mostly owing to missing or inefficient regions of the ITS. These tracks are used for the p T distribution measurements. TPC-only tracks can be constrained to the primary vertex (reconstructed also using the ITS information) to provide better momentum resolution.
The data used for this analysis were collected in 2010, during the first Pb-Pb run at the LHC, at a center-ofmass energy per nucleon √ s NN = 2.76 TeV. The hadronic interaction rate was of the order of 100 Hz, low enough to avoid any space charge distortion effects in the TPC [27]. The trigger was provided by the V0 detector [28], a pair of forward scintillator hodoscopes placed on either side of the interaction region, covering the pseudorapidity regions 2.8 < η < 5.1 (V0A) and −3.7 < η < −1.7 (V0C). Events were requested to have a signal in both sides of the V0, selecting roughly 0%-90% most central collisions [29]. The V0 measures a signal whose average amplitude is proportional to the multiplicity of charged particles. The V0 acceptance times detection efficiency is approximately 90% and flat as a function of the particle p T , with only a small reduction to about 85% for p T < 300 MeV/c. Events are further selected offline using the timing information from the V0 and from a set of two forward zero-degree calorimeters (ZDCs), to reject contamination from beam-induced backgrounds (see Refs. [29][30][31] for a detailed discussion). After all selections, the event sample used in the analysis consists of about 16 × 10 6 events.

A. Centrality and the event-shape selection
The events which pass the basic selection described in Sec. II are divided in centrality classes based on the signal amplitude (proportional to the charged-particle multiplicity) measured in the V0 detector, as described in Ref. [29]. Events in each centrality class are further subdivided into groups with different average elliptic event shapes based on the magnitude of the second-order reduced flow vector q 2 [22] given as

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where M is the multiplicity and | Q 2 | = √ Q 2 2,x + Q 2 2,y is the magnitude of the second-order flow vector.
In this paper, the flow vector Q 2 is calculated using the TPC or V0 detectors. In the TPC, tracks in the range 0.2 < p T < 20 GeV/c and |η| < 0.4 (to avoid an overlap with the η region used for the v 2 and p T distribution measurements) are used to measure where ϕ i is the azimuthal angle of the ith particle and M is the number of tracks in an event.
In the forward rapidity region the V0 is used. This detector is segmented into four rings, each consisting of eight azimuthal sectors; the flow vector is hence calculated as where the sum runs over all 32 channels, ϕ i is the angle of the center of the sector containing channel i, w i is the amplitude measured in channel i, and M is in this case the sum of the amplitudes measured in each channel. The discriminating power of q 2 depends on the magnitude of elliptic flow as well as on the track multiplicity used in the q 2 calculation and on the performance of the detector, including the angular resolution or the linearity of the response to the charged particle multiplicity. The good resolution of the TPC and the large multiplicity at midrapidity are used to maximize the selectivity on q 2 . However, the ALICE central barrel acceptance enables only limited separation in pseudorapidity between the region used to calculate q 2 and the region used to calculate the observables (| η| = 0.1). This separation is introduced to suppress unwanted nonflow correlations, which typically involve only a few particles and are, in general, of short range. To further assess the contribution of nonflow correlations, the flow vector is also calculated using the V0 detectors. This leads to a separation of more than one unit in pseudorapidity between the two regions.
In the absence of correlations, the average length of Q 2 grows as √ M [22]: q 2 is introduced to remove this trivial part of the multiplicity dependence. In case of nonzero correlations (owing to either collective flow or nonflow correlations), q 2 depends on multiplicity and on the strength of the flow as [22,32] where the parameter δ 2 accounts for nonflow correlations and the angular brackets denote the average over all events.
In the case when the multiplicity is measured via the signal amplitude in the V0 detector, the first term in Eq. (4) (unity) has to be substituted by e 2 i / e i 2 , where e i is the energy deposition of a single particle i. The fluctuations in e i lead to an increase in the flow vector length and reduce the corresponding event plane resolution.
The q 2 distribution measured with the TPC (q TPC 2 ) and V0C (q V0C 2 ) is shown in Fig. 1 as a function of centrality and in two narrow centrality classes, 0%-1% and 30%-31%. As can be seen, q 2 reaches values twice as large as the mean value, as expected in case of large initial-state fluctuations [20]. The q V0C 2 is larger than q TPC 2 , as the former is measured in a larger pseudorapidity window (integrating a larger multiplicity) and is sensitive to the fluctuations in e i . Note also that the selectivity (discrimination power) of the two selection cuts is, in principle, different, owing to the different detector resolution, and, in the case of V0C, smaller v 2 value at forward η, fluctuations in e i , and large contribution of secondary particles.
