University of Birmingham Measurement of transverse energy at midrapidity in Pb-Pb collisions at sNN =2.76 TeV

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nearly linearly with the collision volume, or equivalently, the number of participating nucleons at lower energies [24,31,32]. Further studies of heavy-ion collisions revealed deviations from this simple participant scaling law [25]. The causes of this deviation from linearity are still actively discussed and might be related to effects from minijets [33,34] or constituent quark scaling [28,35].
The ALICE detector [36] has precision tracking detectors and electromagnetic calorimeters, enabling several different methods for measuring E T . In this paper we discuss measurements of dE T /dη in Pb-Pb collisions at √ s NN = 2.76 TeV using the tracking detectors alone and using the combined information from the tracking detectors and the electromagnetic calorimeters. In addition we compare to calculations of dE T /dη from the measured identified particle transverse momentum distributions. Measurements from the tracking detectors alone provide the highest precision. We compare our results to theoretical calculations and measurements at lower energies.

II. EXPERIMENT
A comprehensive description of the ALICE detector can be found in Ref. [36]. This analysis uses the V0, zero-degree calorimeters (ZDCs), the inner tracking system (ITS), the time projection chamber (TPC), the electromagnetic calorimeter (EMCal), and the photon spectrometer (PHOS), all of which are located inside a 0.5-T solenoidal magnetic field. The V0 detector [37] consists of two scintillator hodoscopes covering the pseudorapidity ranges −3.7 < η < −1.7 and 2.8 < η < 5.1. The ZDCs each consist of a neutron calorimeter between the beam pipes downstream of the dipole magnet and a proton calorimeter external to the outgoing beam pipe.
The TPC [38], the main tracking detector at midrapidity, is a cylindrical drift detector filled with a Ne-CO 2 gas mixture. The active volume is nearly 90 m 3 and has inner and outer radii of 0.848 and 2.466 m, respectively. It provides particle identification via the measurement of the specific ionization energy loss (dE/dx) with a resolution of 5.2% and 6.5% in peripheral and central collisions, respectively.
The ITS [36] consists of the silicon pixel detector with layers at radii of 3.9 and 7.6 cm, the silicon drift detector with layers at radii of 15.0 and 23.9 cm, and the silicon strip detector with layers at radii of 38.0 and 43.0 cm. The TPC and ITS are aligned to within a few hundred μm using cosmic ray and pp collision data [39].
The EMCal [40,41] is a lead/scintillator sampling calorimeter covering |η| < 0.7 in pseudorapidity and 100 • in azimuth in 2011. The EMCal consists of 11 520 towers, each with transverse size 6 × 6 cm, or approximately twice the effective Molière radius. The relative energy resolution is 0.11 2 /E + 0.017 2 , where the energy E is measured in GeV [40]. Clusters are formed by combining signals from adjacent towers. Each cluster is required to have only one local energy maximum. Noise is suppressed by requiring a minimum tower energy of 0.05 GeV. For this analysis we use clusters within |η| < 0.6. The PHOS [42] is a lead tungstate calorimeter covering |η| < 0.12 in pseudorapidity and 60 • in azimuth. The PHOS consists of three modules of 64 × 56 towers each, with each tower having a transverse size of 2.2 × 2.2 cm, comparable to the Molière radius. The relative energy resolution is √ 0.013 2 /E 2 + 0.036 2 /E + 0.01 2 , where the energy E is measured in GeV [43].
The minimum-bias trigger for Pb-Pb collisions in 2010 was defined by a combination of hits in the V0 detector and the two innermost (pixel) layers of the ITS [8]. In 2011 the minimumbias trigger signals in both neutron ZDCs were also required [44]. The collision centrality is determined by comparing the multiplicity measured in the V0 detector to Glauber model simulations of the multiplicity [8,37]. These calculations are also used to determine the number of participating nucleons, N part . We restrict our analysis to the 0%-80% most central collisions. For these centralities corrections owing to electromagnetic interactions and trigger inefficiencies are negligible. We use data from approximately 70 000 0%-80% central events taken in 2011 for the tracking detector and EMCal measurements and data from approximately 600 000 0%-80% central events taken in 2010 for the PHOS measurement. We focus on a small event sample where the detector performance was uniform to simplify efficiency corrections because the measurement is dominated by systematic uncertainties.
Tracks are reconstructed using both the TPC and the ITS. Tracks are selected by requiring that they cross at least 70 rows and requiring a χ 2 per space point <4. Tracks are restricted to |η| < 0.6. Each track is required to have at least one hit in one of the two innermost ITS layers and a small distance of closest approach (DCA) to the primary vertex in the xy plane as a function of transverse momentum (p T ), defined by DCA xy < (0.0182 + 0.035/p 1.01 T ) cm, where p T is in GeV/c. The distance of closest approach in the z direction is restricted to DCA z < 2 cm. This reduces the contribution from secondary particles from weak decays, which appear as a background. With these selection criteria tracks with transverse momenta p T > 150 MeV/c can be reconstructed.
The typical momentum resolution for low-momentum tracks, which dominate E T measurements, is p T /p T ≈ 1%. The reconstruction efficiency varies with p T and ranges from about 50% to 75% [44].
Particles are identified through their specific energy loss, dE/dx, in the TPC when possible. The dE/dx is calculated using a truncated-mean procedure and compared to the dE/dx expected for a given particle species using a Bethe-Bloch parametrization. The deviation from the expected dE/dx value is expressed in units of the energy-loss resolution σ [45]. Tracks are identified as arising from a kaon if they are within 3σ from the expected dE/dx for a kaon, more than 3σ from the expected dE/dx for a proton or a pion, and have p T < 0.45 GeV/c. Tracks are identified as arising from (anti)protons if they are within 3σ from the expected dE/dx for (anti)protons, more than 3σ from the expected dE/dx for kaons or pions, and have p T < 0.9 GeV/c. Tracks are identified as arising from an electron (positron) and therefore excluded from the measurement of E π,K,p T if they are within 2σ from the expected dE/dx for an electron (positron), more than 4σ from the expected dE/dx for a pion, and more than 3σ from the expected dE/dx for a proton or kaon. With this algorithm approximately 0.1% of tracks arise from electrons or positrons misidentified as arising from pions and fewer than 0.1% of tracks are misidentified as arising from kaons or protons. Any track not identified as a kaon or proton is assumed to arise from a pion and the measurement must be corrected for the error in this assumption.
The PHOS and EMCal are used to measure the electromagnetic energy component of the E T and to demonstrate consistency between methods. Data from 2011 were used for the EMCal analysis owing to the larger EMCal acceptance in 2011. Data from one run in 2010 were used for the PHOS owing to better detector performance and understanding of the calibrations in that run period. The EMCal has a larger acceptance, but the PHOS has a better energy resolution. There is also a lower material budget in front of the PHOS than the EMCal. This provides an additional check on the accuracy of the measurement.

