Multiplicity studies and effective energy in ALICE at the LHC

arXiv:0709.1664v1 [hep-ph] 11 Sep 2007 Multiplicity Studies and Effective Energy in ALICE at the LHC A. Akindinov1 , A. Alici2,3 , P. Antonioli3 , S. Arcelli2,3 , M. Basile2,3 , G. Cara Romeo3 , M. Chumakov1 , L. Cifarelli2,3 , F. Cindolo3 , A. De Caro5 , D. De Gruttola5 , S. De Pasquale5, M. Fusco Girard5 , C. Guarnaccia5 , D. Hatzifotiadou3 , H.T. Jung6 , W.W. Jung6 , D.W. Kim6 , H.N. Kim6 , J.S. Kim6,7 , S. Kiselev1 , G. Laurenti3 , K. Lee6 , S.C. Lee6 , E. Lioublev1 , M.L. Luvisetto3 , A. Margotti3 , A. Martemiyanov1, R. Nania3 , F. Noferini2,3,4 , P. Pagano5, A. Pesci3 , R. Preghenella2,3, G. Russo5 , E. Scapparone3 , G. Scioli2,3 , R. Silvestri5 , Y. Sun7 , I. Vetlitskiy1 , K. Voloshin1 , L. Vorobiev1 , M.C.S. Williams3 , B. Zagreev1, C. Zampolli2,3,4 , A. Zichichi2,3,4 1 2 3 4 5 6 7 Institute for Theoretical and Experimental Physics, Moscow, Russia Dipartimento di Fisica dell’Università, Bologna, Italy Sezione INFN, Bologna, Italy Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy Dipartimento di Fisica dell’Università and INFN, Salerno, Italy Department of Physics, Kangnung National University, Kangnung, South Korea World Laboratory, Lausanne, Switzerland the date of receipt and acceptance should be inserted later In memory of A. Smirnitskiy1 Abstract. In this work we explore the possibility to perform “effective energy” studies in very high energy collisions at the CERN Large Hadron Collider (LHC). In particular, we focus on the possibility to measure in pp collisions the average charged multiplicity as a function of the effective energy with the ALICE experiment, using its capability to measure the energy of the leading baryons with the Zero Degree Calorimeters. Analyses of this kind have been done at lower centre–of–mass energies and have shown that, once the appropriate kinematic variables are chosen, particle production is characterized by universal properties: no matter the nature of the interacting particles, the final states have identical features. Assuming that this universality picture can be extended to ion–ion collisions, as suggested by recent results from RHIC experiments, a novel approach based on the scaling hypothesis for limiting fragmentation has been used to derive the expected charged event multiplicity in AA interactions at LHC. This leads to scenarios where the multiplicity is significantly lower compared to most of the predictions from the models currently used to describe high energy AA collisions. A mean charged multiplicity of about √ 1000 − 2000 per rapidity unit (at η ∼ 0) is expected for the most central P b − P b collisions at sN N = 5.5 TeV. PACS. PACS-key discribing text of that key – PACS-key discribing text of that key 1 Introduction priate definition of the energy available for particle production (the “effective energy”) is used. In high–energy particle collisions, bulk event properties like the average charged particle multiplicity are regarded as experimental observables of fundamental interest, providing important information on the dynamics of the interaction. In particular, the average charged particle multiplicity in multihadronic final states has so far been measured in many different interaction systems (e+ e− and pp(p̄) collisions, DIS processes, etc.) and over a wide range of centre–of–mass √ energies. Although the data show a dependence on s which is characteristic of the specific initial state under consideration, as pointed out in [1,2,3] a universal behaviour can actually be identified if the appro- The aim of this work is to address the possibility to perform an effective energy study at energies of several TeV at LHC, with the ALICE experiment [4,5,6]. With this respect ALICE (A Large Ion Collider Experiment) has an excellent capability, thanks to the presence of several detectors for the measurement of the particle multiplicity over a wide rapidity range [7,8]. Moreover, on both sides of the beam interaction point, the detector will be equipped with very forward calorimeters, the Zero Degree Calorimeters (ZDCs) [9], which will allow to derive the effective energy on an event–by–event basis by measuring the energy of the leading nucleons. 2 What we learned from previous experiments It is well known that the average charged multiplicity in e+ e− collisions follows √ a logarithmic dependence on the centre–of–mass energy s. Figure 1 shows a compilation of data from e+ e− experiments [10,11,12,13,14,15,16,17, 18,19,20,21] over a wide range of centre–of–mass energies (full black symbols), together with the result of a logarithmic fit to the measurements, indicated by the dashed line. As mentioned in section 1, the average charged multiplicity √ is characterized by a significantly different dependence on s if other initial states are considered. In particular, in the case of pp(p̄) collisions the charged particle multiplicity at a fixed centre–of–mass energy is observed to be systematically lower than √ what can be inferred from the e+ e− data