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UNIVERSIT` A DEGLI STUDI DEL PIEMONTE ORIENTALE AMEDEO AVOGADRO FACOLT` A DI SCIENZE M.F.N. UNIVERSIT` A DEGLI STUDI DI TORINO FACOLT` A DI SCIENZE M.F.N. Corso di Laurea Specialistica Interateneo in FISICA DEI SISTEMI COMPLESSI J/

  1. Contents 1 Physics motivation 20 1.1 Quark Gluon Plasma (QGP) . . . . . . . . . . . . . . . . . . 21 1.1.1 Quark Gluon Plasma formation . . . . . . . . . . . . . 23 1.1.2 Probes of Quark Gluon Plasma formation . . . . . . . 23 1.2 The J/ ψ resonance . . . . . . . . . . . . . . . . . . . . . . . . 25 1.2.1 J/ ψ production . . . . . . . . . . . . . . . . . . . . . . 26 1.2.2 J/ ψ suppression . . . . . . . . . . . . . . . . . . . . . 26 2 The ALICE experiment 28 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2 The Large Hadron Collider (LHC) . . . . . . . . . . . . . . . 28 2.3 The ALICE detector: an overview . . . . . . . . . . . . . . . 29 2.3.1 Inner Tracking System (ITS) . . . . . . . . . . . . . . 30 2.3.2 Time Projection Chambers (TPC) . . . . . . . . . . . 30 2.3.3 Transition-Radiation Detectors (TRD) . . . . . . . . . 32 2.3.4 Particle Identification (PID) . . . . . . . . . . . . . . . 32 2.3.5 Photons Spectrometer (PHOS) and Electromagnetic Calorimeter (EMCal) . . . . . . . . . . . . . . . . . . 32 2.3.6 Magnet . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.7 Muon Spectrometer . . . . . . . . . . . . . . . . . . . 33 2.3.8 Zero-Degree Calorimeter (ZDC) . . . . . . . . . . . . . 33 2.3.9 Forward Multiplicity Detector (FMD) . . . . . . . . . 33 2.3.10 Photon Multiplicity Detector (PMD) . . . . . . . . . . 33 2.3.11 T0 and V0 detectors . . . . . . . . . . . . . . . . . . . 33 2.4 ALICE detector coordinate system . . . . . . . . . . . . . . . 34 2.5 Inner Tracking System (ITS) . . . . . . . . . . . . . . . . . . 35 2.6 Muon Spectrometer . . . . . . . . . . . . . . . . . . . . . . . 35 10

  2. 2.6.1 Absorbers . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6.2 Magnetic dipole . . . . . . . . . . . . . . . . . . . . . 36 2.6.3 Tracking system . . . . . . . . . . . . . . . . . . . . . 37 2.6.4 Trigger system . . . . . . . . . . . . . . . . . . . . . . 38 2.7 The ALICE offline framework: AliRoot . . . . . . . . . . . . 38 3 Data analysis 40 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.2 Triggers and data taking at ALICE . . . . . . . . . . . . . . . 40 3.3 Data selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.4 LHC10e and LHC10f periods . . . . . . . . . . . . . . . . . . 44 3.5 Fit of the invariant mass spectrum . . . . . . . . . . . . . . . 44 3.5.1 Fitting with a Gaussian and two exponential function 45 3.5.2 The Crystal Ball function and two exponential . . . . 46 3.5.3 Fits of the invariant mass spectra: results . . . . . . . 47 3.6 Multiplicity associated to the J/ ψ production . . . . . . . . . 49 3.6.1 Multiplicity analysis results: mean values . . . . . . . 51 3.6.2 Multiplicity analysis results: distributions . . . . . . . 52 3.6.3 Correction for the number of active chips in the SPD . 55 3.7 Analysis of the J/ ψ transverse momentum . . . . . . . . . . . 58 3.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . 58 3.7.2 Analysis of the of the J/ ψ transverse momentum with- out any multipicity selection . . . . . . . . . . . . . . 58 3.7.3 Efficiency correction for the J/ ψ reconstruction . . . . 61 3.7.4 Fit of the P T spectra . . . . . . . . . . . . . . . . . . . 62 3.7.5 Analysis of the J/ ψ transverse momentum as a func- tion of multiplicity . . . . . . . . . . . . . . . . . . . . 64 3.7.6 Full statistics analysis . . . . . . . . . . . . . . . . . . 75 4 Simulations 82 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 The PYTHIA event generator . . . . . . . . . . . . . . . . . 82 4.2.1 The Configuration file (Config.C) . . . . . . . . . . . . 84 4.2.2 Event generation and reconstruction . . . . . . . . . . 84 4.3 Minimum bias simulations . . . . . . . . . . . . . . . . . . . . 85 4.3.1 Multiplicity distributions . . . . . . . . . . . . . . . . 86 4.4 J/ ψ production in Pythia . . . . . . . . . . . . . . . . . . . 88 11

  3. 4.4.1 Multiplicity distributions for events containing a J/ ψ . 88 4.4.2 Comparison between data and simulation: multiplicity 89 4.5 Analysis of the LHC10f6a production . . . . . . . . . . . . . . 91 4.5.1 The analysis of the LHC10f6a production . . . . . . . 91 4.5.2 Invariant mass spectrum . . . . . . . . . . . . . . . . . 92 4.5.3 Multiplicity study . . . . . . . . . . . . . . . . . . . . 94 4.5.4 Transverse momentum study . . . . . . . . . . . . . . 96 5 Conclusions 100 A J/ ψ yield as a function of the multiplicity 102 Bibliography 105 12

  4. List of Figures 1.1 The phase diagram of QCD. . . . . . . . . . . . . . . . . . . . 20 1.2 Charged particles multiplicities: the green area refers to the multiplicity obtained in p-p collisions at LHC in the | η | ≤ 1 range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.3 Space-time evolution for ultrarelativistic heavy ion collisions. 24 2.1 The accelerator complex at CERN. . . . . . . . . . . . . . . . 29 2.2 Layout of the ALICE detector. . . . . . . . . . . . . . . . . . 31 2.3 ALICE coordinate system. . . . . . . . . . . . . . . . . . . . . 34 2.4 Schematic view of the Inner Tracking System. . . . . . . . . . 35 2.5 The Muon Spectrometer. . . . . . . . . . . . . . . . . . . . . 37 2.6 Schematic view of the Aliroot framework. . . . . . . . . . . . 39 3.1 A MonALISA screenshot. . . . . . . . . . . . . . . . . . . . . 41 3.2 Multiplicity distributions for the LCH10d/e/f periods. . . . 43 3.3 Fit of the invariant mass spectrum with one Gaussian and two exponential. . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.4 Example of Crystal Ball functions. . . . . . . . . . . . . . . . 47 3.5 LHC10e invariant mass spectrum and fit. . . . . . . . . . . . 48 3.6 LHC10f invariant mass spectrum and fit. . . . . . . . . . . . 48 3.7 Online display of the vertex positions. The figures shows, counter-clockwise from top left, the position in the transverse plane for all events with a reconstructed vertex, the projec- tions along the transverse coordinates x and y, and the dis- tribution along the beam line (z-axis). . . . . . . . . . . . . . 49 13

  5. 3.8 The procedure used to estimate the multiplicity associated to the J/ ψ production. We show the fit of the invariant mass spectrum (top left), the interval from which the signal + back- ground multiplicity distribution is extracted (top right, high- ligted in red), the background in two side bands (bottom left, blue) and the signal region (bottom right, green). . . . . . . . 50 3.9 Multiplicity distributions, for the period LHC10e. . . . . . . . 52 3.10 Multiplicity distributions, for the period LHC10f. The black curve is the multiplicity distribution extracted in the inter- val 2 . 9 ≤ M µµ ≤ 3 . 3 GeV/ c 2 (signal+background), the red curve is the multiplicity distribution of the normalized back- ground, while the green curve is the multiplicity associated to the J/ ψ production (after the subtracting of the background contribution). . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.11 Multiplicity distribution associated to the J/ ψ production, for the LHC10e period, using the side windows number 5 (red points). We superimposed the number of J/ ψ extracted in three multiplicity bins (blue points). . . . . . . . . . . . . . 54 3.12 In this plot we compare the mean values of the multiplicity distribution associated to the J/ ψ production. The mean val- ues has been obtained using six side windows to estimate the background contributions. These values has been presented in Tables 3.3 and 3.4. . . . . . . . . . . . . . . . . . . . . . . 55 3.13 In this figure we show the multiplicity distributions for LHC10e and LHC10f period in the side window #5. The LHC10f dis- tribution is uncorrected for the SPD active chips. . . . . . . . 57 3.14 In this figure the LHC10f multiplicity distribution has been corrected for the SPD active chips. We have a better agree- ment both in mean values, both in the distributions. . . . . . 57 3.15 Invariant mass spectra and fits, for the LHC10e period, in 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c). . . . . . . . . . 59 3.16 Invariant mass spectra and fits, for the LHC10f period, in 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c). . . . . . . . . . 60 3.17 Efficiency correction data for LHC10e and LHC10f periods. . 61 14

  6. 3.18 In this plot we show the number of J/ ψ in each P T bin, cor- rected for the efficiency effects, without any multiplicity cut, for the LHC10e period. The blue line is the results of the fit. 62 3.19 In this plot we show the number of J/ ψ in each P T bin, cor- rected for the efficiency effects, without any multiplicity cut, for the LHC10f period. The blue line is the results of the fit. 63 P T 2 � � 3.20 and � P T � values corresponding to one unit variation of the χ 2 . The values presented in these two figures let us to determine the errors for LHC10e data, presented in Table 3.7. 64 3.21 Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval 0 < N tracklets ≤ 10. . . . . . . . . . 65 3.22 Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval 10 < N tracklets ≤ 20. . . . . . . . . . 66 3.23 Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval N tracklets > 20. . . . . . . . . . . . 67 3.24 Invariant mass spectra and fits, for the period LHC10f , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the corrected multiplicity interval 0 < N tracklets ≤ (10 / 0 . 9). 68 3.25 Invariant mass spectra and fits, for the period LHC10f , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c) in the cor- rected multiplicity interval (10 / 0 . 9) < N tracklets ≤ (20 / 0 . 9). The fit in the last P T bin (8-10 GeV/c) failed due to the very low statistic. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.26 Invariant mass spectra and fits, for the period LHC10f , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the corrected multiplicity interval N tracklets > (20 / 0 . 9). . . 70 15

