Centrality and pseudorapidity dependence of the transverse energy density in pPb collisions at $\sqrt{s_\mathrm{NN}}=$ 5.02 TeV

The almost hermetic coverage of the CMS detector is used to measure the distribution of transverse energy, $E_\mathrm{T}$, over 13.2 units of pseudorapidity, $\eta$, for pPb collisions at a center-of-mass energy per nucleon pair of $\sqrt{s_\mathrm{NN}}=$ 5.02 TeV. The huge angular acceptance exploits the fact that the CASTOR calorimeter at $-6.6<\eta<-5.2$ is effectively present on both sides of the colliding system because of a switch in the proton-going and lead-going beam directions. This wide acceptance enables the study of correlations between well-separated angular regions and makes the measurement a particularly powerful test of event generators. For minimum bias pPb collisions the maximum value of d$E_\mathrm{T}/$d$\eta$ is 22 GeV, which implies an $E_\mathrm{T}$ per participant nucleon pair comparable to that of peripheral PbPb collisions at $\sqrt{s_\mathrm{NN}}=$ 2.76 TeV. The increase of d$E_\mathrm{T}/$d$\eta$ with centrality is much stronger for the lead-going side than for the proton-going side. The $\eta$ dependence of d$E_\mathrm{T}/$d$\eta$ is sensitive to the $\eta$ range in which the centrality variable is defined. Several modern generators are compared to these results but none is able to capture all aspects of the $\eta$ and centrality dependence of the data and the correlations observed between different $\eta$ regions.


Introduction
In a heavy ion or proton nucleus collision the total transverse energy, E T , is a measure of the energy liberated by the deceleration, or "stopping power" of the colliding nucleons while dE T /dy measures the total energy carried by the system of particles or medium, produced in the collision, which is moving with longitudinal rapidity y [1]. In heavy ion collisions the energy density, BJ , of this medium at proper time τ 0 shortly after the impact of the two nuclei can be estimated using the Bjorken formula where A ⊥ is the nuclear transverse area, i.e., the initial size of the medium [2]. For the top 5% most central lead-lead collisions at √ s NN = 2.76 TeV, this formula gives energy densities up to 14 GeV/fm 3 at a time τ 0 = 1 fm/c [3]. This value is much higher than the expected threshold of > 1 GeV/fm 3 for the production of a quark-gluon plasma estimated from quantum chromodynamics, QCD, calculations performed on a lattice [4]. Collective phenomena such as azimuthal flow and strangeness enhancement have been observed in proton-lead (pPb) [5][6][7] and even high-multiplicity proton-proton (pp) collisions [8][9][10]. Given such evidence of collective motion and strangeness enhancement in small systems, it is relevant to study the energy densities achieved in pPb collisions to see if a quark-gluon plasma could be formed in pPb collisions.
The E T spectra in proton-nucleus, pA and deuteron-nucleus, dA, collisions have been measured at center-of-mass energies ranging from √ s NN = 5.5 to 200 GeV with nuclei ranging from deuterium (atomic number A = 2) to uranium (U, A = 238) [11][12][13][14]. At √ s NN = 5.5 GeV, only a weak correlation is observed between the total E T and the charged-particle multiplicity in the forward region [12]. At √ s NN = 5.5, 20, and 30 GeV, the mean pseudorapidity η moves backward, i.e., in the ion-going direction, and the pseudorapidity width of the dE T /dη distribution decreases as the total E T in the event increases [11][12][13]. Event generators such as RQMD and VENUS [15,16] postulate that the initial nucleon-nucleon collisions excite strings that interact with each other to produce more strings, each with a lower energy. At some point the strings freezeout into hadrons, which can also interact with each other, until the point of kinetic freezeout is reached. Such models are able to describe the pseudorapidity shift observed at these energies while those such as FRITIOF, which ignore string/string interactions are not [17].