at the same s (see again Fig. 1, open symbols, data from [22,23,24,25,26]). As pointed out in [1], this behaviour can be understood after considering that, while in e+ e− collisions the energy available for particle production coincides with the full centre–of–mass energy (once the effects from the initial state radiation are removed), in pp(p̄) collisions this energy is reduced with respect to √ s due to a basic feature of the hadronic interactions, the “leading effect”. The leading effect, which is related to the quantum number flow between the initial and the final state, implies that in pp(p̄) collisions there is a high probability to emit a forward baryon with large longitudinal momentum along the direction of the incident beams. Since the leading baryon carries away a fraction of the incident energy, the energy available for particle production is reduced with respect to the total centre–of–mass energy. If the leading effect is taken into account in the definition of the effective energy available for particle production, Eef f , common universal features can be observed in the two different interaction systems, e+ e− and pp(p̄). In particular, as done in [3], the effective energy can be estimated on an event–by–event basis by measuring the energy Eleading of the leading baryon in each event hemisphere (the hemispheres being defined with respect to ch This paper is organized as follows. In section 2 we briefly review the main experimental results which support the existence of a universal behaviour in particle production, independently of the nature of the colliding system. In section 3 a simplified analysis based on the PYTHIA Monte Carlo is presented, showing that this event generator is able to reproduce to a good extent the experimental observations described in section 2, and can therefore be used to evaluate the feasibility of an effective energy study at the LHC energies. A more detailed analysis is then described in section 4, where the capability of the ALICE detector to measure the energy of the leading baryons in pp collisions at the LHC is quantified using a realistic simulation of the ALICE ZDC detector response. Finally, in section 5 we present a prediction for the total charged multiplicity in P b − P b interactions at LHC, assuming that the universality features discussed herein hold also for ultrarelativistic heavy ion collisions. : 〈n 〉 2 60 e+e- data 50 40 pp(pp) data pp(pp) @ s/2 data e+e- data fit 30 20 10 0 1 10 102 3 10 s (GeV) Fig. 1. Average charged particle multiplicity measured in e+ e− (full black symbols) and pp(p̄) (open symbols) collisions. A logarithmic fit to the e+ e− data is also shown as the dashed line. The full grey symbols indicate the pp(p̄) data after the centre–of–mass energies have been scaled by a factor 12 (see text). a plane transverse to the direction of the incident beams in the centre–of–mass system). The effective energy per hemisphere (Eef f )i is then given by: (Eef f )i = √ s/2 − (Eleading )i for i = 1, 2. (1) Notice that, by measuring the energy of the leading particles event by event, a wide range of effective energies can be covered at a fixed centre–of–mass energy. Relying on the experimental observation of the independence of the two event hemispheres with respect to the leading effect [3], the total effective energy Eef f available for particle production in the whole event can be derived from the measurement of only one leading particle per event, using the relation: √ Eef f = 2(Eef f )i = s − 2(Eleading )i . (2) Correspondingly, the average total charged multiplicity in the event is given by : hnch i = 2 hnch ii . (3) Alternatively, in those events where a leading particle is measured in both hemispheres, the total effective energy can also be derived from the relation: p Eef f = s [1 − (xF )1 ][1 − (xF )2 ], (4) : 3 where (xF )i are the measured Feynman–x of the two lead√ ing nucleons, (xF )i = 2 (pL )i / s. 3 Pythia simulations The two methods of defining the effective energy in the event have been proved to be equivalent, as shown in [1]; it should be noticed, however, that the first one has the advantage of making optimal use of the data in terms of the collected event statistics, obviously owing to the much larger acceptance and efficiency of single with respect to double leading particle detection. The PYTHIA6.214 [27] Monte Carlo has been used to simulate pp collisions at a centre–of–mass energy of 14 TeV. An effective energy study carried on for pp collisions requires a precise definition of the type of events to be used. Following the choice of the original ISR–pp experiment [1,2,3], only non diffractive minimum bias events have been considered herein. It should be noted that most of the other pp(p̄) experiments [22,23,24,25,26] quoted in section 2 included double–diffractive processes in their definition of minimum bias. With PYTHIA the double– diffraction contribution is at the √ level of 15% with respect to the non diffractive one at s = 14 TeV (using default generation parameters). A brief