Measurement of the pseudorapidity and centrality dependence of the transverse energy density in PbPb collisions at sqrt(s[NN]) = 2.76 TeV

The transverse energy ET in PbPb collisions at 2.76 TeV nucleon-nucleon center-of-mass energy sqrt(s[NN]) has been measured over a broad range of pseudorapidity eta and collision centrality using the CMS detector at the LHC. The transverse energy density per unit pseudorapidity d(ET)/d(eta) increases faster with collision energy than the charged particle multiplicity. This implies that the mean energy per particle is increasing with collision energy. At all pseudorapidities the transverse energy per participating nucleon increases with the centrality of the collision. The ratio of transverse energy per unit pseudorapidity in peripheral to central collisions varies significantly as the pseudorapidity increases from eta = 0 to abs(eta) = 5.0. For the 5% most central collisions the energy density per unit volume is estimated to be about 14 GeV/fm^3 at a time of 1 fm/c after the collision. This is about 100 times larger than normal nuclear matter density and a factor of 2.6 times higher than the energy density reported at sqrt(s[NN]) = 200 GeV at RHIC.

The transverse energy (E T ) in Pb-Pb collisions at 2.76 TeV nucleon-nucleon center-of-mass energy ( ffiffiffiffiffiffiffiffi s NN p ) has been measured over a broad range of pseudorapidity () and collision centrality by using the CMS detector at the LHC. The transverse energy density per unit pseudorapidity (dE T =d) increases faster with collision energy than the charged particle multiplicity. This implies that the mean energy per particle is increasing with collision energy. At all pseudorapidities, the transverse energy per participating nucleon increases with the centrality of the collision. The ratio of transverse energy per unit pseudorapidity in peripheral to central collisions varies significantly as the pseudorapidity increases from ¼ 0 to jj ¼ 5:0. For the 5% most central collisions, the energy density per unit volume is estimated to be about 14 GeV=fm 3 at a time of 1 fm=c after the collision. This is about 100 times larger than normal nuclear matter density and a factor of 2.6 times higher than the energy density reported at ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV at the Relativistic Heavy Ion Collider. DOI: 10.1103/PhysRevLett.109.152303 PACS numbers: 25.75.Gz The goal of relativistic heavy-ion collisions is to study the behavior of quarks and gluons under extreme conditions of pressure, density, and temperature, such as those that existed shortly after the big bang. Similar conditions can be reproduced in the laboratory by colliding heavy nuclei at the highest possible energies. Experiments at the Relativistic Heavy Ion Collider (RHIC) have shown that at a nucleon-nucleon center-of-mass energy of ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV a strongly interacting medium is produced. This system behaves as an almost perfect quantum fluid [1][2][3][4]. There are also indications from the RHIC experiments that at these energies the initial state of the colliding nuclei may be a color glass condensate [1,5,6]. The presence of such a state may affect the spatial distribution of partons within the nucleus, particularly at high pseudorapidity [7,8]. Measuring the distribution of transverse energy over a wide pseudorapidity range sheds light also on the longitudinal expansion of the system. In 2010, the Large Hadron Collider (LHC) accelerated heavy ions to energies 14 times higher than RHIC in order to produce matter at energy densities never achieved before. One of the basic measurements in this new regime is that of the energy distribution of all the produced particles, which is connected to the initial energy and entropy densities of the produced matter. At lower energies, the measured rapidity distributions of particles are generally well described by Gaussians. The widths of these distributions are consistent with the predictions of Landau hydrodynamics, i.e., y ¼ ffiffiffiffiffiffiffi ffi ln p , where is the Lorentz factor of the colliding beams [9][10][11][12][13]. The rapidity variable y tanh À1 ðv z =cÞ, where v z is the velocity of the particle along the beam direction z, provides a way to describe the longitudinal distribution of matter created in these collisions. Calorimeters measure only the energy deposited at various angles, and therefore the data are presented in terms of the distribution of energy in pseudorapidity, . Pseudorapidity is defined as À ln½tanð=2Þ, with the polar angle with respect to the z axis. When the momentum of a particle is larger than its mass, its % y.
The Compact Muon Solenoid (CMS) experiment is a general-purpose detector designed to study hadron collisions at the TeV scale [14]. In particular, it has almost hermetic calorimetry that is sensitive to the distribution of energy over nearly the complete angular range. The transverse energy is defined by E T ¼ P i E i sin i , where E i is the energy seen by the calorimeter for the ith particle, i is the polar angle of particle i, and the sum is over all particles emitted into a fixed solid angle in an event. The quantity dE T =d is an approximately Lorentz invariant measure of the energy distribution. The transverse energy is studied as a function of the geometry of the collision, i.e., the centrality, of the heavy-ion interaction. Finally, comparisons are made with lower-energy data and theoretical models.