  7. 3.27 In these plots we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, for the LHC10e period. Three multiplicity intervals has been used. The blue line is the results of the fit. . . . . . . . . . . . . . . . . . . . . . . . 71 3.28 In these plots we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, for the LHC10f period. For this period we also corrected data for the SPD active chips, dividing each multiplicity bin extreme values by the factor 0.9 (For further details see paragraph 3.6.3). The blue line is the results of the fit. . . . . . . . . . . . . . . . . . . . 72 P T 2 � � 3.29 variation in three multiplicity bins. . . . . . . . . . . . 74 3.30 � P T � variation in three multiplicity bins. . . . . . . . . . . . . 74 3.31 Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the first multiplicity interval. . . . . 76 3.32 Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6- 8 GeV/c) in the second multiplicity interval. The fit in the last P T bin (8-10 GeV/c) failed due to the low statistic. . . . 77 3.33 Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the third multiplicity interval. . . . . 78 3.34 In these plots we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, for the full statistic. The blue line is the results of the fit. . . . . . . . . . . . . . . . . . 79 � P 2 � 3.35 variation in three multiplicity bins, full statistics analysis. 80 T 3.36 � P T � variation in three multiplicity bins, full statistics analysis. 80 3.37 � P T � variation as a function of charged multiplicity (from: “Transverse momentum analysis in pp at 900 GeV and 7 TeV”), by H. Appelsh¨ auser , Univ. Frankfurt. . . . . . . . . . 81 4.1 Generated multiplicity distribution with Atlas tuning. . . . . 86 4.2 Reconstructed multiplicity distribution. . . . . . . . . . . . . 87 16

  8. 4.3 Reconstructed and generated multiplicity distribution: the area corresponding to | η | ≤ 1 is highlight in red. We can see an asymmetry in the reconstructed distribution due to the detector efficiency losses. This figure was taken from the “Multiplicity analysis and dN/d η reconstruction with the silicon pixel detector ”, by Maria Nicassio, Terzo Convegno Nazionale sulla Fisica di ALICE Frascati (Italy) - November 12-14, 2007. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.4 Generated multiplicity using kPyJpsi production method. . . 89 4.5 Reconstructed multiplicity in the SPD using kPyJpsi produc- tion method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.6 Comparison between simulated (using the Pythia method kPyJpsi ) and LHC10e multiplicity distribution. . . . . . . . 90 4.7 Comparison between simulated (using the Pythia method kPyJpsi ) and LHC10f multiplicity distribution. . . . . . . . 90 4.8 Invariant mass spectrum for opposite sign dimuons for the LHC10f6a production. . . . . . . . . . . . . . . . . . . . . . . 92 4.9 Fit of the invariant mass spectrum with the Crystal Ball func- tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 4.10 The multiplicity distributions coming from: the LHC10e pe- riod, the minimum bias simulation with the Atlas tuning and the LHC10fa production. Mean values of the distributions are presented. . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.11 Comparison between LHC10f6a and LHC10e multiplicity dis- tributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.12 Comparison between LHC10f6a and LHC10f multiplicity dis- tributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 4.13 Invariant mass spectra and fits, for the LHC10f6a produc- tion, corresponding to 6 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c) . . . . . . . . . . 97 4.14 Fit of the P T spectrum, for the LHC10f6a production. . . . . 98 4.15 Comparison between LHC10e data and LHC10f6a production. 99 4.16 Comparison between LHC10f data and LHC10f6a production. 99 A.1 Invariant mass of the dimuons versus the multiplicity. . . . . 102 A.2 Fit of the invariant mass spectra in six multiplicity bins. . . . 104 17

  9. A.3 Linear fit to the number of J/ ψ as a function of multiplicity. . 104 18

  10. List of Tables 3.1 Results of the invariant mass fits. . . . . . . . . . . . . . . . . 47 3.2 Side windows used to estimate the background contribution. . 51 3.3 LHC10e analysis: mean values of the multiplicity distribution. 51 3.4 LHC10f analysis: mean values of the multiplicity distribution. 51 3.5 SPD active chips. . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Parameters of the fit function. . . . . . . . . . . . . . . . . . . 63 P T 2 � � 3.7 Transverse momentum analysis without multiplicity cuts: and � P T � values. . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.8 LHC10e analysis: parameters of the fit function. . . . . . . . 73 P T 2 � � 3.9 LHC10e analysis: and � P T � values. . . . . . . . . . . . 73 3.10 LHC10f analysis: parameters of the fit function. . . . . . . . . 73 P T 2 � � 3.11 LHC10f analysis: and � P T � values. . . . . . . . . . . . 73 3.12 Full statistics analysis: parameters of the fit function. . . . . 75 P T 2 � � 3.13 Full statistics analysis: and � P T � values. . . . . . . . . 75 4.1 Results of the invariant mass fits. . . . . . . . . . . . . . . . . 93 4.2 Transverse momentum analysis without multiplicity cuts. . . 98 A.1 J/ ψ number and CINT1B events as a function of multiplicity. 103 19

  11. Chapter 1 Physics motivation Lattice calculation of Quantum Chromodinamics (QCD) predicts that, in an infinite homogeneous hadronic system at equilibrium, a phase transition occurs from a confined to a deconfined phase, when the temperature reaches the critical value T c ≃ 170 MeV, at vanishing chemical potential µ B = 0. At finite µ B the critical temperature is expected to be lower, as shown in the QCD phase diagram (See Figure 1.1). Figure 1.1: The phase diagram of QCD. In the original works, the lattice QCD calculations were able to explore only the µ B = 0 line (considering an equilibrated system with equal number of 20

  12. 21 CHAPTER 1. PHYSICS MOTIVATION quarks and antiquarks); in recent years the techniques and the computa- tional capabilities have increased so it has become possible to extend these studies to finite (but small) µ B , confirming the expectation. The deconfined phase is called Quark-Gluon Plasma (See Section 1.1). One of the main motivations for studying nucleus-nucleus collisions at high energy, is to achieve large enough energy densities over sufficiently large space-time volumes, that a QGP may be developed and observed. In the last 20 years many efforts have been done to the search for the Quark-Gluon Plasma through ultrarelativistic heavy ion collisions. In 1986 the Alternate Gradient Synchrotron (AGS), in Brookhaven, started accelerating nuclei, thus beginning the era of high energy nucleus-nucleus collisions. Since then, the experimental heavy-ion activity was continued with increasing luminosity and energy of the ion beams. In 1986 the Super Proton Synchrotron (SPS) at CERN, began the heavy ion collision program, with energies √ s NN from 8 to 20 GeV (in the center of mass frame per nucleon pair). In the 2000 began the Relativistic Heavy Ion Collider (RHIC) era with en- ergies of √ s NN =130-200 GeV. More recently, from March 2010 to November 2010, Large Hadron Collider (LHC) at CERN, accelerated protons at √ s =7 TeV. In particular it has been observed (Figure 1.2) that the multiplicities of charged particles obtained in proton-proton collisions (at √ s =7 TeV and in the pseudo-rapidity range | η | ≤ 1) are quite respectable ( dN/d ch ≃ 50-100) and comparable with those obtained at RHIC in semi-peripheral collisions of copper and gold ions. This result lead to the conjecture that QGP might be formed in p-p collisions as well, triggering the study of QGP signals also for these collisions. Finally, from November to December 2010, the LHC accelerated lead ions at √ s NN =2.76 TeV. 1.1 Quark Gluon Plasma (QGP) Hadrons are made of quarks and gluons. If one makes the matter have a high enough energy density, the hadrons overlap and their constituents are free to roam the system without being confined inside the original particle. At this density there is deconfinement and the system is called a Quark- Gluon Plasma (QGP). As the energy density gets to be very large, the

  13. 22 CHAPTER 1. PHYSICS MOTIVATION Figure 1.2: Charged particles multiplicities: the green area refers to the multiplicity obtained in p-p collisions at LHC in the | η | ≤ 1 range. � by compression , i.e. by putting more and more particles in the same interaction between the quarks and gluons becomes weak, in consequence � by heating , i.e. by increasing particles kinetic energies. of the asymptotic freedom of strong interactions. QCD calculation predicts that phase-transition occurs at energy density of ε c ≃ 1 GeV/ fm 3 . This can be obtained in two ways: volume; One expects then a phase diagram as shown in Figure 1.1. The solid lines indicate a first order phase transition and the dashed line a rapid crossover. At high density and small temperature, one goes into a superconductive phase, perhaps multiple phases of superconducting quark matter. The na- ture of matter at high temperatures is an issue of fundamental interest, since it occurred during the Big Bang.