In the present analysis, the effect of the ESE on v 2 and p T distributions is studied. The average flow and particle spectra are measured in the pseudorapidity range 0.5 < |η| < 0.8 to avoid overlap with the region used to calculate q TPC 2 . The V0C selection is used to estimate the contribution of nonflow correlations to the event-shape selection, because it provides a large η gap. As a further cross-check, the analysis was also repeated using the V0A detector. The results obtained with V0A and V0C show a qualitative agreement with a better selectivity when the V0C is used (mostly owing to the larger multiplicity in the acceptance of this detector and to the η dependence of the elliptic flow). We therefore report the results for events selected using q TPC 2 and q V0C 2 in this paper.
Owing to the limited statistics, the analysis has to be performed in relatively wide centrality classes (∼10%). The length of q 2 changes within such large centrality intervals ( Fig. 1), and a cut at a fixed value of q 2 would introduce a dependence on the multiplicity that would obscure the effect of the event-shape selection. The q 2 selection is therefore evaluated in narrow (1%-wide) centrality classes. The results presented in the next sections are obtained in two event-shape classes, corresponding to the 10% of the events having the top (bottom) value of the q 2 (estimated in the narrow centrality classes). In the following, we refer to these two classes as "large-q 2 " (90%-100%) and "small-q 2 " (0%-10%) or, generically, as ESE-selected events. Conversely, we refer to the totality of data within a given centrality class as the "unbiased" sample.
The correlation between q TPC 2 and q V0C 2 is illustrated for events in the 30%-31% centrality class in Fig. 2. The left (right) panel shows the distribution of q 2 measured with the TPC (V0C) for all events and for events in the large-q 2 and small-q 2 classes, selected with the V0C (TPC). The average q 2 changes by about 18% and 14% in the large-q 2 and small-q 2 samples, respectively. To control the effect of fluctuations in a given detector, the detailed comparison of the results obtained with q TPC 2 and q V0C 2 is crucial, as discussed in detail below. To disentangle the effect of the η gap and of the q 2 cut, the selection on q TPC 2 is also adjusted such that the average flow measured at midrapidity is similar to the one in the large-q 2 sample (Sec. IV).
The ESE becomes less selective in peripheral events regardless of the detector used to compute q 2 , owing to the low multiplicity. This limits the present analysis to the 60% most central events. (bottom row) as a function of centrality (left column) and projections for two centrality classes, 0%-1% and 30%-31% (right column). In each of the left panels the solid curve shows the average q 2 as a function of centrality, while the dashed and the dotted curves indicate the top 10% and the bottom 10%, respectively.
Space charge distortion effects in the TPC, which accumulate over many events, could, in principle, bias the q 2 selection. To check for this and other possible instrumental effects, it was verified that the results are not sensitive to the instantaneous luminosity.

B. Elliptic flow measurement
The elliptic flow, v 2 , is measured in the pseudorapidity range 0.5 < |η| < 0.8 using the scalar-product (SP) method [22], according to where u 2,k = exp(i2ϕ k ) is the particle's unit flow vector, ϕ k is the azimuthal angle of the kth particle of interest, Q 2 is the flow vector, and M is the multiplicity. The full event is divided in two independent subevents, labeled A and B, covering two different pseudorapidity ranges, 0.5 < η < 0.8 and −0.8 < η < −0.5. The particle's unit flow vector u 2,k is evaluated in the subevent A, while the flow vector Q 2 and the multiplicity M in the subevent B and vice versa, ensuring a pseudorapidity gap of | η| > 1 between the particle of interest and the reference charged particles, which suppresses the nonflow contribution in the calculation of v 2 {SP}. A flat acceptance in azimuth is achieved in this analysis selecting TPC-only tracks, constrained to the primary vertex. Tracks are required to have at least 70 clusters and a χ 2 4 per TPC cluster (two degrees of freedom). Tracks with a transverse distance of closest approach to the vertex (computed before constraining tracks to the primary vertex) DCA xy > 2. 4  are rejected to reduce the contamination from secondary tracks. The effect of secondary particles is corrected applying the same analysis procedure to Monte Carlo events, simulated with the AMPT event generator [33] and propagated through a GEANT3 [34] model of the detector. The v 2 {SP} computed using reconstructed tracks is then compared with the one computed with generated primary particles, and the difference (<5%) is used as a correction factor.