The central feature of the CMS apparatus is a superconducting solenoid, of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the central field volume are the silicon pixel and strip trackers, lead-tungstate crystal electromagnetic calorimeter and the brass-scintillator hadron calorimeter. These calorimeters are physically divided into the barrel and end cap regions covering together the region of jj < 3:0. The hadronic forward (HF) calorimeters cover jj from 2.9 to 5.2. The HF calorimeters use quartz fibers embedded within a steel absorber. The CMS tracking system, located inside the calorimeter, consists of pixel and silicon-strip layers covering jj < 2:5. A set of scintillator tiles, the beam scintillator counters, are mounted on the inner side of the HF calorimeters to trigger on heavy-ion collisions and reject beam-halo interactions. In addition, two zero degree calorimeters are used for systematic checks. For more details on CMS, see [14].
In 2010, CMS recorded Pb-Pb collision data corresponding to an integrated luminosity of 7:36 b À1 , of which 0:31 b À1 were included in this analysis. This luminosity selection provided a data sample with negligible statistical uncertainties. Minimum bias inelastic Pb-Pb collisions were selected by requiring that either the HF or beam scintillator counters detected a signal on both sides of the interaction point. In the analysis at least two reconstructed tracks were required to form a vertex within AE25 cm of the nominal interaction point along the beam line and within a radius of 2 cm measured perpendicular to the beam relative to the average vertex position. Large-multiplicity beambackground events were removed by requiring the compatibility of the observed pixel-cluster lengths with the hypothesis of a Pb-Pb interaction at the estimated vertex. Finally, events containing beam-halo muons were eliminated by a timing requirement on the beam scintillator counters on opposite sides of the interaction point. The total event selection efficiency of the minimum bias trigger for hadronic Pb-Pb interactions was found to be ð97 AE 3Þ% [15].
Events were sorted into different centrality classes. The centrality of heavy-ion interactions is related to the number of participating nucleons and hence to the energy released in the collisions. In CMS, the centrality is defined as percentiles of the energy deposited in the HF. The most central (peripheral) event class, i.e., ð0-2:5Þ%=ð70-80Þ% in this analysis, has a large (small) number of participants and a large (small) energy deposit in HF. In order to estimate the mean number of participating nucleons (hN part i) and its systematic uncertainty for each centrality class, a Glauber model of the nuclear collision was used [16][17][18].
The data were corrected for detector acceptance and inefficiencies using correction factors CðjjÞ estimated from the HYDJET 1.8 [19] Monte Carlo (MC) event generator coupled to a GEANT4 [20] CMS detector simulation. These correction factors were calculated as the ratio of MC predictions at the particle level and the detector level for each centrality class. The correction factor CðjjÞ % 1:6 for jj < 2 falls to %1:1 by jj ¼ 4 and then rises to 2 at jj % 5. The nonlinearity of the calorimeter response and the effect of the magnetic field cause the CðjjÞ to depend upon the p T spectra, the ratio of charged and neutral particles, and the mixture of mesons and baryons. The value of CðjjÞ increases if the assumed spectra shift to lower p T or if the ratio of charged to neutral particles is larger. To estimate the systematic uncertainties in CðjjÞ, two tunes of HYDJET (1.6 and 1.8) were used. HYDJET 1.8, hp T i ch ¼ 0:66 GeV=c, was tuned to LHC spectra and particle yields as measured by the ALICE Collaboration [21] and successfully tested against a wide range of RHIC data. HYDJET 1.6, hp T i ch ¼ 0:57 GeV=c, was tuned only to RHIC data [19]. At central pseudorapidity, the fraction of E T carried by charged pions, kaons, protons, and antiprotons is 0.60 for HYDJET 1.6 and 0.62 for HYDJET 1.8. The results were cross-checked by using data taken with no magnetic field, and in addition, for B ¼ 3:8 T, data from tracks with p T > 900 MeV=c were combined with energy clusters in the calorimeters to identify different types of particles and measure their energy. Since muons and neutrinos carry a negligible fraction of the total transverse energy and deposit almost no signal in the calorimeters, they are not considered in this analysis and no correction factors are applied to account for them. The corrected transverse energy for N analyzed events is obtained as where the sum over j covers all calorimeters cells located within the range Á