In this paper, we report dE T /dη distributions measured in pPb collisions at √ s NN = 5.02 TeV by the CMS experiment at the CERN LHC. This beam energy is 25 times larger than that for the previous highest energy measurements at RHIC [18]. The analysis combines measurements from both pPb and Pbp data taking to cover 13.2 units of η, i.e., |η| < 6.6 in the laboratory frame. Since the energy per nucleon of the proton beam is higher than that of the lead one, the nucleon-nucleon center of mass is at y lab = 0.465 in the laboratory frame of reference. For symmetric heavy ion collisions, the shape of dE T /dη vs. η has only a weak dependence on the η region, which is used to classify the centrality of the events [3]. To test if this is the case for the much smaller system created in pPb collisions, events are classified according to the E T or charged-particle multiplicity in several different η regions, and the dE T /dη distributions produced by the different classification procedures are compared to each other.
The comparison of these collider data with modern event generator calculations is a significant motivation for this work. The data presented here reach into the forward region that is crucial for understanding the development of cosmic ray air showers. A significant uncertainty in cosmic ray physics arises from the simulation of very high energy hadron-air collisions [19]. This uncertainty has an important effect on the modeling of air showers and the energy calibration of modern cosmic ray observatories. For a proper description of the development of cosmic ray air showers it is crucial to understand the rapidity region within four units of the rapidity of the incoming proton or nucleus [20]. The data are compared in detail to calculations from three event generators: HIJING v2.1, EPOS-LHC and QGSJET II-04 [21-23].

The CMS apparatus
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 solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass and scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Muons are measured in gas-ionization detectors embedded in the steel flux-return yoke outside the solenoid. The silicon detectors provide tracking in the region |η| < 2.5, ECAL and HCAL cover the pseudorapidity interval |η| < 3.0 while the muon system covers the region |η| < 2.4. In the forward region, the hadron forward (HF) calorimeters cover the region 3.0 < |η| < 5.2.
Each HF calorimeter consists of 432 readout towers, containing long and short quartz fibers running parallel to the beam. By reading out the two sets of fibers separately, it is possible to distinguish showers generated by electrons and photons from those generated by hadrons. Very forward angles are covered at one end of CMS (−6.6 < η < −5.2) by the CASTOR calorimeter, and at both ends (|η| > 8.3) by the zero-degree calorimeters (ZDCs). Both CASTOR and the ZDCs consist of quartz plates or fibers embedded in tungsten absorbers. They are segmented longitudinally to allow the separation of electromagnetic and hadronic components of the showers produced by incoming particles. A more detailed description of the CMS detector, together with a definition of the coordinate system used and the relevant kinematic variables, can be found in Ref. [24].
Analysis in the midrapidity region is based upon objects produced by the CMS particle-flow algorithm [25], which reconstructs and identifies each individual particle-flow candidate with an optimized combination of information from the various elements of the CMS detector. The energy of photons is directly obtained from the ECAL measurement, corrected for the effects of the zero-suppression algorithm. The zero-suppression algorithm both speeds up the readout and reduces the volume of data that must be recorded. The energy of electrons is determined from a combination of the electron momentum at the primary interaction vertex, as determined by the tracker, the energy of the corresponding ECAL cluster, and the energy sum of all bremsstrahlung photons compatible with originating from the electron track. The energy of muons is obtained from the curvature of the corresponding track, reconstructed using information from both tracker and muon stations. For |η| < 2.5 the energy of charged hadrons is determined from a combination of their momentum measured in the tracker and the matching of ECAL and HCAL energy deposits. These energy deposits are corrected for the effects of the zero-suppression algorithm and the response function of the calorimeters to hadronic showers. Finally, the energy of neutral hadrons is obtained from the corresponding corrected ECAL and HCAL energy.
For the forward detectors, HF, CASTOR, and ZDC, there is no tracking information, therefore information from the calorimeter towers only is used for the analysis. The two HF calorimeters are each segmented into 13 rings in η. For this analysis, the first two rings, covering 3.00 < |η| < 3.15, are excluded since they are partially located in the shadow of the endcap calorimeter. The subsequent ten rings of width δη = 0.175 are grouped into 5 pairs of consecutive rings. The last ring has a width of δη = 0.3. In total, the transverse energy is measured in these six η bins in each HF calorimeter. The calibration of the HF calorimeter is derived from test beam data, and radioactive sources and has an accuracy of 10% [26]. The energy flow in the HF calorimeter is measured by summing all energy deposits above the threshold of 4 GeV in a given ring. Since CASTOR has no η segmentation, all energy deposits within it are summed together. The absolute calibration of the CASTOR calorimeter is achieved by a combination of extrapolation from the HF region for 7 TeV pp data and simulation-based corrections. The accuracy of the energy scale is estimated to be 22%. The calibration of the ZDCs is based on electromagnetic interactions that produce single neutrons in the calorimeters with the energy E beam /A [27].