The uncertainty on the tracking efficiency was assessed with different track samples and selections: using a set of hybrid tracks, built from a combination of global and TPC-only tracks to obtain a uniform azimuthal acceptance [35], using TPC-only tracks not constrained to the primary vertex, varying the minimum number of TPC clusters required in the analysis from 70 to 50 (track reconstruction in Tables I and II), and weighting each track by the inverse of the (p T -dependent) efficiency (tracking efficiency).
The procedure used to estimate the centrality percentiles leads to a ∼1% uncertainty in the definition of the centrality classes [29]. To propagate this uncertainty to the results presented in this paper, the measurement is repeated displacing the centrality percentile by 1%. For instance, the analysis in the 30%-40% centrality class is repeated for the selection 30.3%-40.4% (centrality resolution). Moreover, tracks reconstructed at midrapidity (instead of the V0 signal) are used as the centrality estimator (centrality estimator).
The correction for the effect of secondary particles mentioned above is strongly model dependent; therefore, the difference between the v 2 estimated using generated AMPT particles and reconstructed tracks was used to estimate the corresponding systematic uncertainty, ∼3.5% (0.7%) at p T = 0.2 (1.5) GeV/c (secondary particles).
Moreover, the following systematic checks were considered. The dependence on the magnetic-field configuration  was studied analyzing separately samples of events collected with different polarities of the magnetic field (magnetic field), analyzing positive and negative particles separately (charge), and analyzing samples of tracks produced at different vertex positions: −10 < z vtx < 0 cm and 0 < z vtx < 10 cm (vertex). These effects are found to be not significant.
The systematic uncertainties in the v 2 measurements and in the ratios of v 2 in ESE-selected over unbiased events are summarized in Tables I and II. Only the checks and variations that are found to be statistically significant are considered in the systematic uncertainties [36]. Whenever the p T dependence of the uncertainty is not negligible, values for characteristic p T are given in the tables.

C. Transverse momentum distribution measurement
The measurement of the p T distributions uses global tracks, which provide good resolution on DCA xy (Sec. II) and hence good separation of primary and secondary particles. The track selection requires at least 70 clusters in the TPC and at least 2 points in the ITS, of which at least one must be in the first two layers to improve the DCA xy resolution. A p T -dependent cut on the DCA xy , corresponding to 7 times the experimental resolution on DCA xy , is applied to reduce the contamination from secondary particles. Tracks with a χ 2 per point larger than 36 in the ITS and larger than 4 in the TPC are rejected. Finally, to further reduce the contamination from fake tracks, a consistency cut between the track parameters of TPC and global tracks was applied. For each reconstructed TPC track, the χ 2 difference between the track parameters computed using only the TPC information constrained to the vertex and the associated global track is required to be less than 36 [37]. Charged tracks are studied in the pseudorapidity window 0.5 < |η| < 0.8, to avoid an overlap with the q TPC 2 calculation. Particles are identified using the specific energy loss dE/dx in the TPC and their arrival time in the TOF. The technique is similar to the one presented in Ref. [15]. A track is identified as either a pion, a kaon, or a proton based on the difference, in the detector resolution units, from the expected energy loss and/or TOF nσ i PID (with i being the particle identity under study). Below p T = 0.5 GeV/c, only the TPC information is used (nσ i PID = nσ i TPC ). For larger p T , the TPC and TOF information is combined using a geometrical mean: Tracks are required to be within 3σ PID of the expected value to be identified as π ± , K ± , or p (p). In the region where the 3σ PID identification bands of two species overlap, the identity corresponding to the smaller nσ PID is assigned. This technique gives a good track-by-track identification in the following p T ranges: 0.2 < p T < 4 GeV/c for π ± , 0.3 < p T < 3.2 GeV/c for K ± , 0.5 < p T < 4 GeV/c for p (p). The misidentification of tracks is below 4% for pions, 25% for kaons, and 10% for protons in those ranges. Further discussion on the ALICE particle identification (PID) performance can be found in Refs. [26,38]. The results for identified particles are provided in the pseudorapidity range 0.5 < |η| < 0.8. However, in the case of the q V0C 2 selection the results were also studied at midrapidity |y| < 0.5. Results for positive and negative particles are consistent. In the following, "pions," "kaons," and "protons," as well as the symbols "π ," "K," and "p," refer to the sum of particles and antiparticles.