and E T;j is the transverse energy measured in a particular cell j. Note that for this summation no threshold is applied to the individual calorimeters cells. Several sources of systematic uncertainties were studied, and their effects are summarized in Table I and described below. Energy scale: All of the calorimeters were initially calibrated with test beam data and radioactive sources. For the barrel and inner end cap calorimeters, these calibrations were refined by using isolated charged hadrons whose momentum was reconstructed in the tracker. For the HF calorimeter the energy scale was cross-checked by reconstructing Z ! e þ e À in pp collisions where either the positron or the electron was recorded in the electromagnetic calorimeter and tracker. Symmetry about : For Pb-Pb collisions the corrected dE T =d should be symmetric about ¼ 0. The values of 152303-2 dE T =d for positive and negative were found to differ by at most 0.5%. This close agreement implies that one can use the average of the two results as a best estimate of dE T =d. Vertex distribution: The z distribution of the vertices is Gaussian with z % 6:1 cm. To test the sensitivity of E T to the position of the interaction vertex along the beam line, z, the data set was divided into two samples with jzj < 10 cm and 10 cm < jzj < 25 cm, respectively. The E T distributions of the two samples differ by less than 2%. Autocorrelations: Since HF is used both to calculate centrality and to measure E T for each centrality class, there is an autocorrelation in the measurement. This effect was estimated to be less than 1.5% by using a combination of the zero degree calorimeters and pixel detectors to measure centrality. Calorimeter noise: The GEANT4 simulation of the calorimeters included electronic noise. This noise was measured by studying a sample of events where the trigger required only the presence of clockwise and anticlockwise bunches of lead ions simultaneously in CMS. The simulation of the noise was checked by comparing the data to the simulated signal from a GEANT4 simulation of the most peripheral events in the data set. Any discrepancy in the simulation of the noise corresponds to a corrected average E T per event of less than 5.8 GeV for jj 2:65 and 1.2 GeV for 2:65 < jj 5:2. This is significant only compared to the signal for hN part i 30. The HF MC description takes into account different ways of describing the dead areas of the HF detector. Centrality determination: The systematic uncertainty related to the centrality determination is applied only to the results that are normalized by hN part i. Figure 1 shows the jj dependence of the transverse energy density for four selected ranges of centrality. For the most central collisions (hN part i ¼ 394), dE T =d reaches 2.1 TeV at ¼ 0. This is much larger than the value of 0.61 TeV measured at ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV [22]. At lower center-of-mass energies, the pion multiplicity distributions are reasonably well described by Gaussians in rapidity with widths that are consistent with Landau-Carruthers hydrodynamics [23,24]. Since the mean p T of all particle species depends only weakly on rapidity, this implies that dE T =dy is roughly Gaussian in rapidity at ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV. Recently, Wong has improved the formulation of Landau hydrodynamics [25]. This new formulation gives a better description of the 200 GeV RHIC data. At ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV and for jj < 5:2, the dE T =d is consistent with a Gaussian (black solid line) with ¼ 3:4 AE 0:1 for the most central collisions. The Gaussian and Landau curves in Fig. 1 are normalized to the CMS data at ¼ 0. Both the Landau-Carruthers (blue dashed line) and Landau-Wong (green dotted line) formulations have distributions that are narrower than the data. Therefore, the longitudinal expansion of the system is stronger than that predicted from either model. HYDJET 1.8, shown by the purple dashed line, has been tuned to LHC data in the small jj region. It gives a good description of dE T =d at small jj but overestimates the data at large jj for central collisions. The AMPT (a multiphase transport) model [26,27] (orange dashed line) overestimates dE T =d for central collisions but is in rough agreement with the shape of dE T =d. Integrating ðdE T =dÞ=ðhN part i=2Þ over between À5:2 and 5.2 gives a total measured E T per participant pair of 80 AE 4 GeV for the most central events. This serves as a lower limit for the total transverse energy per nucleon pair. Extrapolating to the full phase space gives a total transverse energy per pair of participating nucleons of 91 AE 5 GeV for