description of the ALICE pp minimum bias trigger capabilities for both diffractive and non diffractive processes is given in subsection 4.1. To optimize the agreement with respect to the dependence observed in the data for the charged particle multiplicity as a function of the effective energy, some of the PYTHIA parameters regulating the treatment of the multiple parton interactions (MI) have been tuned. This MI model has been introduced and widely discussed in the literature [28,29,30,31] in order to describe the basic features and, in particular, the charged particle multiplicity √ of high energy minimum bias pp(p̄) final states up to s ∼ 1 TeV. It is still under investigation but represents however one possible tool to perform extrapolations in the multi–TeV domain at LHC. The set of values used in the simulation is reported in table 1. As mentioned before, after taking into account the leading effect and using the effective energy instead of the full centre–of–mass energy, a very good agreement between the measured charged particle multiplicity in e+ e− and pp collisions is obtained, as shown in Fig. 2. The pp data in this figure refer to a “minimum bias” event sample from which elastic and diffractive processes were excluded, with leading protons in the range 0.3 . xF . 0.8 (see later on sections 3 and 4). A good agreement between the inclusive pp(p̄) results presented in Fig. 1 and e+ e− results is also obtained if the pp(p̄) centre–of–mass energies are scaled by a factor 21 (full grey symbols). This is a direct consequence of the effective energy being the relevant variable in particle production, and of the assumption, supported by several measurements [1], that the Feynman–x distribution of the leading particles has a mean value equal to ∼ 0.5, resulting in an average effective energy which is about half the full centre–of–mass energy. Parameter MSTP(51) MSTP(81) MSTP(82) PARP(82) PARP(89) PARP(90) Our tuning 7 (CTEQ5L) 1 2 2.15 GeV 1000 GeV 0.215 Default 7 (CTEQ5L) 1 4 1.80 GeV 1000 GeV 0.160 Table 1. Values of the PYTHIA parameters tuned for this work to generate minimum bias (non diffractive) pp events at various centre–of–mass energies. Fig. 2. Average charged multiplicity hnchp i as a function of had 2 the effective energy Eef f (here indicated as (qtot ) ), as measured in minimum bias pp collisions collected by the SFM experiment at the CERN ISR (full circles). The data from e+ e− experiments are also shown (open circles and triangles) √ in terms of s. A fit to ISR–pp data is superimposed. The plot is taken from [2]. Notice that the only three parameters tuned correspond, respectively, to the selection of the MI mechanism features in terms of hadronic matter distribution (MSTP(82)), the regularization scale of the transverse momentum spectrum of the process (PARP(82)) √ which controls the MI rate and the exponent of the s–power law dependence of the MI mechanism (PARP(90)) [27]. Figure 3 shows the mean total charged multiplicity for generated pp collisions √ over a wide range of centre–of– mass energies, with s rescaled by a factor 12 to take into account, on average, the energy carried away by the leading nucleons, as done in section 2. To derive the average charged multiplicity hnch i all primary charged particles in the event (including the decay products of short–lived resonances) with no transverse momentum cutoff and in the 4 : full angular acceptance have been considered. Although hnch i is derived from the Monte Carlo information at the event generator level, notice that the ALICE detector is expected to measure the multiplicity with a good accuracy, high efficiency and over a wide acceptance both in case of pp and P b − P b collisions (as reported in chapter 6.1.5 of the ALICE Physics Performance Report vol. II [8]). ch 〈n 〉 Using the tuned PYTHIA Monte Carlo, √ a very good agreement with the fit that describes the s dependence of the multiplicity for e+ e− collisions (see Fig. 1) is observed in Fig. 3 over the whole range of energies. Using instead the default values, PYTHIA disagrees by ∼ 10% √ with the e+ e− fit for s > 1 TeV. 100 90 e + e - data fit PYTHIA Tuned - pp @ 70 GeV PYTHIA Tuned - pp @ 150 GeV 80 70 PYTHIA Tuned - pp @ 300 GeV PYTHIA Tuned - pp @ 700 GeV PYTHIA Tuned - pp @ 1500 GeV 60 50 PYTHIA Tuned - pp @ 3000 GeV PYTHIA Tuned - pp @ 7000 GeV PYTHIA Tuned - pp @ 14000 GeV 40 30 20 10 0 1 10 102 3 10 104 s/2 (GeV) Fig. 3. Mean charged multiplicity hnch i in pp collisions from √ PYTHIA Monte Carlo, at s = 70 to 14000 GeV. The energy on the horizontal axis is scaled by a factor 12 in order to take into account an average leading effect in the pp final states. The e+ e− fit of Fig. 1 is also plotted. A satisfactory agreement is also observed when studying the multiplicity as a function of the effective energy in each single event. Following the approach described in section 1, for each event the effective energy in a single hemisphere was derived from the energy of the corresponding leading baryon (defined as the highest