Data taking and event selection
The data for this analysis were recorded during the CERN LHC 2013 pPb and Pbp data taking. During these runs, 31 nb −1 of data were collected by CMS, of which 1.14 nb −1 are used for this analysis. For this luminosity the statistical uncertainties on the data are very small compared to the systematic ones. For this paper the proton-going direction is defined to be towards positive rapidity, which implies that negative η is in the lead-going direction. The switch in the proton and lead beam directions allows the use of CASTOR for measuring E T on both the lead-and proton-going sides of the collision. For this analysis, events are selected with an unbiased hardware trigger requiring only the presence of proton and lead bunches in the CMS detector. These bunches are detected by induction counters placed 175 m from the interaction point on each side of the experiment. Furthermore, the presence of at least one single reconstructed charged-particle track with |η| < 2.4 and p T > 400 MeV/c is required. An offline selection reduces events from beam-gas or electromagnetic interactions [28]. Events are required to have at least one HF calorimeter tower with more than 3 GeV of total energy on both the positive and negative sides of the interaction point and at least one reconstructed primary vertex with at least two associated tracks. The effect of noise on the E T measurement is estimated from a sample of events collected with a random trigger when no beams are present.

Event centrality
In heavy ion collisions the activity or violence of a collision can be classified by several theoretical constructs [1]: the number of nucleons that participate in the collision, N part , by the number of collisions between participants, N coll , and by the closest distance between the centers of the colliding nuclei, which is called the impact parameter, b. The term centrality is used as an estimator of the impact parameter of the collisions. It is generally defined in terms of the multiplicity of charged-particles or the E T produced in a given η region. While in Monte Carlo (MC) simulations N part , N coll , and b are known, in data, these variables cannot be measured directly. These quantities are estimated using E T or charged-particle multiplicity, which are both believed to scale monotonically with N part or b.
The centrality of a particular event is defined to be the percentile of events with values of the estimator larger than for that particular event. A Glauber model is then used to relate the centrality to N part , N coll , and b [29].
For symmetric heavy ion collisions the correlation of centrality with N part is strong [3], but for the much smaller pPb system the fluctuations of N part with a given experimental observable are large [30]. For this paper three different measures of centrality are investigated: • HF-Single: E T deposited in the Pb-going side of HF, in −5.0 < η < −4.0, • HF-Double: The sum of E T deposited in both sides of HF, in 4.0 < |η| < 5.0, • N track : number of reconstructed tracks with p T > 400 MeV/c and |η| < 2.4.
When using the charged-particle multiplicity or E T in given η regions to define centrality there is an obvious autocorrelation between the centrality and the multiplicity or E T in that region. It is not known, however, how far these correlations extend over larger η regions. The near hermetic coverage of the CMS calorimeters, 13.2 units of η, allow for the most complete picture of energy production yet performed for proton-lead collisions at the LHC. In order to understand the correlation that can arise from a choice of the centrality variable, a study needs to be made over a large pseudorapidity range for several centrality classes.

Data analysis
The measured transverse energy densities are are presented for |η| < 2.0 in the tracker region, for 3.15 < |η| < 5.20 in the HF calorimeter, and for 5.2 < |η| < 6.6 in the CASTOR calorimeter. Because of a switch of the beam direction during the data taking, the CASTOR calorimeter can be used for both positive and negative η.