The results for the spectra in ESE-selected events are presented in terms of ratios between the distributions measured in the large-q 2 (small-q 2 ) samples and the unbiased sample. The unbiased spectra have already been reported in Refs. [37,38]. Most of the corrections (and uncertainties) cancel out in these ratios, allowing for a precise determination of the effect owing to the event-shape selection, as discussed in detail below. The uncertainties can mostly arise owing to effects that depend on the local track density, which are found to be small [39].
The systematic uncertainties are summarized in Tables III and IV. As mentioned before, only the checks and variations that are found to be statistically significant are considered in the systematic uncertainties [36].  The systematic uncertainty related to the tracking is estimated varying the track selection cuts. Instead of the standard TPC cluster cut, at least 120 (of 159) pad-row hits in the TPC and a fraction of shared clusters in the TPC <0.4 are required (track reconstruction in Tables III and IV).
The possible effect of a track-density-dependent efficiency (which would influence in a different way events with the large-and small-q 2 selection) is investigated using simulations based on the AMPT event generator [33] and a parametric event generator tuned to reproduce the ALICE spectra and v 2 measurements [39]. This effect leads to an uncorrelated systematic error of about 0.2% and a normalization error of 0.4% (tracking efficiency).
The uncertainty on the centrality is estimated varying the definitions of centrality classes by 1% and using tracks as the centrality estimator. These checks lead to an uncorrelated uncertainty of about 0.1% and 0.35%, respectively, and a normalization uncertainty below 1% in the ratios of spectra (centrality resolution and centrality estimator).
The systematic effect related to the particle identification is studied performing several variations to the PID approach described above. The nσ PID cut is varied between 2 and 4. Alternatively, if a track is consistent with more than one particle assignment within the nσ PID cut, double counting is allowed. As compared to the standard strategy where only the identity closest to the measured nσ PID is selected, this approach leads to a slightly larger contamination from misidentified tracks, but also to a larger efficiency. Finally, an exclusive nσ PID strategy was used, which drastically reduces misidentification: a particle is accepted only if it is compatible with only one mass hypothesis at 3σ PID . As a further cross-check, a Bayesian approach [26] was also considered. This method allows for better control of contamination at high p T . Overall, the uncertainty related to the particle identification strategy is less than 0.1% (PID).
The effect of secondary particles depends on the p T distribution of weakly decaying primary particles, and could be different for the large-and small-q 2 samples. This effect is estimated to be at most ∼0.1% for protons with the TPC ESE selection and negligible in all other cases (secondary particles).
Possible effects related to the magnetic field and to the charge state are addressed studying separately events collected with different magnet polarities (magnetic field) and different charges (charge), as in the case of the v 2 {SP} measurement. Particles produced at different longitudinal position cross a different portion of the detector, with different reconstruction efficiency. The samples of events produced with a negative (−10 < z vtx < 0 cm) and positive (0 < z vtx < 10 cm) longitudinal vertex coordinate with respect to the nominal interaction point were studied separately (vertex).

A. Charged-particle elliptic flow
The event-shape selection is studied in Fig. 3, where the v 2 {SP} as a function of p T is reported for the unbiased and ESE-selected samples, with both the q TPC 2 (|η| < 0.4) and q V0C 2 (−3.7 < η < −1.7) selections in different centrality classes. Figure 4 shows the ratio between the v 2 measured with the large-q 2 (small-q 2 ) selection and the unbiased sample. Selecting the 10% highest (lowest) q TPC 2 samples leads to a change of 30%-50% in the v 2 {SP} measured, depending on centrality. The change is smaller (∼10%-25%) in the case of q V0C 2 -based selection, as compared to the q TPC 2 case. As already indirectly inferred from the difference between second-and fourth-order flow cumulants v 2 {2} and v 2 {4} in Ref. [12], the elliptic flow response of the system to geometry fluctuations is almost independent of p T . For all centralities, the change observed in Fig. 4 depends indeed weakly on p T , up to at least 4-5 GeV/c. This indicates that a cut on q 2 selects a global property of the event, likely related to the initial shape in the overlap region. The only exception to the previous observation is the 0%-5% centrality class, where for the q TPC 2 selection an increasing trend with p T is observed. In this centrality class the mean value of v 2 is small, owing to the almost isotropic shape in the initial state. Moreover, relative flow fluctuations are large in central collisions, with a p T dependence similar to the one shown in Fig. 4 [12]. The analysis of the p T spectra presented in Sec. IV B gives additional insight into the trend observed in Fig. 4.