longitudinal momentum baryon in the hemisphere) and then multiplied by 2, according to relation (2). The total charged multiplicity was also derived on a single hemisphere basis, scaled by the same factor of 2. As can be seen from Fig. 4, also in this case the dependence of the total charged multiplicity on the effective energy follows closely1 the fit to the e+ e− data. Notice that in the above analysis the Feynman–x of the leading baryons was restricted to be in the range: 0.3 < xF < 0.8. The lower cutoff, xmin = 0.3, is mainly F motivated by the fact that in a realistic analysis the identity of the leading particle will not be accessible. Some care is therefore required in defining an appropriate Feynman– x acceptance, in order to ensure that the energy measured in the forward region is indeed in most cases due to a leading baryon, and that the contamination from leading particles which are not baryons is kept below a reasonably small level. In Fig. 5 the xF distribution of the leading baryon, defined as the proton/neutron with the highest longitudinal momentum (i.e. with the highest Feynman– √ x xF = 2pL / s) among all baryons produced in a given event hemisphere, is shown as the dark–shaded histogram, √ for 105 pp collisions generated at s = 14 TeV. The xF distribution for the cases where this leading nucleon is also the leading particle among all particles (baryons or non baryons) of the same hemisphere is superimposed as the light–shaded histogram. For Feynman–x greater than 0.3, it can be seen that the leading nucleon is indeed the leading particle in the event hemisphere. Moreover, a request of a minimum xF allows to reduce the contamination from leading particles that are not baryons. At xF = 0.3 this contamination is ∼ 30% and rapidly decreases for xF > 0.3. For what concerns the constraint on the maximum xF , the requirement xmax = 0.8 was ispired by the original efF fective energy data analysis [1,2,3], where the same kind of cutoff on leading protons was imposed. This xF < 0.8 condition, which fairly matches the acceptance of the ALICE ZDC calorimeters for leading baryons (see later on section 4), would also imply the rejection of the proton2 single–diffraction peak (not considered in this study). The PYTHIA generator reproduces to a good extent also other features related to the leading effect which have been observed in the √ data. As an example, Fig. 6 shows, for pp collisions at s = 14 TeV, the ratio between the total charged multiplicity hnch i, measured as a function of the total effective energy Eef f given by equation (4), and the average charged multiplicity in a single hemisphere, measured as a function of the effective energy in a single hemisphere, scaled by a factor 2, Eef f = 2(Eef f )1,2 . The ratio is consistent with the relation hnch i = 2 hnch i1,2 in agreement with the hypothesis of the two event hemispheres being independent with respect to the leading effect, and of the equivalence of the two effective energy Eef f definitions presented in section 1, equations (2) and (4). 1 The values deviate systematically from the e+ e− data fit as Eef f increases whereas they always start well on the fit line. This effect is likely due to the fact that the multiple interaction parametrization of PYTHIA generator slightly depends also on the centre-of-mass energy. 2 For neutrons single–diffraction processes with charge exchange are highly unlike. 100 90 - e +e data fit 0.3 < xF < 0.8 PYTHIA Tuned - pp @ 70GeV 70 PYTHIA Tuned - pp @ 300GeV 50 Leading Particle = Baryon 0.016 0.014 PYTHIA Tuned - pp @ 3000GeV 0.012 PYTHIA Tuned - pp @ 7000GeV 0.01 PYTHIA Tuned - pp @ 14000GeV 40 0.008 30 0.006 20 0.004 10 0.002 0 1 Leading Baryon PYTHIA Tuned - pp @ 700GeV PYTHIA Tuned - pp @ 1500GeV 60 0.02 0.018 PYTHIA Tuned - pp @ 150GeV 80 5 dN/dxF 2 〈n 〉 ch 1,2 : 10 102 3 0 0 104 10 Eeff =2 (E ) eff 1,2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 (GeV) Fig. √ 4. Mean charged multiplicty hnch i in pp PYTHIA events at s = 70 to 14000 GeV with respect to effective energy. The e+ e− fit is also plotted. Here the single hemisphere variables are considered and scaled by a factor of 2 (see text). 4 Tagging of leading nucleons with the ALICE ZDC detector in pp collisions Although the programme of the ALICE experiment has its main focus on heavy ion physics, the detector will also have excellent physics capabilities in the case of pp collisions. In particular, this applies to the analysis we are presenting in this paper. 4.1 ALICE performance for the selection and measurement of pp events A detailed description of the ALICE trigger system can be found elsewhere [8,32]. Here we will limit ourselves to a brief report on both the minimum bias trigger selection and the charged particle multiplicity measurement [8] that ALICE will be able to perform in pp collisions at LHC. The minimum bias trigger is realized coupling different signals coming from the V0 [33] and the SPD [34] detectors. The general purpose of this minimum bias trigger is to select events from pp collisions with an efficiency as high as possible, and a bias as low as possible, and to reject events due to beam–gas or beam–halo. The V0 is made up of two different arrays of scintillators placed along the beam pipe in the forward/backward directions. It provides two kinds of signals: (i) VZERO.OR that requires at least one hit in one counter on one side and (ii) VZERO.AND that requires at least one hit in one counter on both sides. 