The transverse energy density is calculated using the following equation where N is the number of good events that pass the online and the offline event selection, C(η) is a correction factor that accounts for the reconstruction and triggering inefficiencies, and the index j in the summation runs over all reconstructed particle-flow objects. The correction is deduced from simulations and is defined as where the index k in the top summation runs over all generated particles. Using this definition C(η) corrects the data from the detector level of the data to the stable-particle level, i.e., those particles with lifetimes cτ > 1 cm. This correction accounts for the nonlinearity of the calorimeter response and the noise thresholds. The correction factor depends on the particle mix and average transverse momentum of the particles. The EPOS-LHC, HIJING and, QGSJET II generators are used to estimate C(η). For the analysis of the reconstructed simulated events, the event selection and noise reduction requirements are the same as for the data analysis. Events are selected by requiring at least one stable particle to be within the HF η range, 3.2 < |η| < 5.2, on both sides.
In order to focus on the centrality dependence of the transverse energy as a function of η, the events are divided into 10 bins of centrality, 0-10%, 10-20%, etc.. Here we consider 0-10% to be central and any other centrality to be peripheral. Using these definitions the ratio of peripheral to central dE T /dη is defined as This can be written as Since S PC represents a ratio of results for two data samples multiplied by a ratio of two correction factors, correlated uncertainties tend to cancel, which is a major advantage of this approach.

Systematic uncertainties
In this analysis, there are several sources of systematic uncertainties on dE T /dη: 1. The differences in E T spectra and particle composition between data and the MC simulation used to generate correction factors. The impact of these differences is estimated by generating MC samples with different particle mixes and E T spectra. These effects are most important in the tracker, |η| < 2.4, and HF regions, 3.15 < |η| < 5.20, and are less than 3%.
2. Uncertainties in the calorimeter energy scale. These are estimated by the differences in calibration from various methods. These contribute less than 1% in the tracker region, 10% for HF, and 22% for CASTOR.
3. Method of handling the noise in the calorimeters. These uncertainties are estimated by using different sets of noise reduction requirements in the analysis. These uncertainties are less than 3% in the tracker and HF regions, and are negligible for CASTOR. 4. Any asymmetries between the positive and negative sides of CMS, e.g., from dead channels, etc.. The data from pPb collisions at a given positive η are compared to those of Pbp events at the corresponding negative η. These uncertainties are up to 5.0% in the tracker region, and up to 3.5% in the HF region.
The uncertainties described above are evaluated separately in the tracker, HF, and CASTOR regions and summed in quadrature. For the CASTOR region the uncertainty in the energy scale dominates the total systematic uncertainty. Table 1 lists the systematic uncertainties on dE T /dη and S PC for each η region as a function centrality as defined by HF-Double. The systematic uncertainties are the smallest for the most central events. For S PC , there is a high degree of cancellation between the uncertainties in different centrality classes. In particular the energy scale and forward/backward systematic uncertainties cancel almost completely while the uncertainties related to the simulation and noise reduction only partially cancel. The net result is that the systematic uncertainties in S PC are considerably smaller than those in E T .

Results
The most basic measurement of E T production is performed for the minimum bias selection as a function of η. Figure 1 shows the resulting dE T /dη versus η for data and for predictions from the EPOS-LHC, QGSJET II and HIJING models. The HIJING event generator is based on a twocomponent model for hadron production in high-energy nucleon and nuclear collisions. Hard parton scattering is assumed to be described by perturbative QCD, and soft interactions are approximated by string excitations with an effective cross section. For heavy nuclei, initial parton distributions are modified with respect to those of free protons. Also, multiple scatterings inside a nucleus lead to transverse momentum (p T ) broadening of both initial-and final-state partons. Both the EPOS-LHC and QGSJET II models use Gribov-Regge theory to give a self consistent quantum mechanical treatment of the initial parton-level interactions without an arbitrary division into soft and hard interactions [31]. The EPOS-LHC generator also includes From Fig. 1 it can be seen that dE T /dη| η=0 ≈ 22 GeV. This is 1/40 of the value observed for the 2.5% most central PbPb collisions [3]. However, since the cross sectional area of a pPb collision is much smaller than that of a central PbPb collision [32,33], this result implies that the maximum energy density in pPb collisions is comparable to that achieved in PbPb collisions.