III. METHOD
Historically, most E T measurements have been performed using calorimeters, and the commonly accepted operational definition of E T is therefore based on the energy E j measured in the calorimeter's j th tower, where j runs over all M towers in the calorimeter and θ j is the polar angle of the calorimeter tower. The transverse energy can also be calculated using single-particle tracks. In that case, the index j in Eq. (1) runs over the M measured particles instead of calorimeter towers and θ j is the particle emission angle. To be compatible with the E T of a calorimetry measurement, the energy E j of Eq. (1) must be replaced with the single-particle energies E j = ⎧ ⎨ ⎩ E kin for baryons, E kin + 2mc 2 for antibaryons, E kin + mc 2 for all other particles. (2) This definition of E T was used in the measurements of the transverse energy by CMS [30] (based on calorimetry), PHENIX [26] (based on electromagnetic calorimetry), and STAR [29] (based on a combination of electromagnetic calorimetry and charged-particle tracking). To facilitate comparison between the various data sets the definition of E T given by Eqs. (1) and (2) is used here. It is useful to classify particles by how they interact with the detector. We define the following categories of final-state particles: (A) π ± , K ± , p, and p: Charged particles measured with high efficiency by tracking detectors (B) π 0 , ω, η, e ± , and γ , particles measured with high efficiency by electromagnetic calorimeters; (C) , , K 0 S , + , − , and 0 , particles measured with low efficiency in tracking detectors and electromagnetic calorimeters; (D) K 0 L , n, and n, neutral particles not measured well by either tracking detectors or electromagnetic calorimeters.
The total E T is the sum of the E T observed in final-state particles in categories A-D. Contributions from all other particles are negligible. In HIJING 1.383 [46] simulations of Pb-Pb collisions at √ s NN = 2.76 TeV the next-largest contributions come from the ( ) and ( ) baryons with a total contribution of about 0.4% of the total E T , much less than the systematic uncertainty on the final value of E T . The E T from unstable particles with cτ < 1 cm is taken into account through the E T from their decay particles.
When measuring E T using tracking detectors, the primary measurement is of particles in category A and corrections must be applied to take into account the E T which is not observed from particles in categories B-D. In the hybrid method the E T from particles in category A is measured using tracking detectors and the E T from particles in category B is measured by the electromagnetic calorimeter. An electromagnetic calorimeter has the highest efficiency for measuring particles in category B, although there is a substantial background from particles in category A. The E T from categories C and D, which is not well measured by an electromagnetic calorimeter, must be corrected for on average. Following the convention used by STAR, we define E had T to be the E T measured from particles in category A and scaled up to include particles in categories C and D and E em T to be the E T measured in category B. The total E T is given by We refer to E had T as the hadronic E T and E em T as the electromagnetic E T . We note that E had T and E em T are operational definitions based on the best way to observe the energy deposited in various detectors and that the distinction is not theoretically meaningful. and E T from tracking detectors. For centrality-and p Tindependent corrections the correction is listed. For centralityand p T -dependent corrections, the approximate percentage of the correction is listed. In addition, the anchor-point uncertainty in the Glauber calculations leads to an uncertainty of 0%-4%, increasing with centrality.