0.9 1 xF Fig. 5. The xF distribution of the most energetic baryon (dark–shaded histogram) in each hemisphere for pp collisions √ at s = 14 TeV. The xF distribution of this baryon in the case it is also the most energetic particle in the hemisphere is shown as the light–shaded histogram. The SPD (Silicon Pixel Detector) is made up of two coaxial layers of silicon sensors which also provide a trigger signal (GLOB.FO) consisting in a fast–OR signal of all its 1200 chips (400 in the inner layer, 800 in the external one). Different combinations of these signals, coupled to a non background trigger (notBG, defined by requiring no signals in either of the V0 counters within appropriate time windows corresponding to beam–background processes), set different trigger configurations. The three configurations are listed in table 2, while the corresponding efficiencies are reported in table 3. MB 1 MB 2 MB 3 GLOB.FO GLOB.FO GLOB.FO or and and VZERO.OR VZERO.OR VZERO.AND and and and notBG notBG notBG Table 2. Signal configurations for pp minimum bias trigger. The multiplicity can be measured counting the “tracklets” (extracted by the association of the signals in both the two layers of the SPD) with the SPD in the central region and with the FMD (Forward Multiplicity Detector) [33] in the forward region. The pseudorapidity range covered by the ALICE detector is about 8 η–units. In this range an accurancy on the multiplicity better than 10% with 0.1 η–units bin width can be achieved (as estimated in single central HIJING [35] events). : 3.5 PYTHIA - pp @ 14 TeV - total left 0.3 < xF < 0.8 3 ch 1 PYTHIA - pp @ 14 TeV 2.5 ch 2 ch 〈n 〉 / 〈n 〉 , 〈n 〉/ 〈n 〉 ch 1 6 2 right left ment consists of two distinct calorimeters, one for leading neutrons (ZDCN), placed at zero degrees relative to the LHC axis, and one for leading protons (ZDCP), placed externally to the outgoing beam pipe on the side where positively charged particles are deflected by the beam optics. For charged particles, the Feynman–x range experimentally accessible with the ZDCs will be xF ∈ [0.30 − 0.64], as the beam optics selects energies between 2.2 TeV and 4.5 TeV. For neutral particles such constraints are clearly not present. A more detailed description of the calorimeters is given in [9]. 1.5 1 0.5 0 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000 Eeff , 2 (E ) eff 1,2 (GeV) Fig. 6. Average charged multiplicity ratio hnch i / hnch i1 as a function of the total effective energy Eef f (black symbols) and average charged multiplicity ratio hnch i2 / hnch i1 as a function of the effective energy in a single hemisphere scaled by a factor 2, Eef f = 2(Eef f )1,2 (grey symbols). Process (σ14TeV [mb]) Non Diff. (55.22) Single–Diff. (14.30) Double–Diff. (9.78) MB1 (%) 99.9 73.8 87.8 MB2 (%) 99.1 59.5 68.7 MB3 (%) 96.9 38.4 45.6 Table 3. Minimum bias trigger efficiency for different (diffractive and non diffractive) pp processes. In the following we will assume that the uncertainty on the multiplicity measurement is negligible with respect to that on the effective energy measurement. 4.2 ZDC performance for leading nucleons As mentioned in section 1, the ALICE experiment will be able to measure the energy of the leading particles needed for this study thanks to the presence of the Zero Degree Calorimeters (ZDCs) [9]. The aim of this section is to show that this system, although designed for the detection of nearly monochromatic (E √ N ≈ 2.75 TeV) leading nucleons in ion–ion collisions at sN N = 5.5 TeV, will be able to measure on an event–by–event basis leading particles in pp collisions over a wide range of energies and with a good accuracy. A scheme of the ZDC apparatus is shown in Fig. 7; it consists of two identical elements, placed on both sides of the interaction vertex at a distance of 115 m. Each ele- Fig. 7. Transverse section of the LHC beam line at a distance of 115 m from the interaction vertex. The location of the two ZDC calorimeters for protons and neutrons is also shown. The performance of the ALICE ZDC calorimeters were first checked on single highly energetic protons and neutrons, with generated longitudinal momenta in the range between 1 TeV and 6 TeV. As mentioned before, due to the beam optics the ZDC acceptance is restricted to protons with energies in the range 2.2 < E < 4.5 TeV, while in the case of neutrons the whole range of energy is accessible. The GEANT [36] package and the ALICE simulation and reconstruction software, AliRoot [37], were used for the simulation of the detector response, and to perform realistic digitization and reconstruction in the ZDC