  14. � pre-equilibrium (proper time τ < 1 fm/c): in this phase, hard and 23 CHAPTER 1. PHYSICS MOTIVATION 1.1.1 Quark Gluon Plasma formation � thermalization (occurring at τ ∼ 1-2 fm/c): the multiple scattering The main steps for the QGP formation, at LHC energies, are (see Figure 1.3): soft processes occur during the parton scattering, leading to the pro- � QGP phase ( τ ∼ 10-15 fm/c): at high energy densities the system duction of high- p T and low- p T particles; among the quark and gluon constituents of the colliding nucleons and � hadronization ( τ ∼ 20 fm/c): the temperature of the expanding the particles produced during the collisions, lead to a rapid increase of entropy which could eventually result in thermalization; � freeze-out ( τ → ∞ ): the expansion and the temperature fall lead reaches the deconfined phase with partonic and gluonic degrees of free- dom; medium drops down and, below the critica temperature T c , the quarks and gluons becomes again confined into hadrons; first to a reduction of the inelastic processes among hadrons, until the relative abundance of hadrons species is fixed (chemical freeze-out), and finally to the turn-off of any interaction, which fixes the kinematic spectra (kinetic freeze-out). 1.1.2 Probes of Quark Gluon Plasma formation � flow and the equation of state : the phase transition to QGP, Many signals have been proposed to probe the features of the Quark-Gluon Plasma and they are divided in two classes: the “hard probes”, originated in the early stage of the collision and the “soft probes”, generated after the decay of the plasma. Some of these probes are shown in Figure 1.3. Example of soft probes are: according to the models used, must imply a sudden change in the be- haviour of quantities such as entropy, energy density and pressure as

  15. 24 CHAPTER 1. PHYSICS MOTIVATION Figure 1.3: Space-time evolution for ultrarelativistic heavy ion collisions. a function of the baryon chemical potential or the temperature. In or- der to monitor the equation of state, the above mentioned observables must be inferred from measured quantities. The energy density, for example, can be estimated from the total transverse energy per unit of � strangeness enhancement : the production of strange particles in a rapidity of the particles producted in the collision. Information about the evolution of the system can be drawn from the kinematical spectra of particles. The analysis of particle spectra also gives information about the col- lective motion ( flow ), due to the expanding fireball of nuclear matter created in the collision. hadronic environment is strongly suppressed respect to lighter flavours, due to the higher mass of the s quark (which result in a higher pro- duction threshold). In a deconfined medium strange quarks are abun- dantly produced via the gluon-gluon fusion process (gg → s¯ s); subse- quently they survive until hadronization occurs. This result in a higher yield of strange hadrons such as Ξ (qss) and Ω (sss), which can be taken as evidence for deconfinement. The strangeness enhancement was already observed at SPS energies in Pb-Pb collisions.

  16. � high p T hadrons and jets suppression ; � quarkonia suppression . 25 CHAPTER 1. PHYSICS MOTIVATION The most important hard probes are: � collisional energy loss due to scattering with other partons ; � radiative energy loss . The presence of the medium affects the production of hadrons from initial parton scattering. A parton crossing a “coloured” medium loses energy by two mechanism: The leading mechanism at high energies is the radiative one. A parton cre- ated in the hard collisions, on a timescale short with repect to the evolution of the system is slowed down by energy loss. This results in a quenching of the hadron spectrum at high- p T . In a coloured medium, the high p T particle is most probably emitted from the surface of the fireball, so that the parton from which the away-side jets originates has to cross the whole medium: this results in a suppression of the away-side jet in central collisions. The presence of a coloured medium also affects the bound states of heavy quarks: colour screening of the binding potential by partonic matter results in quarkonia (e.g J/ ψ and Υ) suppression, if the temperature reached in the collision is sufficiently high. 1.2 The J/ ψ resonance The J/ ψ is an hadronic resonance. It was discovered in 1974 simultaneously at the “Brookhaven National Laboratory” (BNL) and at the “Stanford Lin- ear Accelerator Center” (SLAC). Hence the two names: it was christened J at Brookhaven and ψ at SLAC. The J/ ψ is a bound state of a charm and anti-charm (c¯ c) quarks in a 1 S triplet state with mass 3096.916 ± 0.011 MeV and a full width of 92.9 ± 2.8 keV. It is detected through its electromagnetic decay products: correlated muon pairs or electron-positron. The branching ratios are: J/ ψ → µ + µ − = 5.93 ± 0.06% and J/ ψ → e + e − = 5.94 ± 0.06%.

  17. 26 CHAPTER 1. PHYSICS MOTIVATION 1.2.1 J/ ψ production The J/ ψ meson is produced in hadronic collisions involving hard processes that proceed primarily through diagrams involving gluons, such as gluon- gluon fusion. Once the c¯ c pair is produced it must evolve through a hadroniza- tion process to form a physical J/ ψ . While this production has been exten- sively studied, the details of the production mechanism and hadronization remain an open question. Attempts at a theoretical description of J/ ψ pro- duction have been made, but it has proven difficult to reproduce both the observed cross sections and polarization. The Color-Singlet Model , which generates a color singlet c¯ c pair in the same quantum state as the J/ ψ , underpredicts the measured J/ ψ cross section by approximately an order of magnitude. However, recently the color sin- glet model has been revisited, since new calculations at next to leading or- der (NLO) and next-to-next-to-leading order (NNLO) have been proposed. These new terms add important contributions to the leading order calcula- tion (LO), improving the agreement between the theory and the data [5]. Alternatively, the color-octet model includes color octet c¯ c pairs that radiate soft gluons during J/ ψ formation. However, the predicted transverse J/ ψ polarization at high p T is not seen in the data. The color evaporation model , a more phenomenological approach, forms the different charmonium states in proportions determined from experimental c pair that has a mass below the D -¯ data for any c¯ D threshold and predicts no polarization. Finally, a recent perturbative QCD calculation including 3-gluon diagrams is able to successfully reproduce both the observed cross section and polar- ization results. High quality experimental results over wide kinematical and collision energy ranges are required to constrain models and to provide an improved understanding of J/ ψ (and other heavy quarkonia) production. 1.2.2 J/ ψ suppression The J/ ψ meson has a long lifetime ( ≈ 3 × 10 3 fm/c) so that, once created in a collision, it will not decay until it is far away from the collision zone. Thus, a J/ ψ born at the early stage of a collision, sees on its way out the matter produced in the collision. If it happens to cross a region occupied by a Quark-Gluon Plasma it may disappear: one expects indeed the binding

  18. 27 CHAPTER 1. PHYSICS MOTIVATION forces responsible for its existence to be severely screened in such a medium. Then, the heavy quarks no longer stay together, but may easily flight apart and, when the system has cooled down to such a temperature that the de- confined phase can no longer exist, they recombine with the surrounding light quarks to form D and ¯ D mesons. On the other hand, the large binding energy of a J/ ψ (defined as the gap mass between a D - ¯ D pair and the J/ ψ , that is about 600 MeV) prevent its breaking up as a consequence of in- teraction with normal hadrons (i.e. confined matter). These considerations have led to the suggestion that by observing a decrease in the rate of J/ ψ production in nucleus-nucleus collisions with respect to the rate observed in nucleon-nucleon collisions (i.e. measuring the J/ ψ suppression), one would have evidence for the formation of a deconfined medium. The proposal of the J/ ψ suppression as a signature of the QGP formation was made in 1986 by Matsui and Satz, while first measurements of J/ ψ production in heavy-ion reactions were performed in O-U and S-U collisions by the NA38 fixed-target experiment at the CERN/SPS. These experiments were followed a few years later by the NA50 data in Pb-Pb collisions, and more recently by the NA60 preliminary results in In-In collisions, at a sim- ilar energy ( √ s NN = 20 GeV). All these experimental results indicate a significant J/ ψ suppression in heavy ions with respect to p-p scattering.

  19. Chapter 2 The ALICE experiment 2.1 Introduction ALICE (A Large Ion Collider Experiment) is a general purpose detector at the CERN LHC. It allows a comprehensive study of hadrons, electrons, muons and photons produced in p-p and heavy nuclei (Pb-Pb) collisions. It is driven by the requirements of tracking and identifying particles in a wide momentum range (from about 100 MeV/c to about 100 GeV/c ), of reconstructing short-lived particles (such as D and B mesons), of detect- ing quarkonia and of performing these tasks in an environment with high charged particle multiplicities. 2.2 The Large Hadron Collider (LHC) With a circumference of 27 km, the Large Hadron Collider (see Figure 2.1) at the CERN of Geneva, is the largest collider in the world. It is housed in the tunnel of the previous Large Electron Positron collider (LEP), at a depth between 50 and 175 m underground. It serves as both a proton and ion collider. The nominal luminosity for p-p collisions is of 10 34 s − 1 cm − 2 , while for Pb-Pb collisions it is about 10 27 s − 1 cm − 2 . The PS and SPS rings will be used as injectors for the machine; in partic- ular the SPS injects protons in the LHC ring with an energy of 450 GeV. The beams are accelerated in two separate rings, with intersections corre- sponding to the experiments. The main experiments running at the LHC are: 28

  20. 29 CHAPTER 2. THE ALICE EXPERIMENT � A Toroidal LArge Solenoid (ATLAS): a large general purpose experi- � Compact Muon Solenoid (CMS): same as ATLAS; � LHC-beauty (LHCb): an experiment designed to study CP violation Figure 2.1: The accelerator complex at CERN. � A Large Ion Collider Experiment (ALICE): the only LHC experiment ment whose main goal is the search for the Higgs boson; � Total Cross Section, Elastic Scattering and Diffraction Dissociation in the sector of b-hadrons; � LHC-forward (LHC-f): an experiment designed to measure the energy dedicated to heavy ion physics; (TOTEM): a detector which will measure total and elastic cross sec- tions and diffractive processes; shares the interaction point with CMS; and number of forward neutral pions produced in the collisions; shares the interaction point with ATLAS. 2.3 The ALICE detector: an overview ALICE (see Figure 2.2) has the typical aspect of detectors at colliders: a cylindrical shape around the beam axis, but with in addition a Forward Muon Spectrometer, detecting muons in a large pseudorapidity domain. The ALICE detector can be divided in the following parts:

  21. � an Inner Tracking System (ITS); 30 CHAPTER 2. THE ALICE EXPERIMENT � a cylindrical Time Projection Chamber (TPC); � a Transition-Radiation Detector (TRD); 1. The central part, which covers the the pseudorapidity interval | η | ≤ 0 . 9 � a large area Particle Identification (PID) array of Time Of Flight is embedded in a large magnet with a weak solenoidal field (0.5 T). From the inside it consist of: � an electromagnetic calorimeter (PHOS); � an array of counters optimized for High-Momentum inclusive Par- � timing (T0) and vertex (V0) detectors. (TOF) counters; ticle Identification (HMPID). � a Zero-Degree Calorimeter (ZDC); � a Forward Multiplicity Detector (FMD); � a Photon Multiplicity Detector (PMD). 2. The Forward Muon Spectrometer (FMS) which covers the pseudora- pidity region − 4 . 0 < η < − 2 . 5. 3. The forward detectors, consists of: In this thesis we mainly used datas collected with the Muon Spectrometer and the Inner Tracking System (ITS) : I will describe these detectors in the next paragraph. In this paragraph the features of the others detectors are briefly presented. 2.3.1 Inner Tracking System (ITS) For a detailed description of the ITS see Section 2.5. 2.3.2 Time Projection Chambers (TPC) This is the main tracking detector of ALICE. It was designed for momentum measurement and particle identification by dE/dx. The mean momentum of particles tracked in the TPC is around 500 MeV/c.