Correction
Value Relative uncertainty Several corrections are calculated using HIJING [46] simulations. The propagation of final-state particles in these simulations through the ALICE detector material is described using GEANT3 [47]. Throughout the paper these are described as HIJING + GEANT simulations.

A. Tracking detector measurements of E T
The measurements of the total E T using the tracking detectors and of the hadronic E T are closely correlated because the direct measurement in both cases is E π,K,p T , the E T from π ± , K ± , p, and p from the primary vertex. All contributions from other categories are treated as background. For E had T the E T from categories C and D is corrected for on average and for the total E T the contribution from categories B, C, and D is corrected for on average. Each of these contributions is taken into account with a correction factor.
The relationship between the measured track momenta and E π,K,p T is given by (4) where i runs over the n reconstructed tracks and η is the pseudorapidity range used in the analysis; ε(p T ) corrects for the finite track reconstruction efficiency and acceptance, f bg (p T ) corrects for the , , and K 0 S daughters and electrons that pass the primary track quality cuts; f notID corrects for particles that could not be identified unambiguously through their specific energy loss dE/dx in the TPC; and f p Tcut corrects for the finite detector acceptance at low momentum. Hadronic E T is given by E had T = E π,K,p T /f neutral , where f neutral is the fraction of E had T from π ± , K ± , p, and p and total E T is given by E T = E π,K,p T /f total where f total is the fraction of E T from π ± , K ± , p, and p. The determination of each of these corrections is given below and the systematic uncertainties are summarized in Table I. Systematic uncertainties are correlated point to point.

Single-track efficiency × acceptance ε( p T )
The single-track efficiency × acceptance is determined by comparing the primary yields to the reconstructed yields using 034903-3 HIJING + GEANT simulations, as described in Ref. [48]. When a particle can be identified as a π ± , K ± , p, or p using the algorithm described above, the efficiency for that particle is used. Otherwise the particle-averaged efficiency is used. The 5% systematic uncertainty is determined by the difference between the fraction of TPC stand-alone tracks matched with a hit in the ITS in simulations and data.

Background f bg ( p T )
The background comes from photons which convert to e + e − in the detector and decay daughters from , , and K 0 S , which are observed in the tracking detectors but do not originate from primary π ± , K ± , p, and p. This is determined from HIJING + GEANT simulations. The systematic uncertainty on the background owing to conversion electrons is determined by varying the material budget in the HIJING + GEANT simulationsby ±10% and found to be negligible compared to other systematic uncertainties. The systematic uncertainty owing to , , and K 0 S daughters is sensitive to both the yield and the shape of the , , and K 0 S spectra. To determine the contribution from , , and K 0 S decay daughters and its systematic uncertainty, the spectra in simulation are reweighted to match the data and the yields are varied within their uncertainties [49]. Because the centrality dependence is less than the uncertainty owing to other corrections, a constant correction of 0.982 ± 0.008 is applied across all centralities.

Particle identification f notID
The E T of particles with 0.15 < p T < 0.45 GeV/c with a dE/dx within two standard deviations of the expected dE/dx for kaons is calculated using the kaon mass and the E T of particles with 0.15 < p T < 0.9 GeV/c with a dE/dx within two standard deviations of the expected dE/dx for (anti)protons is calculated using the (anti)proton mass. The E T of all other particles is calculated using the pion mass. Because the average transverse momentum is p T = 0.678 ± 0.007 GeV/c for charged particles [50] and over 80% of the particles created in the collision are pions [45], most particles can be identified correctly using this algorithm. At high momentum, the difference between the true E T and the E T calculated using the pion mass hypothesis for kaons and protons is less than at low p T . This is therefore a small correction. Assuming that all kaons with 0.15 < p T < 0.45 GeV/c and (anti)protons with 0.15 < p T < 0.9 GeV/c are identified correctly and using the identified π ± , K ± , p, and p spectra [45] gives f notID = 0.992 ± 0.002. The systematic uncertainty is determined from the uncertainties on the yields.
Assuming that 5% of kaons and protons identified using the particle-identification algorithm described above are misidentified as pions only decreases f notID by 0.0002, less than the systematic uncertainty on f notID . This indicates that this correction is robust to changes in the mean dE/dx expected for a given particle and its standard deviation. We note that either assuming no particle identification or doubling the number of kaons and protons only decreases f notID by 0.005.

Low p T acceptance f p Tcut
The lower momentum acceptance of the tracking detectors is primarily driven by the magnetic field and the inner radius of the active volume of the detector. Tracks can be reliably reconstructed in the TPC for particles with p T > 150 MeV/c. The fraction of E T carried by particles below this momentum cutoff is determined by HIJING + GEANT simulations. To calculate the systematic uncertainty, we follow the prescription given by STAR [29]. The fraction of E T contained in particles below 150 MeV/c is calculated assuming that all particles below this cutoff have a momentum of exactly 150 MeV/c to determine an upper bound, assuming that they have a momentum of 0 MeV/c to determine a lower bound, and using the average as the nominal value. Using this prescription, f p Tcut = 0.9710 ± 0.0058. We note that f p Tcut is the same within systematic uncertainties when calculated from PYTHIA simulations [51] for pp collisions with √ s = 0.9 and 8 TeV, indicating that this is a robust quantity.