calorimeters. In Fig. 8 the energy reconstructed in the ZDCs for protons and neutrons as a function of the generated energy is shown. While a good linearity is observed in the case of neutrons over the whole range of energies, in the case of protons the reconstructed energy is underestimated with respect to the true energy above ∼ 3 TeV. This is because with increasing energy, the impact point of these particles falls closer and closer to the edge of the detector due to the beam optics, and the hadron cascade is no longer fully contained in the calorimeter. The energy resolution, shown in Fig. 9, ranges between 10% and 20% both in the neutron and proton cases in the selected energy range (from 2.2 to ZDC recontructed energy (GeV) : 7000 Neutron ZDC 6000 Proton ZDC 5000 4000 3000 2000 1000 0 0 1000 2000 3000 4000 5000 6000 7000 Energy (GeV) ZDC energy resolution (%) Fig. 8. Reconstructed energy in the proton (grey symbols) and neutron (black symbols) ZDC calorimeters, as a function of the proton/neutron generated energy. 100 Neutron ZDC 90 Proton ZDC 80 70 60 50 40 30 20 10 0 0 1000 2000 3000 4000 5000 6000 7000 Energy (GeV) Fig. 9. Energy resolution δE/E of the proton (grey symbols) and neutron (black symbols) ZDC calorimeters, as a function of the proton (neutron) generated energy. 4.5 TeV). The absolute error on the energy measurement is about 500 GeV. For protons the ZDCP energy resolution could likely be improved using the information of the impact point of the track on the calorimeter front face. After checking that the ZDCs can measure the energy of forward–going nucleons over an extended xF range, 7 their performance has been tested on fully simulated pp collisions. Starting from 14000 generated events, in about 75% of the events a signal is recorded in either the proton (ZDCP) or the neutron (ZDCN) calorimeter, in the forward or backward regions. In the majority of cases the proton calorimeter is hit by a single particle, while in the case of the neutron calorimeter the multiplicity is higher, due to additional photons coming from the decay of high–energy forward π 0 mesons produced in the interaction (in the case of the proton calorimeter, the corresponding contamination which would be expected from charged pions is to a large extent removed by the beam optics). This is demonstrated in Fig.s 10.a) and 10.b), where the multiplicity of particles detected in each of the ZDC calorimeters3 and their particle species composition are respectively shown. Moreover, looking at the fraction of deposited energy of the most energetic particle hitting the ZDCs (Fig 11), it can be seen that in nearly all cases more than 95% of the total energy released in the ZDCP is due to a single particle, while in the ZDCN this happens only in about 50% of the cases. This is again mostly due to the background coming from photons from π 0 decays mentioned above. The presence of additional particles impinging on the neutron calorimeter causes a substantial distorsion when the total energy measured in the calorimeter is used to estimate the energy of the leading particle entering the ZDCN, as can be seen in Fig 12.b, where the difference between the total energy measured in the ZDCN calorimeter and the generated leading particle energy is shown. In the case of the proton calorimeter, where this type of background is much lower, the distribution is nearly gaussian (see Fig 12.a), although the energy is, on average, slightly underestimated due to hadronic showers not being fully contained for E > 3 TeV. Therefore, in terms of the effective energy reconstruction, the proton calorimeter ZDCP is expected to provide a cleaner measurement with respect to the ZDCN. On the other hand, the neutron calorimeter covers a range in Feynman–x which is more extended than in the case of the proton calorimeter, as discussed before in this section. √ The reconstructed xreco = 2EZDC / s distribution, F where EZDC is the total energy in either the ZDCP or the ZDCN, is shown in Fig 13. In those cases where a signal is detected in both calorimeters, the highest among the two energies was taken as an estimate of the leading particle energy. The empty and the dark–shaded histograms indicate respectively the Feynman–x distribution of the reconstructed leading particles and the contamination from cases where the highest energy deposit in the calorimeter was not due to a leading baryon. This latter component, which can be regarded as a source of contamination in the measurement of the effective energy, is about 30% in the case of the ZDCP and 40% in the case of the ZDCN over the Feynman–x range used in the analysis (0.3 < xreco < 0.8). This contamiF nation, however, is expected not to affect significantly the quality of the measurement of the multiplicity as a fuction 3 In order to reject very low–energy background, only particles with Feynman–x xF > 0.1 were considered. : j hit 1 5000 0.9 ZDCP 0.8 ZDCN j (a) ZDCP ∑E 6000 P Ehit / N. of events 8 ZDCN 0.7 0.6 4000 0.5 0.4 3000 0.3 0.2 2000 0.1 0 0 1000 0.4 0.6 0.8 1 Ehit / 0 1 2 3 4 5 6 7 8 9 ∑E j hit j 10 nparticle Fig. 11. Probability distribution with respect to the fraction of deposited energy of the fastest particle in the ZDCP or ZDCN. 5000 ZDCN 4000 3000 2000 200 (a) ZDCP N. of events (b) ZDCP N. of events N. of events 0.2 (b) ZDCN 200 100 100 1000 p n e/µ K π γ p n 0 -4000 0 Fig. 10. Multiplicity of particles (nparticle ) detected in each section of the ZDC calorimeters (a) and the corresponding particle species composition (b), per single hemisphere. 