  22. 31 CHAPTER 2. THE ALICE EXPERIMENT Figure 2.2: Layout of the ALICE detector.

  23. 32 CHAPTER 2. THE ALICE EXPERIMENT 2.3.3 Transition-Radiation Detectors (TRD) This detector fills the radial space between the TPC and the TOF. The TRD detectors will provide electron identification for momenta greater than 1 GeV/c, where the pion rejection capability through energy-loss measurement in the TPC is no longer sufficient. Such identification, in conjunction with ITS, is used in order to measure open charm and open beauty, as well as light and heavy vector mesons. The combined use of TRD and ITS will allow to separate the directly produced J/ ψ mesons from those coming from B decays. 2.3.4 Particle Identification (PID) There are two detector systems dedicated exclusively to PID: a Time Of Flight (TOF) and a small system specialized on higher momenta. The TOF system has a time resolution better than 100 ps: it is used to separate pions from kaons in the momentum range 0 . 5 < p < 2 GeV/c. In addition it is able to distinguish between electrons and pions in the range 140 < p < 200 MeV/c. The High Momentum Particle Identification (HMPID), which covers a limitated acceptance in the central barrel, was designed for hadron identification in the momentum region above 1.5-2 GeV/c. 2.3.5 Photons Spectrometer (PHOS) and Electromagnetic Calorimeter (EMCal) The PHOS is an electromagnetic calorimeter designed to search for direct photons, but it can also detect γ coming from π 0 and η decays at the highest momenta, where the momentum resolution is one order of magnitude better than for charged particles measured in the tracking detectors. The study of the high momentum particles spectrum is useful because it gives informa- tion about the propagation of jets in the dense medium created during the collision. Electomagnetic calorimetry is performed over a wider portion of the phase space by EMCal, a Pb scintillator used to improve the ALICE performance in the detection of jets. 2.3.6 Magnet Central barrel detectors are enclosed in a large magnet. The optimal choice for the experiment is a large solenoid with a weak field. The field strength of

  24. 33 CHAPTER 2. THE ALICE EXPERIMENT ∼ 0.5 T allows full tracking and particle identification down to 100 MeV/c in p T . The magnet, due to its large inner radius, can accomodate a single-arm electomagnetic calorimeter for prompt photon detection. 2.3.7 Muon Spectrometer For a detailed description of the Muon Spectrometer see Section 2.6. 2.3.8 Zero-Degree Calorimeter (ZDC) The aim of the ZDC is the estimate of the heavy-ion collision geometry through the measurement of the non-interacting beam nucleons (the “spec- tators”). The ZDC consist of four calorimeters, two for neutrons and two for protons, placed at 116 m from the interaction point, where the distance between beam pipes allows insertion of the detector. At this distance, spec- tator protons are spatially separated from neutrons by the magnetic elements of the LHC beam line. 2.3.9 Forward Multiplicity Detector (FMD) The purpose of the FMD is to measure dN/d η in the rapidity region outside the central acceptance. This detector is designed in order to measure charged particle multiplicities from tens (in p-p runs) to thousands (in Pb-Pb runs) per unit of pseudorapidity. 2.3.10 Photon Multiplicity Detector (PMD) The PMD measures the multiplicity and spatial distribution of photons in order to provide estimates of the transverse electomagnetic energy and re- action plane. It is installed at 350 cm from the interaction point, on the opposite side of the muon spectrometer. 2.3.11 T0 and V0 detectors The T0 detector, made of 24 Cerenkov radiators, generates the T0 signal for the TOF with a precision of ∼ 50 ps, and measures a rough vertex position. The V0 detector, consisting of scintillators, provides a minimum bias trigger for the central barrel detectors and can be used as a centrality indicator. It also provides a first level trigger and helps to discriminate against beam-gas

  25. 34 CHAPTER 2. THE ALICE EXPERIMENT interaction. Both T0 and V0 consist of two modules installed on each side of the interaction point. 2.4 ALICE detector coordinate system The officially adopted coordinate system is a right-handed orthogonal Carte- sian system with the origin at the beam intersection point (see Figure 2.3). � x-axis is perpendicular to the mean beam direction, aligned with the � y-axis is perpendicular to the x-axis and to the mean beam direction, Figure 2.3: ALICE coordinate system. � z-axis is parallel to the mean beam direction: hence the positive z-axis local horizontal and pointing to the accelerator center; pointing upward; is pointing in the direction opposite to the muon spectrometer.

  26. 35 CHAPTER 2. THE ALICE EXPERIMENT 2.5 Inner Tracking System (ITS) The main purposes of the ITS are the detection of the primary and sec- ondary vertices, to improve the momentum resolution at high momenta, to reconstruct low energy particles and to identify them via energy loss. The ITS surrounds the beam pipe and the system consists of six cylindrical layer of silicon detectors. It covers the rapidity range of | η | ≤ 0 . 9. Because of the high particle density expected in heavy-ion collisions at LHC, and in order to achieve the required impact parameter resolution, Silicon Pixel Detectors (SPD) have been chosen for the innermost two layers, and Silicon Drift De- tectors (SDD) for the following two layers. The two outer layers, where the track density is lower, are equipped with double-sided Silicon micro-Strip Detectors (SSD). Figure 2.4: Schematic view of the Inner Tracking System. In this work we used data collected with the SPD. The SPD detector oper- ates in a region where the track density could be as high as 50 tracks/ cm 2 , and in a relatively high radiation levels. The SPD is based on hybrid sili- con pixels, consisting of a two-dimensional matrix of reverse-biased silicon detector diodes. The SPD is equipped with a dedicated cooling system to dissipate the heat produced by the detector. 2.6 Muon Spectrometer Muon detection is performed by the spectrometer in the pseudorapidity region − 4 . 0 < η < − 2 . 5 . With this detector, the complete spectrum of heavy-quark vector mesons resonances (e.g J/ ψ , ψ ′ , Υ, Υ ′ and Υ ′′ ) can

  27. 36 CHAPTER 2. THE ALICE EXPERIMENT � an absorber complex; � a high granularity tracking system; be measured in the µ + µ − decay channel. Muon identification in the LHC environment is only feasible for muon momenta above ∼ 4 GeV, because � a large dipole magnet; of the amount of absorber material required to reduce the flux of hadrons. � four planes of trigger chambers; The spectrometer consists of the following components: 2.6.1 Absorbers The front absorber, whose length is 4.13 m ( ∼ 10 λ int ), is located inside the solenoid magnet. The volume of the absorber is made of carbon and con- crete to limit small-angle scattering and energy loss by traversing muons. At the same time the absorber is designed to protect other ALICE detectors from secondaries producted within the absorbing material itself. The spec- trometer is shielded throughout its length by a dense absorber tube. It has a conical shape to reduce background particle interaction along the length of the spectrometer. Additional protection is needed for the trigger chambers. For this reason the muon filter, an iron wall 1.2 m thick ( ∼ 7 . 2 λ int ), is placed after the last tracking chambers, in front of the first trigger chamber. 2.6.2 Magnetic dipole The size and bending strength of the muon spectrometer magnet are defined by the requirements on mass resolution and geometrical acceptance. Given the reduced requirements on the magnetic field ( ∼ 0.7 T), it is not necessary to use a superconductiong magnet. It was therefore chosen a window-frame warm magnet equipped with resistive coils and arranged so as to produce a magnetic field in the horizontal direction, along the x-axis. With its integral magnetic field of 3 Tm, the dipole will be able to bend the muons along the y-axis and will allow a mass resolution of the order of 70 MeV/ c 2 in the J/ ψ mass region. The magnet is placed directly adjacent to the ALICE L3 magnet.

  28. 37 CHAPTER 2. THE ALICE EXPERIMENT Figure 2.5: The Muon Spectrometer. 2.6.3 Tracking system The tracking chambers were designed to achieve a spatial resolution of about The tracking system covers a total area of about 100 m 2 . 100 µ . The chambers are arranged in five stations: two are placed before, one inside and two after the dipole magnet. Each station is made of two chamber planes; each of them has two cathode planes, which are both read out to provide two- dimensional hit information. Cathode Pad Chambers (CPC) and Cathode Strip Chambers (CSC) are the best suited segmentation configurations for the muon arm. They, in fact, allow a fine segmentation of the cathode plane which, in addition, can be continuously varied across the chamber area. Since the hit density decrease with the distance from the beam, larger pads are used at larger radii, keeping the total number of channels at about one million. The design of the electronics of the tracking system was driven by two main requirements: to read about one million channels up to rate of the order of 1 kHz and to achieve a space resolution of the tracking system of at least 100 µ m.