Correction factors f neutral and f total
Under the assumption that the different states within an isospin multiplet and particles and antiparticles have the same E T , f neutral can be written as and f total can be written as where E K T is the E T from one kaon species, E π T is the E T from one pion species, E p T is the average of the E T from protons and antiprotons, E T is the average E T from and , and E T is the average E T from + , − , and 0 and their antiparticles. The contributions E π T , E K T , E p T , and E T are calculated from the particle spectra measured by ALICE [45,49] as for the calculation of E T from the particle spectra. The systematic uncertainties are also propagated assuming that the systematic uncertainties from different charges of the same particle species (e.g., π + and π − ) are 100% correlated and from different species (e.g., π + and K + ) are uncorrelated. The contribution from the + , − , and 0 and their antiparticles is determined from the measured spectra. The total contribution from species and their antiparticles should be approximately equal to that of the and , but because there are three isospin states for the , each species carries roughly 1/3 of the E T that the carries. Because the 0 decays dominantly through a and has a short lifetime, the measured spectra include from the 0 decay. The ratio of F = (E + T + E − T )/E T is therefore expected to be 0.5. HIJING [46] simulations indicate that F = 0.67 and if the E T scales with the yield, THERMUS [52] indicates that F = 0.532. We therefore use F = 0.585 ± 0.085.
The contribution E ω,η,e ± ,γ T is calculated using transverse mass scaling for the η meson and PYTHIA simulations for the  ω, e ± , and γ , as described earlier. Because most of the E T is carried by π ± , K ± , p, p, n, and n, whose contributions appear in both the numerator and the denominator, f total and f neutral can be determined to high precision, and the uncertainty in f total and f neutral is driven by E T and E ω,η,e ± ,γ T . It is worth considering two special cases. If all E T were carried by pions, as is the case at low energy where almost exclusively pions are produced, Eq. (6) would simplify to f total = 2/3. If all E T were only carried by kaons, (anti)protons, and (anti)neutrons, Eq. (6) would simplify to f total = 1/2.
To calculate the contribution from the η meson and its uncertainties, we assume that the shapes of its spectra for all centrality bins as a function of transverse mass are the same as the pion spectra, using the transverse mass scaling [53], and that the η/π ratio is independent of the collision system, as observed by PHENIX [54]. We also consider a scenario where the η spectrum is assumed to have the same shape as the kaon spectrum, as would be expected if the shape of the η spectrum was determined by hydrodynamical flow. In this case we use the ALICE measurements of η/π in pp collisions [55] to determine the relative yields. We use the η/π ratio at the lowest momentum point available, p T = 0.5 GeV/c, because the E T measurement is dominated by low-momentum particles. Because no ω measurement exists, PYTHIA [51] simulations of pp collisions were used to determine the relative contribution from the ω and from all other particles which interact electromagnetically (mainly γ and e ± ). These contributions were approximately 2% and 1% of E π T , respectively. With these assumptions, E ω,η,e ± ,γ T /E π T = 0.17 ± 0.11. The systematic uncertainty on this fraction is dominated by the uncertainty in the η/π ratio. We propagate the uncertainties assuming that the E T from the same particle species are 100% correlated and that the uncertainties from different particle species are uncorrelated.
The f neutral , f total , and f em = 1 − f total /f neutral are shown in Fig. 1 along with the fractions of E T carried by all pions f π , all kaons f K , protons and antiprotons f p , and baryons f versus N part . While there is a slight dependence of the central value on N part , this variation is less than the systematic uncertainty. Because there is little centrality dependence, we use f em = 0.240 ± 0.027, f neutral = 0.728 ± 0.017, and f total = 0.553 ± 0.010, which encompass the entire range for all centralities. The systematic uncertainty is largely driven by the contribution from , ω, η, e ± , and γ because these particles only appear in the denominator of Eqs. (5) and (6). The systematic uncertainty on f total is smaller than that on f neutral because f neutral only has E T in the denominator.
These results are independently interesting. There is little change in the fraction of energy carried by different species with centrality and the changes are included in the f total used for the measurement of E T . Additionally, only about 1/4 of the energy is in E em T , much less than the roughly 1/3 of energy in E em T at lower energies, where most particles produced are pions with the π 0 carrying approximately 1/3 of the energy in the collision. Furthermore, only about 3.5% of the E T is carried by ω, η, e ± , and γ . Because charged and neutral pions have comparable spectra, this means that the tracking detectors are highly effective for measuring the transverse energy distribution in nuclear collisions. , and (f ) and the correction factors f total , f neutral , and f em as functions of N part . The fraction f is scaled by a factor of two so that the data do not overlap with those from protons. Note that f neutral is the fraction of E had T measured in the tracking detectors, while f total and f em are the fractions of the total E T measured in the tracking detectors and the calorimeters, respectively. The vertical error bars give the uncertainty on the fraction of E T from the particle yields. Figure 2 shows the distributions of the reconstructed E had T measured from π ± , K ± , p, and p tracks using the method described above for several centralities. No correction was done for the resolution, leaving these distributions dominated by resolution effects. The mean E had T is determined from the average of the distribution of E had T in each centrality class.