0 4000 0 -4000 EZDCP - Etrue (GeV) 0 4000 EZDCN - Etrue (GeV) Fig. 12. Difference between the reconstructed and the generated energy in the ZDCP (a) and ZDCN (b). In the case of the ZDCN, the clear distortion on the positive side of the distribution in (b) is due to the presence of high energy γ’s from π 0 decays, which cause an overestimate of the reconstructed energy. 5 Nucleus–nucleus collisions of the effective energy. This is shown in Fig. 14, where the generated average charged event multiplicity√as a fuction reco s − 2EZDC of the reconstructed effective energy Eef f = (black symbols), and of the effective energy calculated at the generator level (grey symbols) are compared. In both cases equation (2) was used. The width of the horizontal binning is determined by the energy resolution of the ZDC calorimeters. The results are consistent, indicating that the limitations related to the reconstruction of the effective energy in the ZDCs and the background from other particles in the forward region do not introduce a significant bias in the measurement. We therefore expect that the ALICE experiment will have a good capability to perform an effective energy study in pp collisions at LHC. As described in the previous sections, hadron–hadron collisions produce a mean charged multiplicity in good agreement with the e+ e− collisions at the same effective energy. Another question is still open. What happens in nucleus– nucleus? The aim of this section is to investigate the possible scenario which we expect to be observed at LHC. The PHOBOS experiment at RHIC has recently shown (Fig. 15) how the total charged multiplicity in AA collisions,√scaled by the number of participant nucleons, varies with sN N energy [38]. In particular, the AA data indicate that the scaled total charged multiplicity does not depend, to a good approximation, √ of the √ on the centrality collision and that its value vs. sN N , for 20 < sN N < 200 GeV/nucleon pair, is in good √ agreement with the one measured in e+ e− collisions vs. s. These findings favour the hypotesis that in AA collisions, at very high energy, (a) good+fake 350 fake 300 700 (b) good+fake fake 600 500 250 400 200 150 300 100 200 50 100 9 〈 N ch 〉 (/ 〈 N part /2 〉 ) 400 N. of events N. of events : 40 30 20 pp( p p) Data pp( p p) (@ s /2) e +e - Data + Fit to e e PHOBOS PHOBOS interp. NA49 E895 10 0.4 0.6 0.8 1 xF 0 0.2 0.4 0.6 0.8 1 xF Fig. 13. Distribution of the leading Feynman–x reconstructed with the ZDCP (a) and ZDCN (b) (empty histograms). The contamination from the cases where the highest energy deposit in the calorimeter was not due to a leading baryon are shown as dark shaded histograms. + 0.2 0 〈 N ch 〉 / e e - Fit 0 0 (a) 1 0.5 1 (b) 10 10 2 10 3 s (GeV) Fig. 15. (a) Average charged multiplicity for pp, pp̄, e+ e− and central Au − Au events as a function of the centre–of– mass energy per binary collision. The Au − Au (P b − P b for NA49 experiment) data are scaled by a factor hNpart /2i. The dotted line is a perturbative QCD fit to the e+ e− data. The diamonds are the pp(p̄) data plotted at energy values scaled by a factor 1/2. (b) The data in (a) divided by the e+ e− fit, to allow direct comparison of different data at the same energy. Both plots (a) and (b) are taken from [38]. 100 ZDC reconstructed Eeff 95 90 PYTHIA Monte Carlo Eeff 85 ch 〈n 〉 80 75 70 multiplicity, scaled by the number of participants (Npart ), would in fact be: 65 60 2 hnch i = 72 ± 2, Npart 55 50 2000 4000 6000 8000 10000 12000 14000 Eeff (GeV) Fig. 14. Average charged multiplicity as a function of the effective energy reconstructed in the ZDC calorimeters (black symbols) and of the effective energy calculated at the generator level (grey symbols). √ Eef f would coincide with sN N for each nucleon–pair system. Assuming that this will hold also at LHC energies, it is then possible, on the basis of an extrapolation from the e+ e− fit, to derive a prediction for the mean total charged multiplicity per nucleon pair in nucleus–nucleus collisions √ at sN N = 5.5 TeV. The predicted mean total charged (5) resulting then in a total charged multiplicity in very central P b − P b collisions at the LHC (using the maximum possible value Npart = 416, which is the total number of nucleons available in P b − P b collisions): hnch i = 15000 ± 400. (6) Once the total multiplicity is fixed, a prediction for the charged multiplicity at midrapidity (which is relevant for the measurement of a lot of observables in P b − P b collisions) can be derived in the so–called limiting