  29. 38 CHAPTER 2. THE ALICE EXPERIMENT 2.6.4 Trigger system In central Pb-Pb collision, about eight low p T muons from π and K decays are expected to be detected per event in the spectrometer. To reduce to an acceptable level the probability of triggering on events where these low- p T muons are not accompanied by the high p T ones emitted in the decay of heavy quarkonia, a p T cut has to be applied at the trigger level on each individual muon. A dimuon trigger signal is issued when at least two tracks above a predefined p T threshold are detected in an event. According to simulation results, a low- p T cut (1 GeV/c) will be used for J/ ψ and a high one (2 GeV/c) for Υ selection. The trigger is performed by two trigger stations, each consisting of two single gap Resistive Plate Chamber (RPC), placed behind the muon filter. RPCs match all the requirements concerning position resolution, fast response and low sensitivity to neutron and photon background. 2.7 The ALICE offline framework: AliRoot In this section the ALICE framework is described. The project for the AL- � the simulation of the primary hadronic collisions and the resulting ICE offline framework, AliRoot, started in 1998 and has been developed continously by the offline team. AliRoot is based on Object Oriented tech- nology (C++) and depends on the ROOT framework, which provides an � the reconstruction of the physics data (raw-data) coming from simu- environment for the development of software package for event generators, detector simulations, event reconstruction and data acquisition and analysis. The objectives of the AliRoot framework are: � the analysis of reconstructed data. detector response; lated and real events; The core of the system is the STEER module, which provides steering, run management, interface classes and base classes. The codes from differents detectors are independent so that different detector groups can work concur- rently on the system, minimizing the interferences. The hadronic collisions

  30. 39 CHAPTER 2. THE ALICE EXPERIMENT can be simulated with different Monte Carlo generator, like PYTHIA, which are interfaced to the framework in a trasparent way. The detector response simulation follows the same logic, allowing the user to switch among different transport packages like GEANT3, GEANT4 and FLUKA. Figure 2.6: Schematic view of the Aliroot framework. Let us illustrate the simulation mechanism: the primary interactions are simulated via event generators and the resulting kinematic tree is then used in the transport package. The tree contains the produced particles, defined through a set of kinematics variables, such as momenta and energies, and keep track of the production history (in term of mother-daughters relation- ship and production vertex). Each particle is then transported into the set of detectors: the point where the energy is deposited together with the amount of such energy constitutes an hit. The hits contains also information about the particle that generated them. At the next step the detector information is taken into account. The hits are “dis–integrated”: the information on the parent track is lost and the spatial position is translated into the cor- responding detector readout element (strips, pad, etc.), thus generating the digits. The digits are eventually converted in raw-data, which are stored in binary format as a “payload ”. The reconstruction chain can then start, allowing the creation of track candidates. The final ouput is an Event Sum- mary Data (ESD), a root file containing the output of the reconstruction for physics studies.

  31. Chapter 3 Data analysis 3.1 Introduction This chapter is dedicated to the analysis of the experimental data taken dur- ing the first year of p-p collisions at √ s =7 TeV, in the ALICE experiment. In the first part of this chapter I will briefly introduce the data-taking con- ditions in the ALICE experiment, and I will explain the requirements used to select good runs for physics analysis. Then I will present the fits of the invariant mass spectra, that are used to extract the number of J/ ψ and other physical variables such as its mass and width. The following section is dedicated to the study of the multiplicity associated to the J/ ψ production. In the end I’ll present the analysis of the transverse momentum distributions � CINT1B: this trigger uses the signals coming from two detectors (called of the J/ ψ both integrated and as a function of the multiplicity. 3.2 Triggers and data taking at ALICE During 2010, ALICE has collected data relative to p-p collisions at √ s =7 TeV. Two main trigger conditions have been defined for the data taking: V0A and V0B ), installed close to the interaction point. Furthermore, the signal coming from the Silicon Pixel Detector is also used. The logic OR of the signals coming from the V0s and the SPD detectors is used to define this trigger that corrensponds, to a good approximation, to the occurence of an inelastic p-p collision. 40

  32. � CMUS1B: this trigger is produced when a muon or a muon pair (dimuon) 41 CHAPTER 3. DATA ANALYSIS is detected in the muon spectrometer, in coincidence with the CINT1B trigger. During data taking, at the ALICE experiment, data are read out by the Data Acquisition (DAQ) system as raw data streams produced by the sub- detectors, and is moved and stored over several media. On this way, the raw data is formatted, the events are built, and then data is objectified in ROOT. Afterwards the raw data is automatically queued for the recon- struction. To optimize this process, data is split into parts of approximately same size called “chunks”, which are processed in parallel. At the end of the reconstruction chain the Event Summary Data (ESD) files are stored on disks and collected by period. For example, LHC10f refers to data taken in the year 2010 in the f period (the letter indicate a specific time interval). Informations about the reconstructed events and other important features (for example about the number of the working detectors, the quality of the run, etc.) are available using the “MONitoring Agent using a Large Inte- grated Services Architecture” (http://alimonitor.cern.ch/). A screenshot of the MonALISA system is reported in Figure 3.1. � AliAODs.root: these AODs contain all the information on the recon- Figure 3.1: A MonALISA screenshot. In this work we used AOD files (Analysis Object Data) which are similar to ESD (Event Summary Data). The AOD files are smaller than ESD, because they don’t contain all the informations on the event reconstruction mode. We have three type of AOD (sorted by dimensions in decreasing order): structed events.

  33. � AliAODMuons.root: these files contain the information on the recon- � AliAODDimuons.root: at least a muon pair (dimuon) detected. 42 CHAPTER 3. DATA ANALYSIS structed events when at least one muon is detected. For our purpose (i.e. the study of the dimuon kinematic variables) the dimuon AODs have been systematically used. 3.3 Data selection Data selection is a very important step to be made in the analysis in order to extract a clean sample of data. In the following pages data selection methods are discussed. In particular, data selection is performed in three levels: 1. Run selection : The first data selection has been performed in order to select those runs that passed some preliminary quality check, based on the stability of the muon spectrometer tracking and trigger perfor- mances. This study is centrally performed and the results are available at https://twiki.cern.ch/twiki/bin/view/ALICE/PWG3Muon . Data taking at the ALICE experiment is a complex task: configura- tion runs (called Technical runs ) are needed to prepare the detectors to acquire data and cannot be used for Physics analysis. The quality of data depends on several factors, strictly linked to the stability of the proton beams. For this reason each run is labeled with a special flag that give information about the type and the quality of the run. In the following analysis we only used those runs with the “PHYSICS” and “GOOD runs” labels. � The beam energy must be in the range between 3499-3501 GeV. Since we want to study the correlation between the J/ ψ production � The L3/Dipole Magnet current must be either [-30/-6 (kA)] or and the charged particles multiplicity in the central barrel, we need to select those runs in which we have data both from the Muon Spec- trometer and the Silicon Pixel Detector. We also considered the runs with the following requirements for the beam energy and the magnetic fields: [30/6 (kA)].

  34. 43 CHAPTER 3. DATA ANALYSIS 2. Pile-up events : In high-luminosity colliders, like LHC, there is a non- negligible probability that one single bunch crossing may give rise to several interactions, originating the so-called pile-up. In other words the pile-up is a sort of “events-stacking” due to the limited space and time resolution of the detectors. To quantify this effect we can refer to the pile-up correction factor . The pile-up correction factor is the mean number of collisions occured when one event has been observed in the ALICE detectors. In particular we analyzed (Figure 3.2) the multi- plicity distribution from the period LHC10d (high luminosity period), LHC10e (low luminosity period) and LHC10f (mainly low luminosity). We found a non negligible increase of the average multiplicity in the runs taken at high luminosity. For this reason, in order to avoid the pile-up effect, we decided to only analyze runs relative to lower beam luminosity, that have a pile-up correction factor smaller than 1.10. LHC10d -1 10 LHC10e LHC10f -2 10 -3 10 -4 10 -5 10 -6 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 3.2: Multiplicity distributions for the LCH10d/e/f periods. 3. Dimuons events selection : Dimuons event selection and analysis has been performed using analysis tasks in AliROOT. A task is based on a main analysis macro written in C++ language, in which we run

  35. 44 CHAPTER 3. DATA ANALYSIS � We require a CMUS1B trigger to be fired. � At least one of the muon tracks detected in the tracking chambers over the events, define cuts, fill the histograms etc. The input of these macros are the dimuon AODs files, stored on a local disk. The � Rapidity of the muon pair has to be in the range: 2 . 5 < y < 4. following selection criteria have been used for the dimuon production analysis: must have a corresponding trigger signal in the trigger chambers. 3.4 LHC10e and LHC10f periods Taking into account the previous discussion, we decided to use only data coming from LHC10e and LHC10f periods. The LHC10e period is characterized by high-statistics and low luminosity runs. The mean value of the pile-up correction factor is 1.02: this means that the pile-up effect, in this period, is negligible. During this period the detectors were in stable conditions. According to the quality check studies we discarded only a few runs (tracking problems and luminosity scans). The LHC10f period includes runs with low luminosity and some runs (at the end of the period) with high intensity. The mean values of the pile-up correction factor are 1.04 and 1.60 for the two group respectively. We didn’t consider the runs with a pile-up factor larger than 1.10. Some more runs not correctly reconstructed and others didn’t contain data from the SPD detectors (because it was turned-off) were also rejected. 3.5 Fit of the invariant mass spectrum The following analysis is based on the invariant mass spectrum of the muon pairs. We remind that for a pair of particles with mass m 1 and m 2 , energy E 1 and E 2 and momentum � p 1 and � p 2 the invariant mass M is given by the following formula (in natural units): M 2 = m 2 1 + m 2 2 + 2( E 1 E 2 − � p 1 · � p 2 ) The dimuon invariant mass spectrum, in the region 1 ≤ M µµ ≤ 5 GeV/ c 2 , is the sum of a continuum and of the J/ ψ → µ + µ − signal. In order to fit

  36. 45 CHAPTER 3. DATA ANALYSIS the dimuon spectrum and to separate the J/ ψ signal from the background, we used different methods, depending on the available statistics. 3.5.1 Fitting with a Gaussian and two exponential function When the statistic wasn’t sufficiently high, the fit was performed using a simple Gaussian function to fit the J/ ψ peak and the sum of two exponential functions to fit the background. µ µ dN/dM 3 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 5 2 M (GeV/c ) µ µ Figure 3.3: Fit of the invariant mass spectrum with one Gaussian and two exponential. Specifically, the gaussian function used is given by the following formula: � − ( x − b )) 2 � f ( x ) = a · exp 2 c where a , b and c are free parameters. The exponential function we used is the following: f ( x ) = exp ( a + b · x ) + exp ( c + d · x ) where a , b , c and d are free parameters. In Figure 3.3 I show an example of a fit to the invariant mass spectrum, using the sum of these two functions.