the most central events. It is clear from Fig. 1 that the magnitude of dE T =d increases rapidly with the number of nucleons participating in the collision. Figure 2 shows the evolution of ðdE T =dÞ=ðhN part i=2Þ with hN part i for several jj regions. At all jj values ðdE T =dÞ=ðhN part i=2Þ increases with hN part i. This figure shows that the hN part i dependence of transverse energy density changes as a function of pseudorapidity. This effect can be quantified by comparing peripheral (60-70)% (hN part i ¼ 30) to central (0-2.5)% collisions (hN part i ¼ 394) at various pseudorapidities. The ratio of peripheral to central ðdE T =Þ=ðhN part i=2Þ changes from 54 AE 2% at ¼ 0 to 68 AE 2% at jj ¼ 5:0. The PHENIX Collaboration at RHIC has studied transverse energy density in Au-Au collisions for jj < 0:35 over a wide range of centralities and for ffiffiffiffiffiffiffiffi s NN p from 19.6 to 200 GeV [22]. At ffiffiffiffiffiffiffiffi s NN p ¼ 19:6 GeV, ðdE T =dÞ=ðhN part i=2Þ at ¼ 0 increases by a factor of 1:25 AE 0:17 as hN part i increases  Figure 3 shows the energy dependence of ðdE T =dÞ=ðhN part i=2Þ for central collisions at ¼ 0. For the top 5% most central events, ðdE T =dÞ=ðhN part i=2Þ reaches 10:5 AE 0:5 GeV at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV. The E T rises more quickly with the center-of-mass energy than the logarithmic dependence used to describe data up to ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV [22]. For energies between 8.7 GeV and 2.76 TeV, dE T =d at ¼ 0 can be reproduced by a powerlaw dependence of the type s n NN with n % 0:2. A similar effect has been seen in the measurement of the ffiffiffiffiffiffiffiffi s NN p evolution of the charged particle multiplicity [18,28]. The ðdE T =dÞ=ðhN part i=2Þ increases by a factor of 3:07 AE 0:24 from ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV to 2.76 TeV. This is to be compared to a factor of 2:17 AE 0:15 for the pseudorapidity density, ðdN ch =dÞ=ðhN part i=2Þ [18,21,22]. For the 5% most central collisions, CMS has measured dN ch =d ¼ 2007 AE 100 GeV and dN ch =d ¼ 1612 AE 55 [18]. Dividing the measured transverse energy by the observed charged particle multiplicity for the same centrality gives a transverse energy per charged particle of 1:25 AE 0:08 GeV at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV. This compares to 0:88 AE 0:07 GeV at ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV [22]. The sum of the transverse energies of all particles produced in the event depends upon both the entropy and the temperature of the system. Using geometrical considerations, Bjorken [29] suggested that the energy density per unit volume in nuclear collisions could be estimated from the energy density per unit rapidity. A commonly used estimate of energy density is given by [22] where A is the overlap area of the two nuclei and 0 is the formation time of the produced system. The Jacobian Jðy; Þ depends on the momentum distributions of the produced particles. In the limit that the rest masses of the particles are much smaller than their momenta, Jðy; Þ ¼ 1.  [22]. For the top 5% most central collisions, this formula gives ¼ 14 GeV=fm 3 at a time 0 ¼ 1 fm=c and for a transverse surface of A ¼ Â ð7 fmÞ 2 [22]. This is a factor of 2.6 times larger than the energy density calculated at ffiffiffiffiffiffiffiffi s NN p ¼ 200 GeV [22]. In summary, for the most central Pb-Pb collisions at ffiffiffiffiffiffiffiffi s NN p ¼ 2:76 TeV, the maximum of the transverse energy distribution has been found to be 2.1 TeV at ¼ 0. Even at a very forward pseudorapidity of jj ¼ 5:0, dE T =d and hence the energy density of the produced system at the LHC is larger than that measured for ¼ 0 at RHIC.  At 2.76 TeV, the shape of dE T =d is consistent with a Gaussian function of width ¼ 3:4 AE 0:1 for central collisions. This distribution is wider than the prediction of Landau hydrodynamics but narrower than that given by the HYDJET 1.8 simulation. The ðdE T =dÞ=ðhN part i=2Þ increases with hN part i at all pseudorapidities. The ratio of transverse energy in peripheral compared to central collisions increases by a factor of 1:26 AE 0:06 from ¼ 0 to jj ¼ 5. The transverse energy density at ¼ 0 grows more rapidly with the center-of-mass energy than the logarithmic scaling with ffiffiffiffiffiffiffiffi s NN p that describes lower-energy data. It also grows faster with energy than the multiplicity, implying a significant increase of the mean transverse energy per particle compared to lowerenergy data.
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC machine. We thank the technical and administrative staff at CERN and other CMS institutes and acknowledge sup-