For p T 4-5 GeV/c, the ratio ESE-selected/unbiased v 2 {SP} increases for the large-q 2 selection. This trend is more pronounced for the q TPC  selection. Fitting the ranges p T < 5 GeV/c and p T > 5 GeV/c with two different constants indicates an increase for the large-q 2 selection of order 5% and 10% for the q V0C 2 and q TPC 2 selections, respectively. This difference could be attributable to a small nonflow-induced bias. At high p T the v 2 is believed to be determined by the path-length dependence of parton energy loss [12].
The difference between the q TPC 2 and q V0C 2 is attributed to the different selectivity (see Sec. III A), but also to a different contribution of nonflow correlations between the q 2 and the v 2 measurements. Replacing the q TPC   one changes both nonflow and selectivity at the same time.

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To disentangle these two contributions, the selectivity of the q TPC 2 selection was artificially reduced. This is achieved either relaxing the selection itself or rejecting a random fraction of tracks for the computation of q TPC 2 , while still selecting 10% of the events. It is found that selecting the class 65%-100% for the large-q 2 sample (0%-55% for the small-q 2 sample) with q TPC 2 , or alternatively rejecting 70% of the TPC tracks, leads to an average variation of the v 2 {SP} in the range 0.2 < p T < 4 GeV/c comparable to the one obtained with the standard 10% q V0C 2 selection. The results are shown in Fig. 5 for the centrality class 30%-40%. Not only is it possible to find a cut which leads to the same average variation in v 2 {SP}, but the p T dependence is very similar in both cases. Rejecting randomly 70% of the tracks changes the selectivity of q TPC 2 without affecting nonflow correlations between the q TPC 2 selection and v 2 {SP} measurement (as the η gap is not varied). Also in this case, it is found that the effect of the q 2 selection does not depend on p T . A similar result, with the same value of the relaxed cut or fraction of rejected tracks, is found for the centrality interval 10%-50%. Moreover, as discussed in the next section, the same relaxed selections lead to the same effect on the p T distributions.
These checks demonstrate that the selectivity of the cut is the main reason for the difference between the TPC and V0C selections. Owing to the large η gap, the nonflow contribution is expected to be negligible in the case of the q V0C 2 selection. The agreement observed in Fig. 5 indicates that, in the centrality classes 10%-50%, this is also the case for the q TPC 2 selection in the range p T < 5 GeV/c, a transverse momentum region dominated by hydrodynamic effects [38]. It is worth noticing that the ATLAS Collaboration measured a modification of the elliptic flow of ∼35%, nearly independent of p T up to ∼12 GeV/c in the 20%-30% centrality class, while measuring v 2 and q 2 with a pseudorapidity gap of 0.7 Centrality (%) units [23]. The increasing trend in the centrality class 0%-5% is also observed in Ref. [23]. 1 To study the centrality and the q 2 dependence of v 2 {SP} in ESE-selected event classes, we quantified the average change for each centrality class fitting the ratios in the range 0.2 < p T < 4 GeV/c with a constant. 2 The centrality dependence of the average change in the large-q 2 and small-q 2 selection is reported in Fig. 6. The trend obtained with the q TPC 2 and q V0C 2 selections is very similar, except for the most central class 0%-5%, where the average is influenced by the nonflat trend seen in Fig. 4. This once again reinforces the conclusion that the nonflow contamination is small also in the TPC selection case for the bulk of particles. The relative importance of nonflow changes with centrality. A large nonflow bias would therefore introduce a centrality dependence in the relative trend between the q TPC 2 and the q V0C 2 selections, which is not observed. The dependence of the v 2 {SP} variation on q TPC 2 and q V0C 2 is shown for the centrality classes 5%-10%, 30%-40%, and 50%-60% in Fig. 7. The left panel shows the absolute q 2 values on the x axis, while the right panel depicts the self-normalized values, defined as the average q 2 value in ESE-selected events over the average q 2 values for all events in a given centrality class. The V0C selection spans a larger range but the TPC is more selective, as is clearly seen from the different slope of the TPC and V0C curves. In both cases the average q 2 reaches values twice as large compared to those in the unbiased sample (Fig. 7,  right).