  37. 46 CHAPTER 3. DATA ANALYSIS The green line represents the result of the J/ ψ peak, the yellow line is the result of the background fit and the blue line is the total fit (Gaussian + two exponentials). 3.5.2 The Crystal Ball function and two exponential The simple Gaussian fit function was used when the statistics was low. However, after the complete recontruction of the LHC10e period, we started to use a Crystal Ball function to fit the J/ ψ . The Crystal Ball function is a probability density function commonly used to model various lossy processes in high-energy physics. In this analysis it was used to match data in a better way respect to the simple gaussian function, since the J/ ψ signal is not very well fitted with a symmetric function (like the Gaussian). More specifically, the Crystal Ball consists of a Gaussian core portion and a power-law low-end tail, below a certain threshold. The function itself and its first derivative are both continuous. The Crystal Ball function is given by:  � x ) 2 � − ( x − ¯ x − ¯ x exp for > α  2 σ 2 σ    f ( x ; α, n, ¯ x, σ ) = N · � − n  � B − ( x − ¯ x ) x − ¯ x  A · for ≤ − α   σ σ where: � n � n � −| α | 2 � A = · exp | α | 2 B = n | α | − | α | N is a normalization factor, α, n, ¯ x and σ are parameters which are fitted to the data. In Figure 3.4 I present some examples of the Crystal Ball function. ' resonance. We also fitted the signal of the ψ ′ In order to fit the background we used the sum of two exponential function: f ( x ) = exp ( a + b · x ) + exp ( c + d · x ) where a , b , c and d are free parameters. In the following sections, because of the high statistics, we’ll systematically use the Crystal Ball function. At high statistics we can also observe (although its contribution is quite low) the peak associated to the ψ resonance using the Crystal Ball function.

  38. 47 CHAPTER 3. DATA ANALYSIS Figure 3.4: Example of Crystal Ball functions. 3.5.3 Fits of the invariant mass spectra: results In Figures 3.5, 3.6 the fit of the invariant mass spectrum, for the LHC10e and LHC10f periods are presented. In order to obtain these results we applied the run selection previously discussed. We can clearly see the peak of the J/ ψ . The peak of the ψ ′ is also visible. The yellow line is the result of the background fit, while the green line is the Crystal Ball function used to fit the J/ ψ . The Crystal Ball function is also used to fit the ψ ′ . The blue line is the result of the total fit. In Table 3.1 I summarize the results obtained with the fit of invariant mass spectra, using the Crystal Ball and the sum of two exponential functions. We report the number of dimuon events, number, mass, and width of the J/ ψ and, finally, the signal to background ratio. We can see that the S/B ratio, for the LHC10f period, is lower than in LHC10e (due to the fact that we required only one trigger matching). M J/ψ (GeV/ c 2 ) Γ J/ψ (MeV/ c 2 ) Period Events N J/ψ S/B LHC10e 316083 3185 ± 84 3.113 ± 0.002 92.458 ± 0.671 2.185 LHC10f 378827 2261 ± 86 3.116 ± 0.003 92.116 ± 0.305 0.918 Table 3.1: Results of the invariant mass fits.

  39. 48 CHAPTER 3. DATA ANALYSIS µ µ dN/dM ± N = 3185 84 ψ J/ 3 10 2 10 10 1.5 2 2.5 3 3.5 4 4.5 5 2 M (GeV/c ) µ µ Figure 3.5: LHC10e invariant mass spectrum and fit. µ µ dN/dM ± N = 2261 86 ψ J/ 3 10 2 10 10 1 1.5 2 2.5 3 3.5 4 4.5 5 2 M (GeV/c ) µ µ Figure 3.6: LHC10f invariant mass spectrum and fit.

  40. 49 CHAPTER 3. DATA ANALYSIS Figure 3.7: Online display of the vertex positions. The figures shows, counter-clockwise from top left, the position in the transverse plane for all events with a reconstructed vertex, the projections along the transverse co- ordinates x and y, and the distribution along the beam line (z-axis). 3.6 Multiplicity associated to the J/ ψ production In this paragraph I will present the procedure we used to obtain the charged multiplicity associated to the J/ ψ production (See also Figure 3.8). The charged multiplicity, in the central barrel, is estimated by counting the number of tracklets associated to the reconstructed vertex (Figure 3.7). In particular, in the SPD analysis, the position of the interaction vertex is reconstructed by correlating hits in the two silicon pixel layers to obtain tracklets [12]. The number of charged particles is then estimated by counting the number of these tracklets. In order to extract the multiplicity associated to the J/ ψ production we used this procedure: 1. The first task is to make a fit of the invariant mass spectrum, in order to estimate the number of J/ ψ events. Also in this case we used a Crystal Ball function to fit the J/ ψ , and two exponential to fit the background. 2. We extracted the multiplicity distribution corresponding to events with a dimuon in the J/ ψ invariant-mass interval 2 . 9 ≤ M µµ ≤ 3 . 3 GeV/ c 2 : this multiplicity distribution includes both the contribution

  41. 50 CHAPTER 3. DATA ANALYSIS of signal and background. 3. In order to estimate the background we considered the multiplicity distribution in one (or two) side windows. We decided to use different side windows, in order to find possible dependences on the region used to subtract the background contribution. These intervals are listed in Table 3.2. The background multiplicity distribution, extracted from these side windows, is then normalized to the number of background events under the J/ ψ peak. 4. The normalized multiplicity distribution for background events is fi- nally subtracted from the multiplicity distribution for events in 2 . 9 ≤ M µµ ≤ 3 . 3 GeV/ c 2 . In this way we obtained the multiplicity distribu- tion associated to the J/ ψ production. Figure 3.8: The procedure used to estimate the multiplicity associated to the J/ ψ production. We show the fit of the invariant mass spectrum (top left), the interval from which the signal + background multiplicity distribution is extracted (top right, highligted in red), the background in two side bands (bottom left, blue) and the signal region (bottom right, green).

  42. 51 CHAPTER 3. DATA ANALYSIS Value ( GeV/c 2 ) Interval 1 1.5 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.5 2 2.0 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.0 3 1.5 ≤ M µµ ≤ 2.5 4 2.0 ≤ M µµ ≤ 2.5 5 3.5 ≤ M µµ ≤ 4.5 6 3.5 ≤ M µµ ≤ 4.0 Table 3.2: Side windows used to estimate the background contribution. 3.6.1 Multiplicity analysis results: mean values In the next Tables I will present the results of the multiplicity analysis. In Tables 3.3 and 3.4 I summarize the mean values of the multiplicity distri- butions. LHC10e period Value ( GeV/c 2 ) Interval � N tracklets � 1 1.5 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.5 15.5 ± 0.2 2 2.0 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.0 15.6 ± 0.2 3 1.5 ≤ M µµ ≤ 2.5 15.5 ± 0.2 4 2.0 ≤ M µµ ≤ 2.5 15.5 ± 0.2 5 3.5 ≤ M µµ ≤ 4.5 16.1 ± 0.3 6 3.5 ≤ M µµ ≤ 4.0 16.2 ± 0.3 Table 3.3: LHC10e analysis: mean values of the multiplicity distribution. LHC10f period Value ( GeV/c 2 ) Interval � N tracklets � 1 1.5 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.5 12.7 ± 0.3 2 2.0 ≤ M µµ ≤ 2.5 + 3.5 ≤ M µµ ≤ 4.0 12.9 ± 0.3 3 1.5 ≤ M µµ ≤ 2.5 12.5 ± 0.3 4 2.0 ≤ M µµ ≤ 2.5 12.6 ± 0.3 5 3.5 ≤ M µµ ≤ 4.5 14.5 ± 0.3 6 3.5 ≤ M µµ ≤ 4.0 14.3 ± 0.4 Table 3.4: LHC10f analysis: mean values of the multiplicity distribution.

  43. 52 CHAPTER 3. DATA ANALYSIS 3.6.2 Multiplicity analysis results: distributions In Figures 3.9 and 3.10 we show the multiplicity distributions. For each interval (side window) we present the multiplicity distribution obtained in the interval 2 . 9 ≤ M µµ ≤ 3 . 3 GeV/ c 2 before subtracting the background (black points), the normalized background distributions (red points) and, finally, the multiplicity distribution associated to the J/ ψ production (green points). counts counts Side window #1 Side window #2 signal signal background background signal+background signal+background 2 2 10 10 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets counts counts Side window #3 Side window #4 signal signal background background signal+background signal+background 10 2 10 2 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets counts counts Side window #5 Side window #6 signal signal background background signal+background signal+background 2 2 10 10 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets Figure 3.9: Multiplicity distributions, for the period LHC10e.

  44. 53 CHAPTER 3. DATA ANALYSIS counts counts signal signal Side window #1 Side window #2 background background signal+background signal+background 2 2 10 10 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets counts counts signal signal Side window #3 Side window #4 background background signal+background signal+background 2 2 10 10 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets counts counts signal signal Side window #5 Side window #6 background background signal+background signal+background 10 2 10 2 10 10 1 1 0 10 20 30 40 50 60 70 80 90 0 10 20 30 40 50 60 70 80 90 N N tracklets tracklets Figure 3.10: Multiplicity distributions, for the period LHC10f. The black curve is the multiplicity distribution extracted in the interval 2 . 9 ≤ M µµ ≤ 3 . 3 GeV/ c 2 (signal+background), the red curve is the multiplicity distribu- tion of the normalized background, while the green curve is the multiplicity associated to the J/ ψ production (after the subtracting of the background contribution).