B. Calculation of E T and E had T from measured spectra
We use the transverse momentum distributions (spectra) measured by ALICE [45,49]   of each particle carry the same E T , e.g., E π + T = E π − T = E π 0 T , and that the E T carried by (anti)neutrons equals the E T carried by (anti)protons. These assumptions are consistent with the data at high energies where positively and negatively charged hadrons are produced at similar rates and the antibaryon to baryon ratio is close to one [56,57]. Because the spectra [49] are only measured for five centrality bins, the contribution is interpolated from the neighboring centrality bins. The same assumptions about the contributions of the η, ω, γ , and e ± described in the section on f total and f neutral are used for these calculations. The dominant systematic uncertainty on these measurements is attributable to the single track reconstruction efficiency and is correlated point to point. The systematic uncertainty on these calculations is not correlated with the calculations of E T using the tracking detectors because these measurements are from data collected in different years. The mean E had T per N part /2 obtained from the tracking results of Fig. 2 are shown as a function of N part in Fig. 3, where they are compared with results calculated using the particle spectra measured by ALICE. The two methods give consistent results. Data are plotted in 2.5% wide bins in centrality for 0%-40% central collisions, where the uncertainty on the centrality is <1% [58]. Data for 40%-80% central collisions are plotted in 5% wide bins.

C. Electromagnetic calorimeter measurements of E em T
The E em T is defined as the transverse energy of the particles of category B discussed above, which are the particles measured well by an electromagnetic calorimeter. While the definition of E em T includes π 0 , ω, η, e ± , and γ , the majority of the E T comes from π 0 → γ γ (85%) and η → γ γ (12%) decays, meaning that the vast majority of E em T arises from photons reaching the active area of the electromagnetic calorimeters. Reconstructed clusters are used for the analysis, with most clusters arising from a single γ . Clusters reduce contributions from detector noise to a negligible level, as compared to using tower energies as done by STAR [29]. However, clusters also require additional corrections for the reconstruction efficiency, nonlinearity, and minimum energy reconstructed. In addition, both the EMCal and the PHOS have limited nominal acceptances so an acceptance correction must be applied. Backgrounds come from charged hadrons in category A (π ± , K ± , p, and p), kaon decays into π 0 from both category A (K ± ) and category C (K 0 S ), neutrons from category D, and particles produced by secondary interactions with the detector material.
The corrected E em T is given by where j runs over the reconstructed clusters in the calorimeter and η is the pseudorapidity range used in the analysis.
The correction factor f acc corrects for the finite nominal azimuthal detector acceptance, f E Tmin is a correction for the minimum cluster energy used in the analysis, δ m is zero when a cluster is matched to a track and one otherwise, ε γ is the product of the active acceptance and the reconstruction efficiency in the nominal acceptance of the detector, f E NL is the correction for the nonlinear response of the calorimeter, and E bkgd T is the sum of the contributions from charged hadrons, kaons, neutrons, and particles created by secondary interactions. These correction factors are discussed below and their systematic uncertainties are summarized in Table II. All of the systematic uncertainties except for that owing to the background subtraction are correlated point to point. Systematic uncertainties on measurements of E em T from the EMCal and the PHOS and calculations of E em T from the spectra are not correlated. Systematic uncertainties on hybrid measurements are dominated by systematic uncertainties on E had T and are therefore dominantly correlated point to point and with the tracking detector measurements.

Acceptance correction f acc and cluster reconstruction efficiency ε γ
The correction for the acceptance is divided into two parts, the correction owing to the nominal acceptance of the detector 034903-6 and the correction owing to limited acceptance within the nominal acceptance of the detector owing to dead regions and edge effects. To reduce edge effects, clusters in the PHOS are restricted to |η| < 0.1 and in the EMCal to |η| < 0.6. The correction f acc accounts for the limited nominal acceptance in azimuth and is therefore 5/18 for the EMCal, which has a nominal acceptance of 100 • , and 1/6 for the PHOS, which has a nominal acceptance of 60 • . It does not correct for acceptance effects owing to dead regions in the detector or for noisy towers omitted from the analysis. This is accounted for by the cluster reconstruction efficiency × acceptance within the nominal detector acceptance, ε γ , calculated from HIJING + GEANT simulationsusing photons from the decay of the π 0 meson. The efficiency is calculated as a function of the energy of the cluster.