In summary, the observations reported in this section indicate that the ESE selects a global property of the collisions, as suggested by the flat modification in the v 2 as a function of p T . The q TPC 2 leads to a change twice as large than the 1   corresponding q V0C 2 selection. The difference between the two seems to be mostly attributable to the different discriminating power rather than to nonflow effects.

B. Transverse momentum distributions
To study the interplay between the initial configuration of the system and the dynamics of the expansion of the fireball, the effect of the ESE selection on the single particle p T distribution is reported in Fig. 8, for the q TPC 2 and q V0C 2 selections. As discussed in Sec. III A, the reduced flow vector is calculated in the TPC detector in the pseudorapidity range |η| < 0.4. To avoid overlap between the q TPC 2 and p T distribution measurements, only the region 0.5 < |η| < 0.8 is used to measure the p T distributions. This ensures at least 0.1 units of pseudorapidity separation between the q 2 and spectra measurements, thus suppressing the effect of short-range correlations. For consistency with the TPC analysis, the same pseudorapidity range is used in the case of the V0C selection. In the q V0C 2 case, it is also possible to study the spectra at midrapidity |η| < 0.8 without any overlap with the q 2 measurement. The results agree within uncertainty with those in 0.5 < |η| < 0.8.
The spectra in the large-q 2 sample are harder than those in the small-q 2 one. The ratio to the unbiased spectra reaches a maximum around p T = 4 GeV/c and then stays approximately constant within large uncertainties.
The effect of the selection is more pronounced in semicentral events (∼30%-50%) and decreases both towards more central and more peripheral collisions. This can be attributable to the fact that the q 2 spans a larger dynamic range in semicentral collisions (Figs. 1 and 7). In the most peripheral centrality class studied in this paper (50%-60%) the effect of the TPC-based selection is still very pronounced, while   9. Ratio of the p T distribution of charged hadrons in the large-q 2 or small-q 2 sample to the unbiased sample. Comparison between the effect of the event-shape selection obtained with the standard V0C and with the tuned TPC selections (see text for details), in the centrality class 30%-40%. the q V0C 2 selection is less effective. This may indicate a small contamination from nonflow effects in the most peripheral class, consistent with observations discussed for the v 2 {SP} measurement in Sec. IV A. In the most central class (0%-5%) the modification of the spectrum is very small. This suggests that the trend observed in the same centrality class in Fig. 4 is likely to be dominated by flow fluctuations rather than nonflow contributions.

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As in the previous section, we disentangle the effect of nonflow and q 2 selectivity either relaxing the q TPC 2 selection or randomly rejecting a fraction of the tracks. The relaxed cut and the fraction of rejected tracks tuned to reproduce the v 2 variation in 0.2 < p T < 4 GeV/c in Sec. IV A are used. Figure 9 shows that these selections yield results compatible with the standard q V0C 2 selection. A similar result (with the same relaxed cuts or fraction of rejected tracks) is found for all centralities up to ∼50%, after which nonflow effects seem to become relevant.
As discussed in Sec. IV A, we conclude that the effect of nonflow is small and that the main factor driving these observations is the average v 2 at midrapidity.
The modification on the spectra of identified π , K, and p is reported in Figs. 10 and 11 for different centrality classes. The same pattern measured in the case of nonidentified hadrons is observed. Moreover, a clear mass ordering is seen: the modification is more pronounced for heavier particles. Conversely, the spectra in the small-q 2 sample are softer. In the case of the V0C selection the analysis was also repeated in the region |y| < 0.5, yielding consistent results.
These observations suggest that the spectra in the large-q 2 (small-q 2 ) sample are affected by a larger (smaller) radial flow push. This hypothesis was tested with a blast-wave [40] study. A ratio of two blast-wave functions was used to fit the spectra ratios shown in Figs. 10 and 11. The parameters were initially fixed to the values from Ref. [38], where they were tuned to describe the inclusive spectra of pions, kaons, and protons. Then, the β T parameter of the numerator function was allowed to change (while keeping the overall integral of the function constant). The fit was performed as in Ref. [38] in the transverse momentum ranges 0.5-1, 0.2-1.5, and 0.3-3 GeV/c for π , K, and p, respectively. The agreement with the data is good, also outside the range used to determine the parameters, up to p T ∼ 3 GeV/c. The fits yield the following result for the difference β T between the β T parameter of the numerator and denominator function: β T = (0.41 ± 0.03)% (large-q 2 ) and β T = (−0.22 ± 0.03)% (small-q 2 ) for the centrality class 30%-40%, as shown in Fig. 12.