  45. 54 CHAPTER 3. DATA ANALYSIS We can see that, within the same period, the distributions are quite simi- lar: there isn’t a big dependence on the side windows used to subtract the background contribution. On the contrary, the multiplicity distributions ob- tained from LHC10e data are different from those obtained in the LHC10f period. This is also clear comparing the � N tracklets � values reported in Tables 3.3 and 3.4. In Figure 3.11 I show the multiplicity distribution associated to the J/ ψ production, for the LHC10e period (red points). We choose the side windows number 5 (3.5 ≤ M µµ ≤ 4.5 ( GeV/c 2 )) to subtract the back- ground. We have then considered another approach to obtain the multiplic- ity distribution associated to J/ ψ production. We have obtained the mass spectra for three multiplicity bins (0 < N tracklets ≤ 10, 10 < N tracklets ≤ 20, 20 < N tracklets ≤ 40,) and fitted them with the Cristal Ball function. The number of J/ ψ was extracted for each multiplicity bin and superimposed to the multiplicity distribution. We find a good agreement between the two methods. counts Data (LHC10e) 2 10 10 1 0 10 20 30 40 50 60 70 N tracklets Figure 3.11: Multiplicity distribution associated to the J/ ψ production, for the LHC10e period, using the side windows number 5 (red points). We superimposed the number of J/ ψ extracted in three multiplicity bins (blue points).

  46. 55 CHAPTER 3. DATA ANALYSIS 3.6.3 Correction for the number of active chips in the SPD In Figure 3.12 I present the mean values of the multiplicity associated to the J/ ψ production (obtained with LHC10e and LHC10f data), versus the side windows used to subtract the background. We can see an increase of multiplicy in the side windows 5 and 6, both in the LHC10e and LHC10f data. However, the most striking difference is visible between the average multiplicity values of the two periods. 〉 tracklets LHC10e LHC10f N 18 〈 16 14 12 10 1 2 3 4 5 6 Side window Figure 3.12: In this plot we compare the mean values of the multiplicity distribution associated to the J/ ψ production. The mean values has been obtained using six side windows to estimate the background contributions. These values has been presented in Tables 3.3 and 3.4. If we consider the side windows 5 and calculate the ratio between the mean values of the two period, we obtain: � N tracklets � LHC 10 f = 14 . 5 16 . 1 = 0 . 90 � N tracklets � LHC 10 e This difference, of about 10%, can be caused by a variation in the number of active chips in the Silicon Pixel Detector. We calculated (See Table 3.5) the approximate number of active chips in the two periods: we obtained a ratio of 0.97. Although the reduction in the number of SPD chips cannot fully

  47. 56 CHAPTER 3. DATA ANALYSIS explain the difference obtained between the two periods, we have assumed that the difference between the LHC10e and LHC10f comes from a reduction in the SPD efficiency. Period Number of active SPD chips LHC10e 954 LHC10f 928 Ratio(f/e period) 0.97 Table 3.5: SPD active chips. We decided therefore to correct the raw multiplicity distribution for the period LHC10f using this formula: � N trackletsraw � LHC 10 f � N trackletscorrected � LHC 10 f = 0 . 9 while we assume a 100% efficiency for the period LHC10e: � N trackletscorrected � LHC 10 e = � N trackletsraw � LHC 10 e In order to see the effect of this correction we show the multiplicity distribu- tions, associated to the J/ ψ production, obtained from LHC10e and LHC10f data, using the side window 5. In Figure 3.13 I show the multiplicity before the correction: we can see a difference both in the mean values and in the shape of the distributions. In Figure 3.14 I show the multiplicity after the correction: we have a better agreement both in mean values and in the the distributions. � N tracketscorrected � LHC 10 e = 16 . 1 ± 0 . 3 � N tracketscorrected � LHC 10 f = 15 . 8 ± 0 . 4 Since the correction for the SPD active chips seems to improve the agreement between the multiplicity distributions in the two periods, we decided to apply this correction to the following work, dedicated to the study of the J/ ψ transverse momentum. The use of this correction is essential to have a more uniform value of multiplicity, and allows to combine together the results from the two periods under discussion.

  48. 57 CHAPTER 3. DATA ANALYSIS counts Side band #5 -1 10 Data (LHC10e) Data (LHC10f) 〈 〉 ± N = 16.1 0.3 tracklets -2 10 〈 〉 ± N = 14.5 0.3 tracklets -3 10 -4 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 3.13: In this figure we show the multiplicity distributions for LHC10e and LHC10f period in the side window #5. The LHC10f distribution is uncorrected for the SPD active chips. counts Side band #5 -1 Data (LHC10e) 10 Data (LHC10f) 〈 〉 ± N = 16.1 0.3 tracklets -2 〈 〉 ± 10 N = 15.8 0.4 tracklets -3 10 -4 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 3.14: In this figure the LHC10f multiplicity distribution has been corrected for the SPD active chips. We have a better agreement both in mean values, both in the distributions.

  49. 58 CHAPTER 3. DATA ANALYSIS 3.7 Analysis of the J/ ψ transverse momentum 3.7.1 Introduction In this section I will present the study of the J/ ψ transverse momentum. In this analysis, in order to estimate the background contribution, we cannot use the side windows method, because we found that the value that we extracted for the J/ ψ transverse momentum strongly depends on the side band used to subtract the background. For this reason we followed this procedure: 1. First we obtained the invariant mass spectra corresponding to eight dimuon P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c). 2. We fitted the invariant mass spectra (using a Crystal Ball and two exponential functions) in order to extract the number of J/ ψ in each of the eight P T bins. Afterwards, we divided the number of J/ ψ in the two last P T bins (6-8 GeV/c, 8-10 GeV/c), by a factor two, because the amplitude of these bins is twice the others. Then we corrected these values bin per bin by the reconstruction efficiencies of the J/ ψ in the muon spectrometer. 3. We plotted the number of J/ ψ versus P T and fitted these distributions P T 2 � � to obtain � P T � and . 4. This procedure was first performed without any multiplicity selection. 5. Afterwards we repeated this procedure in three intervals of multiplic- ity. We considered the following intervals: 0 < N tracketscorrected ≤ 10, 10 < N tracketscorrected ≤ 20, N tracketscorrected > 20. 3.7.2 Analysis of the of the J/ ψ transverse momentum with- out any multipicity selection In Figures 3.15 and 3.16 I will show the invariant mass spectra and the fit results for LHC10e and LHC10f periods. The number of J/ ψ is reported in each figure.

  50. 59 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM ± dN/dM Bin 1 N = 491 32 ± Bin 2 N = 950 43 ψ ψ J/ J/ 3 10 3 10 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ 3 µ 10 µ µ dN/dM ± dN/dM ± Bin 3 N = 717 35 Bin 4 N = 444 28 ψ ψ J/ J/ 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± 2 ± Bin 5 10 N = 141 16 N = 259 21 Bin 6 ψ ψ J/ J/ 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM 2 dN/dM ± 10 ± Bin 7 N = 132 15 Bin 8 N = 59 10 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.15: Invariant mass spectra and fits, for the LHC10e period, in 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c).

  51. 60 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM ± dN/dM ± Bin 1 Bin 2 N = 346 29 N = 593 39 ψ ψ J/ J/ 3 10 3 10 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ 10 3 µ dN/dM ± dN/dM ± Bin 3 N = 474 34 Bin 4 N = 334 10 ψ ψ J/ J/ 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± Bin 5 ± N = 230 21 Bin 6 N = 157 18 ψ ψ J/ 10 2 J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM Bin 7 Bin 8 ± N = 122 17 N = 22 10 ψ ψ 2 J/ J/ 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.16: Invariant mass spectra and fits, for the LHC10f period, in 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c).

  52. 61 CHAPTER 3. DATA ANALYSIS 3.7.3 Efficiency correction for the J/ ψ reconstruction As mentioned in the previous sections, we need to correct the number of J/ ψ for the acceptance of the muon arm detectors and for the J/ ψ reconstruction and triggering efficiencies. This task has been performed generating, with a Monte Carlo simulation, a large sample of signal events with P T and y distribution parameterized with theoretical calculations. The events have then been reconstructed with the same algoritm applied to real data, and the acceptance has been obtained as the ratio between reconstructed and generated events, as a function of P T . The tracking efficiency for the muon spectrometer is calculated taking into account the intrinsic efficiency per chamber and the conditions of the tracking algorithm: a (97.1 ± 0.8)% effi- ciency is obtained. In a similar way the efficiency of the trigger detectors is found to be around 96%. In Figure 3.17 I show the acceptance per efficiency as a function of the transverse momentum, for the LHC10e and LHC10f pe- riods. We corrected data dividing the number of J/ ψ in each P T bin by the corresponding value acceptance per efficiency extracted from Figure 3.17. 0.65 LHC10e LHC10f 0.6 0.55 0.5 0.45 0.4 0.35 0 1 2 3 4 5 6 7 8 9 10 P (GeV/c) T Figure 3.17: Efficiency correction data for LHC10e and LHC10f periods.

  53. 62 CHAPTER 3. DATA ANALYSIS 3.7.4 Fit of the P T spectra The next step consists in plotting the corrected number of J/ ψ versus P T . Then we fitted these distributions using the following function: dN P T = c 1 · � 2 � x dP T � � P T 1 + c 2 where c1 , c2 and x are free parameters. The function that we have chosen is very similar to the one used at the RHIC to fit the P T spectra: dN P T = c 1 · � 2 � 6 dP T � � P T 1 + c 2 The only difference is the exponent at the denominator: in our analysis we used a free exponent, while it was fixed to 6 at RHIC. This choice is due to the fact that, at the LHC higher energies are used and the slope of the P T spectrum becomes less steep. The results of the fits are presented in Figures 3.18, 3.19 and in Tables 3.6, 3.7. ψ Number of J/ LHC10e 3 10 2 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 3.18: In this plot we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, without any multiplicity cut, for the LHC10e period. The blue line is the results of the fit.