By comparing dE T /dη to dN ch /dη, which was previously measured by our experiment in proton-lead collisions at the same energy [34], it is possible to calculate the transverse energy per charged-particle. At the center-of-mass rapidity we find E T /N ch = 1.31 ± 0.07 GeV/particle for minimum bias pPb collisions at √ s NN = 5.02 TeV. This is somewhat higher than the value of 1.0 ± 0.1 GeV/particle reported by PHENIX for dAu collisions at √ s NN = 200 GeV [35]. If one assumes a thermalized system at kinetic freezeout this implies a freezeout temperature for these small systems that is about 7 ± 1% higher at RHIC than the LHC.
Predictions from the EPOS-LHC model are close to the data over the entire pseudorapidity range while those from the HIJING model are consistent with the data for η < −3 and η > 2, but are significantly below the data at midrapidity, i.e., |η| < 2. Predictions from the QGSJET II generator are consistently above the data over the entire η range. The peak of the data distribution is around η = −0.5. Both EPOS-LHC and QGSJET II generators peak close to this value while HIJING has a maximum at η = −2.5.   The rate of increase of dE T /dη| η=0 with √ s NN is stronger for AA than for pA collisions. This is expected because of the increased stopping power, i.e., the ability to decelerate nucleons, of heavy nuclei compared to protons [46,47]. The stopping power controls the total amount of energy available for particle production. The rapidity shift of the incoming nucleons is proportional to the beam rapidity for energies up to √ s NN = 63 GeV, but then seems to saturate [47-50]. This limit to the deceleration may be the reason for the change in slope of the AA data near √ s NN ≈ 10 GeV. The pA data also seems to change slope in this region but unfortunately the sparsity of data with √ s NN between 5 and 20 GeV make it difficult to determine where this change happens in pA collisions.
For energies above √ s NN ≈ 10 GeV the scaled transverse energy density increases as a power law according to s γ NN . Such an energy dependence has been previously observed for the charged-particle multiplicity density, dN ± /dη, near η = 0 [14, 34,37]. Table 2 lists the results of fitting the energy dependence of the scaled dN ± /dη and dE T /dη for central events to a function of the form s γ NN . The E T rises more rapidly with energy than the charged-particle multiplicity. Again this is expected because the mean transverse momentum is also increasing with beam energy [51]. This difference in the energy dependence of E T and multiplicity production is stronger for AA than for pA collisions. This suggests that the mean transverse momentum rises faster with energy in AA than in pA collisions.  TeV. The QGSJET model is consistent with the 20 and 200 GeV data, but is somewhat higher than the data at √ s NN = 5.02 TeV. The HIJING generator has a similar energy dependence of the data, but is consistently below the experimental results. Figure 3 shows dE T /dη versus η for pPb collisions at √ s NN = 5.02 TeV for several centralities and for three different definitions of centrality for both data and simulations. For 0-10% central collisions, dE T /dη| η=0 exceeds 50 GeV. To calculate an energy density using Eq. (1) requires knowledge of the ratio dy/dη, which depends upon the particle mix and p T spectra. This factor is evaluated using simulated events from the three MC generators and is found to be 1.12 ± 0.03. From Eq. (1) this implies an energy density at a time τ 0 = 1 fm/c of the order of 4.5 GeV/fm 3 for the top 10% pPb collisions. This is much higher than the expected threshold for the production of a quark-gluon plasma estimated from lattice QCD calculations [4]. lead-going side as the centrality increases. Predictions from the EPOS-LHC model are closest to the data for |η| < 2, whereas the HIJING generator gives a better description of the data in the lead-going region, i.e., η < −3. In the proton-going region, i.e., η > 3, the two generators are closer to each other and the data. The QGSJET II predictions significantly exceed the data at all rapidities for the 0-10% most central collisions, but are close to the data for the 40-50% and 70-80% centrality classes. As the centrality increases, dE T /dη| η=0 increases faster for the N track centrality definition than for the HF-Single or HF-Double definitions. This effect results from the autocorrelation with the centrality definition. Figure 4 shows dE T /dη scaled by the number of participant nucleon pairs as a function of N part for the far lead-going region −6.6 < η < −5.2, the midrapidity region |η| < 0.8, and the far proton-going region 5.2 < η < 6.6. The centrality definition is based on the HF-Single selection, i.e., −5.0 < η < −4.0. It is clear that the centrality dependence of E T production varies strongly with η. For N part > 3 we find that dE T /dη per participant nucleon pair rises with N part in the lead-going and midrapidity regions, but falls for the far proton-going region. This is consistent with the backward shift of the mean η with centrality observed in Fig. 3. Figure 4 also shows model predictions from EPOS-LHC, QGSJET II, and HIJING. At midrapidity none of the generators is consistent with the data over the whole range of N part . In particular, the QGSJET II model has a much stronger centrality dependence than the data. For the leadgoing region all three generators are consistent with the data within errors. For the protongoing region, all three generators are above the data, but predictions from the QGSJET II model are closer to the data than those from either EPOS-LHC or HIJING. Figure 5 shows S PC as a function of η for three centrality ranges and for all three centrality definitions for data as well as for predictions from the EPOS-LHC, QGSJET II, and HIJING event generators. As expected, S PC increases with centrality for all centrality definitions. The S PC value tends to rise with η since the centrality dependence of E T production is stronger on the lead-going side than on the proton-going side. This is presumably because particles moving in the lead direction are more likely to have multiple interactions than particles moving in the proton-going region.