fragmentation hypothesis. As shown in Fig. 16, several measurements from pp(p̄) [39,40] at different centre–of–mass energies support the fact that the multiplicity at rapidities close to the beam rapidity (the so–called fragmentation region) has a shape which is independent of the energy in the collision. This effect [41] has been observed at very different centre–of–mass energies also in DIS events. It 10 : depends only on the nature of the incident systems and, in the case of nuclei, on the centrality of the collision. The same behaviour is indeed preserved in AA collisions at RHIC, as shown in Fig. 17 by the measurements of the rapidity distribution for different centralities from the PHOBOS collaboration. dNch/d η ’/〈 Npart/2 〉 Fig. 16. Limiting fragmentation in pp and pp̄ collisions at different centre–of–mass energies. 200 GeV 19.6 GeV 2 -6 2 Npart 3 0 Fig. 18. Limiting fragmentation at LHC based on an extrapolation from RHIC results in central (0–6%) ion–ion collisions. The dashed line indicates the value of the charged multiplicity per rapidity unit (scaled by the number of participants) which results in a total multiplicity (given by the integral under the curve) equal to the prediction from the e+ e− fit. The rapidity of the beam at LHC is ybeam = 8.6. The result is: 4 1 Therefore, in these hypotheses it is possible to fix the shape of the pseudorapidity distribution [39,40,41,42,43, 44,45] and derive the mean charged multiplicity at midrapidity in central P b − P b collisions at LHC, as it is shown in Fig. 18. 0-6% 0-6% 35-40% 35-40% a) -4 b) -2 0 η ’ 2 -6 -4 -2 0 η ’2 Fig. 17. PHOBOS (RHIC) results for Au − Au collisions at √ sNN = (19.6, 200) GeV. In this figure, taken from [38], the 2 results of Npart dNch /dη ′ , where η ′ = η − ybeam , are presented for different centrality bins. As shown in [39,40,41], the behaviour of the pseudorapidity distribution has some universal features and this allows to fix the shape of the pseudorapidity distribution a priori, independently of the centre–of–mass energy of the collision. Anyway such universal behaviour doesn’t allow to establish the height at which the distribution is cut. This information can be found requiring that the integral under the curve should give the total charged multiplicity as predicted from the extrapolation logarithmic fit to the e+ e− data. < dnch > |η=0 = 5.3 ± 0.5, dη (7) corresponding to about 1100 ± 100 charged tracks per rapidity unit. There are a lot of predictions for this observable based on as many models. These models, that are compatible with the actual experimental results or are tuned on them, produce a very wide spread of predictions. In particular, a recent direct extrapolation from RHIC data seems to indicate that the charged multiplicity at LHC, in heavy ion central collisions at midrapidity, could be very small (hdnch /dηi ∼ 1200) [46], in good agreement with our prediction. Figure 19 taken from [47] is a review of the results of the main models. It can be noted that there are predictions of over 6k charged tracks per rapidity unit and others of less than 3k. Our prediction is significantly low when compared with the predictions of widely used Monte Carlo generators (such as HIJING, for example). It should be noted however that other effects, in particular the jet quenching [48], could sizeably increase the multiplicity in the central rapidity region. In Fig. 19 only the point relative to HIJING takes somehow into account such an effect (averaging on the two possible scenarios with and without quenching) [47]. An increase by a factor ∼ 2 is actually predicted : 11 This will be possible taking advantage of the acceptance and energy resolution (∼ 500 GeV) of the ZDC calorimeters to measure protons and neutrons with Feynman–x 0.3 < xF < 0.8. The rather low multiplicity prediction obtained herein for large centrality P b − P b collisions√at LHC, namely hdnch /dηi = 1000 − 2000 at η ∼ 0 and sN N = 5.5 TeV, adds to the so far uncertain mosaic of the predictions of such a very fundamental quantity for the description of AA phenomena. References Fig. 19. Mean charged multiplicity per rapidity unit at η = 0 √ from different models, at sNN = 5.5 TeV. For those models for which the extrapolation to LHC energies has not been performed, the corresponding value is set to zero [47]. by HIJING when its default4 jet quenching algorithm is switched on. Even considering this additional effect, if the universality features hold at LHC energies, a relatively low value for the charged multiplicity at midrapidity is expected to be observed. In that case, while the physics reach of ALICE will not be endangered, as illustrated in [8] versus many representative physics observables, its background conditions would correspondingly improve. 6 Conclusions In this work we have estimated the average charged particle multiplicity at midrapidity of the events that will be produced in P b − P b interactions at LHC, in an extremely high energy density domain. 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