Minimum cluster energy f E Tmin
There is a minimum energy for usable clusters analogous to the minimum p T in the acceptance of the tracking detectors. Thresholds of 250 MeV for PHOS and 300 MeV for the EMCal are applied. These energies are above the peak energy for minimum ionizing particles (MIPs), reducing the background correction owing to charged hadrons. We apply the threshold in E T rather than energy because it simplifies the calculation of the correction for this threshold and its systematic uncertainty. We use the charged pion spectra to calculate the fraction of E em T below these thresholds. PYTHIAis used to simulate the decay kinematics and the measured charged pion spectra are used to determine the fraction of E T from pions within the acceptance. As for the calculation of f total for the measurement of E had T described above, we assume transverse mass scaling to determine the shape of the η spectrum and the η/π ratio measured by ALICE [55] to estimate the contribution of the η meson to f E Tmin . The uncertainty on the shape of the charged pion spectrum and on the η/π ratio is used to determine the uncertainty on f E Tmin . This correction is centrality dependent and ranges from 0.735 to 0.740 for the PHOS and from 0.640 to 0.673 for the EMCal with a systematic uncertainty of 3.5%-5%.

Nonlinearity correction f E NL and energy scale uncertainty
For an ideal calorimeter the signal observed is proportional to the energy. In practice, however, there is a slight deviation from linearity in the signal observed, particularly at low energies. A nonlinearity correction is applied to take this into account. For the EMCal this deviation from linearity reaches a maximum of about 15% for the lowest energy clusters used in this analysis. The systematic uncertainty for the EMCal is determined by comparing the nonlinearity observed in test beam and the nonlinearity predicted by HIJING + GEANT simulationsand reaches a maximum of about 5% for the lowest energy clusters. The PHOS nonlinearity is determined by comparing the location of the π 0 mass peak to HIJING + GEANT simulationsand cross checked using the energy divided by the momentum for identified electrons. The systematic uncertainty is derived from the accuracy of the location of the π 0 mass peak. The nominal correction is about 1% with a maximum systematic uncertainty of around 3% for the lowest energy clusters. The raw E em T is calculated with the maxima and minima of the nonlinearities and the difference from the nominal value is assigned as a systematic uncertainty. The final systematic uncertainty on the measurement with the EMCal owing to nonlinearity is about 0.8% and 1.3% for the PHOS. For both the PHOS and the EMCal, the energy scale uncertainty was determined by comparing the location of the π 0 mass peak and the ratio of energy over momentum for electrons. This systematic uncertainty is 2% for the EMCal [59] and 0.5% for the PHOS [60].

Background E bkgd T
Charged particles (category A) are the largest source of background in E em T . Clusters matched to tracks are omitted from the analysis. The track matching efficiency determined from HIJING + GEANT simulationsis combined with information from clusters matched to tracks to calculate the number and mean energy of remaining deposits from charged particles. The systematic uncertainty on this contribution comes from the uncertainty on the track matching efficiency and the uncertainty in the mean energy. The former is dominated by the uncertainty on the single-track reconstruction efficiency and the latter is determined by comparing central and peripheral collisions, assuming that the energy of clusters matched to tracks in central collisions may be skewed by overlapping clusters owing to the high occupancy.
The background contributions from both charged kaons (category A) through their K ± → Xπ 0 decays and K 0 S (category C) through its K 0 S → π 0 π 0 decay are non-negligible. The amount of energy deposited by a kaon as a function of p T is determined using HIJING + GEANT simulations. This is combined with the kaon spectra measured by ALICE [45] to calculate the energy deposited in the calorimeters by kaons. The systematic uncertainty on the background from kaons is determined by varying the yields within the uncertainties of the spectra. Contributions from both neutrons and particles from secondary interactions are determined using HIJING + GEANT simulations. The systematic uncertainty on these contributions is determined by assuming that they scale with either the number of tracks (as a proxy for the number of charged particles) or with the number of calorimeter clusters (as a proxy for the number of neutral particles).
The background contribution is centrality dependent and ranges from 61% to 73% with both the background and its systematic uncertainty dominated by contributions from charged hadrons. This correction is so large because E em T comprises only about 25% of the E T in an event while π ± , K ± , p, and p carry roughly 57% of the E T in an event.

Acceptance effects
The limited calorimeter acceptance distorts the distribution of E em T for events with very low E em T because it is difficult to measure the mean E T when the mean number of clusters observed is small (about 1-10). While it is possible to correct for acceptance, this was not done because the measurement of E T from the tracking method has the highest precision. The hybrid method using both the calorimeters and the tracking 034903-7

FIG. 4. Distribution of E em
T measured with the EMCal at midrapidity for several centrality bins. Not corrected for resolution effects. Only statistical error bars are shown. detectors is therefore restricted to the most central collisions where distortions of the E em T distribution are negligible. Figure 4 shows the distributions of the reconstructed E em T measured using the EMCal and Fig. 5 shows the distributions of the reconstructed E em T measured using the PHOS. No resolution correction was applied for the resolution leaving the distributions in Figs. 4 and 5 dominated by resolution effects. The resolution is primarily determined by the finite acceptance of the detectors in azimuth, limiting the fraction of E em T sampled by the calorimeter. The distributions are broader for PHOS than EMCal because of the smaller azimuthal acceptance of the PHOS. The mean E em T is determined from the average of the distribution of E em T in each centrality bin. The E em T per N part pair measured using the electromagnetic calorimeters is compared to that calculated using the measured pion spectra in Fig. 6, demonstrating that these methods

E em T distributions
100 200 300 400 500 600  lead to comparable results. The E em T calculated from the spectra is determined using the same ratio of E ω,η,e ± ,γ T /E π T = 0.171 ± 0.110 for all centralities.