V. DISCUSSION
In this paper the first application of the ESE [20] to the analysis of ALICE data was presented.
The results on the v 2 {SP} measurement suggest that the ESE technique selects a global property of the collision, likely related to the eccentricity in the initial state. The measurement of p T spectra indicates that events with larger eccentricity show an increased radial flow. A correlation between elliptic and radial flow could be introduced either at the initial stage, owing to the specific fluctuation patterns in the energy deposition, or during the hydrodynamic evolution of the system, owing to an interplay of bulk and shear viscosity [7].
A Glauber Monte Carlo simulation was performed to estimate the possible correlation between the initial eccentricity and azimuthally averaged pressure gradients. In the model, the multiplicity of charged particles in the acceptance of the V0 detector, used to determine the centrality classes, is computed following Ref. [29]. A "number of ancestors" N ancestors is derived from the number of participant nucleons (N part ) and binary collisions (N coll ) as Each ancestor is assumed to produce particles following a negative binomial distribution with parameters taken from Ref. [29]. The participant density, defined following Refs. [9,[41][42][43] as N part /S, is used as a proxy for the average pressure gradients. The average cross-sectional area S and participant eccentricity are computed as where The unprimed coordinates are given in the fixed laboratory coordinate frame. Primed coordinates, x and y , are calculated in the so-called participant coordinate system, rotated with respect to the laboratory coordinate frame such that the minor symmetry axis of the participant nucleon distribution coincides with the x direction. The normalization of the area is chosen such that for a Gaussian distribution the average density coincides with N part /S.  Two narrow centrality classes, selected based on the simulated charged particle multiplicity, roughly corresponding to 0%-2% (central) and 30%-32% (semicentral), are studied in Fig. 13. The observed correlation between the density and the participant eccentricity is reminiscent of the correlation between radial flow and event shape measured in this paper. The average density in events with the 10% largest is about 1% (7%) larger than in events with the smallest for central (semicentral) collisions, qualitatively consistent with what is observed in Figs. 10 and 11, where the effect of the ESE selection is much stronger for semicentral collisions. This reinforces our conclusion that ESE is an effective tool to select the initial shape and density, thereby opening the possibility of further studies.
A quantitative comparison would require a full hydrodynamical calculation. The correlation can, in fact, be modified by the transport in the hydrodynamic phase. In particular, it was shown [7,44] that in a system with a finite shear viscosity the flow coefficients, obtained for a given set of initial eccentricities, are reduced as compared to the ideal hydrodynamics case. At the same time, shear viscosity increases the radial flow. In principle, bulk viscosity reduces the radial flow, reducing 034916-12  the correlation observed in this paper, but the latter effect was estimated to be negligible [44]. Therefore, the measurement we present in this paper is sensitive to the interplay of initial conditions and transport coefficients in the hydrodynamic phase. As such, it poses stringent constraints on hydrodynamic calculations, and it could allow the extraction of the value of average shear viscosity at the LHC.
A study of the relation of the fluctuation in the initial size to the spectra was performed in Refs. [45,46] with a full hydrodynamic simulation. It was shown that the eventby-event fluctuations in the Glauber initial conditions lead to fluctuations in the initial size of the system that reflect in fluctuations of the radial flow and hence p T . It is found that the relative p T fluctuations computed with Glauber initial conditions overestimate the data, indicating a strong sensitivity of event-by-event measurements on the initial conditions model. It is also shown that the p T fluctuations are not sensitive to the shear viscosity. The study in Refs. [45,46] (fluctuations in p T ), however, does not address the relation between the elliptic and the radial flows. It may be expected that the present measurement will also be sensitive to the transport coefficient of the medium.   12. Ratio of the p T distribution of identified charged hadrons in the large-q 2 (top) and small-q 2 (bottom) sample to the unbiased sample (q TPC 2 selection), in 30%-40% centrality class. Lines: ratio of the blast-wave parametrizations (see text for details).