The autocorrelation between the centrality definition and the measure of dE T /dη suppresses dE T /dη for peripheral events and enhances it for central events in the η region that is used for the centrality determination. These two effects naturally induce a dip in the ratio of peripheral to central distributions in that particular η region. However these dips persist for a significant η range beyond that used in a particular centrality definition. For the HF-Double and HF-Single definitions of centrality these dips are more pronounced than for the N track definition, which is based on a much larger η range. None of the considered generators is able to reproduce the η and centrality dependence of S PC , suggesting that they do not correctly model the correlations present in proton-lead collisions. The QGSJET II model, in particular, underestimates S PC for all three centrality definitions at both the 40-50% and 70-80% centrality ranges. The HIJING generator does the best job of reproducing the S PC behavior, but it too has significant tension with the data, in particular for the 40-50% centrality range.

Summary
In this paper we report the centrality and pseudorapidity (η) dependence of transverse energy (E T ) production from pPb collisions at √ s NN = 5.02 TeV over 13.  is of order of 4.5 GeV/fm 3 for the top 10% most central pPb collisions, which is comparable to those observed in PbPb collisions. As the centrality of the collision increases, the total E T increases dramatically and the mean η of the E T distribution moves towards the lead-going side of the collision. For central collisions, the peak of dE T /dη is 1.4 units below the center-of-mass rapidity. This pseudorapidity shift is almost the same as for pU collisions at √ s NN = 20 GeV.
The EPOS-LHC event generator gives a good description of the minimum bias dE T /dη distribution and peaks at an η value close to that of the data for all centralities. The centrality dependence of E T production for QGSJET II is stronger than that of the data. This model is below the data for 70-80% peripheral events and almost a factor of two above the data for the 10% most central events. Near midrapidity the HIJING generator tends to underestimate the magnitude of dE T /dη and for central collisions predicts a peak that is at significantly lower η than in the data.
Similarly to what has been seen in particle production at lower energy [52], the dE T /dη per participating nucleon-nucleon pair increases with the number of nucleons that participate in the collisions (N part ) for η values on the lead side; it is rather independent of N part near midrapidity; and it decreases with N part for η values on the proton side. The η region used to define centrality has a strong impact on the nature of the events selected. There is a significant autocorrelation of the η range used to define centrality with dE T /dη both for data, and the EPOS-LHC, QGSJET II and HIJING event generators. None of the tested event generators are able to capture all aspects of the autocorrelations seen in data.
It is clear that cosmic ray event generators have difficulties modeling proton-lead collisions. While the proton-lead system is significantly larger than the proton-nitrogen and proton-oxygen collisions occurring in air showers, these data illustrate the need for a better understanding of nuclear effects. Ultimately, protons colliding with light nuclei would be most valuable for this purpose. [45] E802 Collaboration, "Simultaneous multiplicity and forward energy characterization of particle spectra in Au+Au collisions at 11.6 A GeV/c", Phys.