IV. RESULTS
The dE T /dη / N part /2 versus N part is shown in Fig. 7 using tracking detectors, using EMCal + tracking, using PHOS + tracking, and as calculated from the measured particle spectra. All methods lead to comparable results, although the systematic errors are largely correlated owing to the dominant correction from the tracking inefficiency. The determination of N part and its uncertainties are calculated using a Glauber model as in Refs. [58,61] and the uncertainties on N part are added in quadrature to the uncertainties on E T .
As discussed above, the small number of clusters observed in the calorimeters in peripheral collisions make acceptance corrections difficult. Because the measurements with the tracking detectors alone have higher precision, only these measurements are used in the following.   from STAR [29] and PHENIX [26,27]. Data from RHIC have been scaled by a factor of 2.7 for comparison of the shapes. The factor of 2.7 is approximately the ratio of p T dN ch /dη at the LHC [45] to that at RHIC [62,63]. The shapes observed by ALICE and PHENIX are comparable for all N part . STAR measurements are consistent with PHENIX measurements for the most central collisions and above the PHENIX measurements, although consistent within systematic uncertainties, for more peripheral collisions. CMS measurements are consistent with ALICE measurements for peripheral collisions but deviate beyond the systematic uncertainties for more central collisions. The E T in 0%-5% Pb-Pb collisions is 1737 ± 6(stat.) ± 97(sys.) GeV and the E T per participant is 9.02 ± 0.03(stat.) ± 0.50(sys.) GeV, two standard deviations below the value observed by CMS [30]. All methods resulted in a lower E T than that reported by CMS, although the systematic errors on the measurements are significantly correlated. One possible explanation of the differences is that the corrections for the CMS calorimetry measurement are determined by Monte Carlo [30], while the corrections for the ALICE measurement are mainly data driven. PHENIX [28] reported that while dE T /dη scaled by N part has a pronounced centrality dependence, as seen in Fig. 8 d min = 0.4 ± 0.4 fm. The three constituent quarks in each nucleon have been sampled from the nucleon density distribution ρ nucleon = ρ 0 e −ar with a = 4.28 fm −1 using the method developed by PHENIX [64]. The inelastic quark-quark cross section at √ s NN = 2.76 TeV was found to be σ inel qq = 15.5 ± 2.0 mb, corresponding to σ inel NN = 64 ± 5 mb [58]. The systematic uncertainties on the N quark calculations were determined following the procedure described in Refs. [58,61]. Unlike at RHIC, we observe an increase in dE T /dη / N quark /2 with centrality below N part ≈ 200. Figure 10 shows dE T /dη / dN ch /dη , a measure of the average transverse energy per particle, versus N part in Pb-Pb collisions at √ s NN = 2.76 TeV from ALICE and in Au-Au collisions at √ s NN = 200 GeV from STAR [29] and PHENIX [26,27] [30] and central collisions at other energies [26,29,64] at midrapidity. All measurements are from 0%-5% central collisions except the NA49 data, which are from 0%-7% collisions. on the charged-particle multiplicity except in peripheral collisions [50]. The absence of a strong centrality dependence is consistent with the development of radial flow seen in the spectra of identified particles [50], where the kinetic energy is conserved during the hydrodynamic expansion instead of producing a higher p T . Figure 11 shows a comparison of dE T /dη / N part /2 versus √ s NN in 0%-5% central Pb-Pb collisions at √ s NN = 2.76 TeV from ALICE and CMS [30] and central collisions at other energies [26,29,64] at midrapidity. The data are compared to an extrapolation from lower energy data [26], which substantially underestimates the dE T /dη / N part /2 at the LHC. The data are also compared to the EKRT model [65,66]. The EKRT model combines perturbative QCD minijet production with gluon saturation and hydrodynamics. The EKRT calculation qualitatively describes the √ s NN dependence at RHIC and SPS energies [29]. However, at LHC energies EKRT overestimates E T substantially, indicating that it is unable to describe the collision energy dependence. Figure 12 shows  [26] and we observe 1.06 ± 0.05. Increasing the incident energy increases both the particle production and the mean energy per particle at LHC energies, in contrast to lower energies ( √ s NN = 19.6-200 GeV) where increasing the incident energy only led to increased particle production [26]. Figure 13 shows a comparison of dE T /dη / N part /2 versus N part to various models. AMPT [68] is a Monte Carlo event generator that builds on HIJING [46], adding explicit interactions between initial minijet partons and final-state hadronic interactions. HYDJET [19,23,25,26,29,64,67]. The band shows the extrapolation from lower energies with the width representing the uncertainty on the fit [26]. event generator that introduces jet quenching via gluon bremsstrahlung to PYTHIA [51] events. The HYDJET values use the E T from HYDJET and the N part from ALICE, similar to comparisons to HYDJET by CMS [30]. The curves labeled UDG are calculations from a color glass condensate model [70] with different normalization K factors. None of the available models is able to describe the data very well, but we find that AMPT does best in describing the shape and level of dE T /dη / N part /2 . HYDJET describes the relative shape changes as a function of centrality as well as AMPT, but overestimates dE T /dη / N part /2 . Both CGC calculations overestimate dE T /dη / N part /2 and predict a larger increase as a function of centrality than is observed in the data. The volume-averaged energy density ε can be estimated from dE T /dη using the expression [18] [68], HYDJET 1.8 [69], and UDG [70]. The boxes indicate the systematic uncertainties. where A is the effective transverse collision area, c is the speed of light, J is the Jacobian for the transformation between dE T /dη and dE T /dy , and τ 0 is the formation time. The Jacobian is calculated from the measured particle spectra [45,49]. While J has a slight centrality dependence, it is smaller than the systematic uncertainty so a constant Jacobian of J = 1.12 ± 0.06 is used. The formation time of the system τ 0 is highly model dependent and we therefore report ετ 0 .
The transverse overlap area corresponding to the measured dE T /dη was determined by a calculation using a Glauber Monte Carlo method. Using the Glauber parameters from Ref. [58] and assuming each participating nucleon has an effective transverse radius of R = (σ inel NN /4π ) 1/2 = 0.71 fm results in A = 162.5 fm 2 for central collisions (b = 0 fm). This is equivalent to a transverse overlap radius of R = 7.19 fm, which is close to the value of 7.17 fm often used in estimates of energy densities using a Woods-Saxon distribution to determine the effective area [28,64]. The centrality dependence of A is obtained by assuming it scales as (σ 2 x σ 2 y − σ 2 xy ) 1/2 [71], where σ 2 x and σ 2 y are the variances and σ 2 xy is the covariance of the spatial distribution of the participating nucleons in the transverse plane in the Glauber Monte Carlo calculation. For 0%-5% central collisions this leads to a reduction of A by 3%, resulting in ετ 0 = 12.5 ± 1.0 GeV/fm 2 /c. For comparison, using R = 7.17 fm gives ετ 0 = 12.3 ± 1.0 GeV/fm 2 /c, roughly 2.3 times that observed in 0%-5% central Au-Au collisions at √ s NN = 200 GeV. Some of this increase comes from the higher N part in central Pb-Pb collisions relative to central Au-Au collisions. The energy density times the formation time ετ 0 is shown in Fig. 14 for R = 7.17 fm, the same value of R used by PHENIX at RHIC energies [28,64]. In addition to estimating the volume-averaged energy density, it is also interesting to estimate the energy density attained at the core of the collision area. This can be done by rewriting the Bjorken Eq. (8) as where A c is the area of the transverse core, dE T dη c is dE T dη produced in the core, and σ c = N part c /A c is the transverse area density of nucleon participants at the core. The area A c was chosen arbitrarily to be a circle with a radius of 1 fm at the center of the collision. Equation (9) assumes that the local energy density scales with the participant density in the transverse plane and that the measured value of dE T dη / N part , which is averaged over the total transverse collision area, is also representative of the transverse energy production at the core, dE T dη c / N part c . The increase of this quantity with increasing centrality indicates that this is a conservative estimate. From a Glauber Monte Carlo calculation we find for 0%-5% centrality σ c = 4.2 ± 0.1 nucleon/fm 2 , resulting in a core energy density of ε c τ 0 = 21 ± 2 GeV/fm 2 /c. For the most central 80 fm 2 (half the total overlap area) the energy density is still above 80% of the core energy density, emphasizing that the core energy density may be more relevant for judging the initial conditions of the QGP than the volumeaveraged energy density.