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In a recent series of theoretical studies [47][48][49], it was suggested to use the principal component analysis (PCA) to study flow fluctuations. It was argued that most of the current methods to study flow do not fully capture the complexity of the initial state. Indeed, the PCA studies revealed the presence of subleading flow components (arising from radial geometry excitations), which break the factorization of flow harmonics [47,48], In particular, in Ref. [49] it is argued that the subleading component of v 2 reflects a nonlinear mixing with radial flow, which could address the same physics as reported in this paper.
To further understand the observed effect, we studied it in AMPT, a model known to reproduce many of the flow observables measured at the LHC [33]. This model is based on HIJING [50] to describe the initial conditions and on the Zhang's parton cascade [51] to describe the partonic evolution. The string melting configuration, described in Ref. [52], is used. To assess the impact of the detector resolution on the q 2 selection, the simulated AMPT events were transported through the ALICE apparatus using the GEANT [34] transport model. The q 2 was computed in |η| < 0.4 using either the reconstructed Monte Carlo tracks (q rec 2 ) or the generated primary particles in the same kinematic range (q gen 2 ). The elliptic flow and the transverse momentum distribution are calculated using generated Monte Carlo particles. Because the charged-particle multiplicity distribution is different in AMPT and data, the q 2 selection is calibrated in the model as a function of multiplicity. The results are shown in Fig. 14 for the charged-hadron elliptic flow and in Fig. 15 for the transverse momentum distribution of charged hadrons. Using either q rec 2 or q gen 2 does not introduce any significant difference on the effect of the selection. This indicates that detector resolution effects are negligible for the q TPC 2 selection. The V0 detectors, however, have a coarser azimuthal resolution and are sensitive to fluctuations in the energy deposition of incident particles. However, the study with the relaxed TPC selection discussed in Sec. IV demonstrates that the properties of the ESE-selected events are mostly determined by the average v 2 {SP} value. It is therefore advised that in any comparison of this data to theoretical models the selection in the model is tuned as to reproduce the average change in v 2 {SP} at midrapidity.
The p T dependence of the elliptic flow observed in data is not reproduced in AMPT (top panel). This model reproduces, however, the magnitude of the modification, as well as the flatness of the ratio as a function of p T .
The effect of the ESE selection on the p T distribution of charged particles is well reproduced by AMPT below p T = 2 GeV/c, as shown in Fig. 15. However, the magnitude of the effect at intermediate p T (2 < p T < 6 GeV/c) is underestimated in AMPT. As previously observed for the v 2 measurement, a good agreement is observed between the selection based on q gen 2 and q rec 2 .

VI. CONCLUSIONS
In summary, the first application of the ESE technique to Pb-Pb collision data measured by ALICE at √ s NN = 2.76 TeV has been presented.
The elliptic flow at midrapidity is observed to increase as a function of the q 2 calculated in the central or forward rapidity regions. The modification of the v 2 coefficient as a function of p T is nearly flat below p T = 4 GeV/c, suggesting that this technique allows the selection of a global property of the collision, likely related with the geometry of the participant nucleons in the initial state. In the region above p T > 5 GeV/c a small increase is observed within the large statistical uncertainties, possibly owing to a small nonflow contamination. In this transverse momentum range the elliptic flow is believed to be driven by the different path length traversed in and out of plane by high-p T partons in the deconfined medium, rather than by the hydrodynamic evolution of the system.
The p T distributions of unidentified hadrons in the p T region (0 < p T < 5 GeV/c) are harder (softer) in events with large-q 2 (small-q 2 ) values.
Identified pions, kaons, and protons show a similar behavior with a clear mass ordering in the ratio between the large-q 2 and the unbiased spectra, thus suggesting this effect to be attributable to a stronger radial flow in such events. Glauber Monte Carlo calculations reveal a correlation between the transverse participant density and the participant eccentricity which could be the origin of this effect. This indicates that at least part of the correlation is generated in the initial state. However, these measurements are also sensitive to the transport coefficients in the hydrodynamic evolution. A quantitative comparison would require a full hydrodynamic calculation and may provide stringent constraints on both shear and bulk viscosity.

ACKNOWLEDGMENTS
The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support provided by all Grid centers and the Worldwide LHC Computing Grid (WLCG) collaboration. The ALICE Collaboration acknowledges the following funding agencies for their support in building and running the