V. CONCLUSIONS
We have measured dE T /dη at midrapidity in Pb-Pb collisions at √ s NN = 2.76 TeV using four different methods. All methods lead to comparable results, although the systematic uncertainties are largely correlated. Our results are consistent with results from CMS [30] for 10%-80% central collisions; however, we observe a lower dE T /dη in 0%-10% central collisions. The dE T /dη observed at √ s NN = 2.76 TeV in 0%-5% central collisions is 1737 ± 6(stat.) ± 97(sys.) GeV. The shape of the centrality dependence of dE T /dη / N part /2 is similar for RHIC and the LHC. No centrality dependence of dE T /dη / dN ch /dη is observed within uncertainties, as was observed at RHIC. Unlike at RHIC, we observe an increase in dE T /dη / N quark /2 with centrality below N part ≈ 200. Both dE T /dη / N part /2 and dE T /dη / dN ch /dη in central collisions exceed the value expected from naive extrapolations from data at lower collision energies. Assuming that the formation time τ 0 is 1 fm/c the energy density is estimated to be at least 12.3 ± 1.0 GeV/fm 3 in 0%-5% central Pb-Pb collisions at √ s NN = 2.76 TeV and the energy density at the core of the collision exceeds 21 ± 2 GeV/fm 3 .

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 ALICE detector: State Committee of Science, World Federation of Scientists (WFS) and Swiss Fonds Kidagan, 034903-11