  54. 63 CHAPTER 3. DATA ANALYSIS ψ Number of J/ LHC10f 3 10 2 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 3.19: In this plot we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, without any multiplicity cut, for the LHC10f period. The blue line is the results of the fit. Period c1 c2 x (3 . 139 ± 0 . 170) · 10 3 LHC10e 3 . 341 ± 0 . 284 3 . 113 ± 0 . 216 (3 . 105 ± 0 . 168) · 10 3 LHC10f 3 . 360 ± 0 . 228 3 . 124 ± 0 . 207 Table 3.6: Parameters of the fit function. P T 2 � ( GeV/c ) 2 � Period � P T � ( GeV/c ) 8.53 ± 0 . 82 2 . 42 ± 0 . 11 LHC10e 0 . 79 0 . 10 8.56 ± 0 . 68 2 . 43 ± 0 . 10 LHC10f 0 . 72 0 . 10 P T 2 � � Table 3.7: Transverse momentum analysis without multiplicity cuts: and � P T � values. P T 2 � � The and � P T � errors, presented in Table 3.7, has been estimated using the following method: 1. We fitted the transverse momentum spectrum considering c2 and x as free parameters. 2. We extracted the value of the parameters (Table 3.6) and computed P T 2 � � the and � P T � .

  55. 64 CHAPTER 3. DATA ANALYSIS 3. We let the c2 parameter varying in a symmetric interval, in which c2 is the mean value. The same procedure was considered for the exponent ( x ). 4. For each couple of c2 and x parameters we fitted the transverse mo- mentum spectrum (considering c2 and x as fixed parameters). 5. We computed the χ 2 as a function of P T 2 � � and � P T � . P T 2 � � 6. We searched for the and � P T � values corresponding to one unit variation of the χ 2 . These values are shown by the red arrows in Figures 3.20. P T 2 � � 7. The difference between these and � P T � values and those ob- tained with the free parameters fit, let us to determine the error. Entries Entries 200 250 180 160 200 140 120 150 100 80 100 60 40 50 20 0 0 7 7.5 8 8.5 9 9.5 10 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 <p 2 > <p > T T P T 2 � � Figure 3.20: and � P T � values corresponding to one unit variation of the χ 2 . The values presented in these two figures let us to determine the errors for LHC10e data, presented in Table 3.7. 3.7.5 Analysis of the J/ ψ transverse momentum as a function of multiplicity The analysis of the transverse momentum of the J/ ψ has been performed in three multiplicity bins, using the same approach described in the previous sections. The results are showed in Figures 3.21, 3.22, 3.23, 3.24, 3.25, 3.26, 3.27, 3.28 and in Tables 3.8, 3.9, 3.10, 3.11.

  56. 65 CHAPTER 3. DATA ANALYSIS µ µ µ µ 3 ± 10 dN/dM Bin 1 dN/dM Bin 2 ± N = 215 20 N = 430 27 3 ψ ψ 10 J/ J/ 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM Bin 3 ± dN/dM ± N = 277 20 Bin 4 N = 163 17 ψ 2 ψ J/ 10 J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM Bin 5 ± dN/dM ± Bin 6 N = 35 N = 91 12 8 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM Bin 7 ± dN/dM ± Bin 8 N = 44 7 N = 13 5 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.21: Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval 0 < N tracklets ≤ 10.

  57. 66 CHAPTER 3. DATA ANALYSIS µ µ µ µ ± dN/dM Bin 1 dN/dM ± N = 136 18 10 3 Bin 2 N = 257 22 ψ ψ 3 J/ J/ 10 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM Bin 3 Bin 4 ± N = 257 22 N = 137 16 ψ 10 2 J/ ψ J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± ± Bin 5 Bin 6 N = 51 9 N = 88 13 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ ± dN/dM dN/dM Bin 7 N = 44 9 ± Bin 8 N = 27 6 ψ J/ ψ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.22: Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval 10 < N tracklets ≤ 20.

  58. 67 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM ± dN/dM Bin 1 N = 132 17 ± 3 Bin 2 N = 255 24 ψ 10 J/ ψ J/ 3 10 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± Bin 4 ± Bin 3 N = 187 20 N = 143 16 10 2 ψ ψ J/ J/ 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± ± Bin 6 Bin 5 N = 54 10 N = 79 13 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM Bin 7 ± N = 44 9 Bin 8 N = 19 5 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.23: Invariant mass spectra and fits, for the period LHC10e , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the multiplicity interval N tracklets > 20.

  59. 68 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM Bin 1 ± dN/dM ± N = 196 21 Bin 2 N = 319 28 ψ J/ ψ 3 J/ 10 10 3 10 2 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 3 ± ± N = 255 23 Bin 4 N = 154 18 ψ ψ J/ J/ 10 2 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ 2 µ 10 µ dN/dM dN/dM ± Bin 6 ± Bin 5 N = 104 15 N = 65 12 ψ J/ ψ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM Bin 7 Bin 8 ± N = 42 11 N = 11 7 ψ J/ ψ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.24: Invariant mass spectra and fits, for the period LHC10f , corre- sponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the corrected multiplicity interval 0 < N tracklets ≤ (10 / 0 . 9).

  60. 69 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM dN/dM ± ± Bin 1 N = 126 18 Bin 2 N = 177 22 3 ψ 10 ψ J/ J/ 3 10 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± Bin 4 ± Bin 3 N = 156 19 N = 119 16 ψ ψ J/ J/ 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ 2 10 µ µ µ µ dN/dM dN/dM Bin 5 ± Bin 6 ± N = 88 13 N = 55 10 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ dN/dM ± Bin 7 N = 49 11 ψ J/ 10 1 1.5 2 2.5 3 3.5 4 4.5 2 M (GeV/c ) µ µ Figure 3.25: Invariant mass spectra and fits, for the period LHC10f , cor- responding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c) in the corrected multiplicity interval (10 / 0 . 9) < N tracklets ≤ (20 / 0 . 9). The fit in the last P T bin (8-10 GeV/c) failed due to the very low statistic.

  61. 70 CHAPTER 3. DATA ANALYSIS µ µ 3 µ µ 10 dN/dM dN/dM ± 10 3 Bin 1 ± Bin 2 N = 16 10 N = 81 18 ψ ψ J/ J/ 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ 2 µ µ 10 µ µ dN/dM ± dN/dM Bin 3 ± N = 68 14 Bin 4 N = 61 12 ψ J/ ψ J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± ± Bin 5 Bin 6 N = 34 8 N = 40 9 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 7 ± ± Bin 8 N = 19 5 N = 29 8 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.26: Invariant mass spectra and fits, for the period LHC10f , corre- sponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the corrected multiplicity interval N tracklets > (20 / 0 . 9).

  62. 71 CHAPTER 3. DATA ANALYSIS ψ Number of J/ ≤ 0 < N 10 tracklets 3 10 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T ψ Number of J/ 3 10 ≤ 10 < N 20 tracklets 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T ψ Number of J/ 3 10 N > 20 tracklets 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 3.27: In these plots we show the number of J/ ψ in each P T bin, cor- rected for the efficiency effects, for the LHC10e period. Three multiplicity intervals has been used. The blue line is the results of the fit.

  63. 72 CHAPTER 3. DATA ANALYSIS ψ Number of J/ ≤ 0 < N (10/0.9) 3 10 tracklets 2 10 10 1 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T 3 10 ψ Number of J/ ≤ (10/0.9) < N (20/0.9) tracklets 2 10 0 1 2 3 4 5 6 7 8 p (GeV/c) T ψ Number of J/ N > (20/0.9) tracklets 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 3.28: In these plots we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, for the LHC10f period. For this period we also corrected data for the SPD active chips, dividing each multiplicity bin extreme values by the factor 0.9 (For further details see paragraph 3.6.3). The blue line is the results of the fit.

  64. 73 CHAPTER 3. DATA ANALYSIS LHC10e period: results Multiplicity interval c1 c2 x (1 . 467 ± 0 . 156) · 10 3 0 < N tracklets ≤ 10 3 . 202 ± 0 . 278 3 . 264 ± 0 . 271 (8 . 506 ± 0 . 851) · 10 2 10 < N tracklets ≤ 20 3 . 431 ± 0 . 441 2 . 987 ± 0 . 386 (7 . 954 ± 0 . 886) · 10 2 N tracklets > 20 3 . 500 ± 0 . 480 3 . 073 ± 0 . 413 Table 3.8: LHC10e analysis: parameters of the fit function. P T 2 � ( GeV/c ) 2 � Multiplicity interval � P T � ( GeV/c ) 7.28 ± 0 . 96 2 . 24 ± 0 . 14 0 < N tracklets ≤ 10 0 . 84 0 . 14 9.60 ± 1 . 65 2 . 58 ± 0 . 21 10 < N tracklets ≤ 20 1 . 55 0 . 20 9.43 ± 1 . 52 2 . 56 ± 0 . 21 N tracklets > 20 1 . 49 0 . 21 P T 2 � � Table 3.9: LHC10e analysis: and � P T � values. LHC10f period: results Multiplicity interval c1 c2 x (1 . 089 ± 0 . 114) · 10 3 0 < N tracklets ≤ 10 3 . 550 ± 0 . 486 3 . 327 ± 0 . 476 (6 . 249 ± 1 . 060) · 10 2 10 < N tracklets ≤ 20 3 . 080 ± 0 . 713 2 . 454 ± 0 . 518 (8 . 010 ± 0 . 885) · 10 2 N tracklets > 20 3 . 501 ± 0 . 503 2 . 970 ± 0 . 418 Table 3.10: LHC10f analysis: parameters of the fit function. P T 2 � ( GeV/c ) 2 � Multiplicity interval � P T � ( GeV/c ) 8.41 ± 1 . 53 2 . 42 ± 0 . 22 0 < N tracklets ≤ 10 1 . 47 0 . 21 11.43 ± 2 . 57 2 . 80 ± 0 . 40 10 < N tracklets ≤ 20 2 . 50 0 . 30 13.57 ± 3 . 51 3 . 19 ± 0 . 47 N tracklets > 20 3 . 33 0 . 44 P T 2 � � Table 3.11: LHC10f analysis: and � P T � values. LHC10e and LHC10f analysis results: a summary P T 2 � � In Figures 3.29 and 3.30 I present the and � P T � for the J/ ψ for the three multiplicity bins, for the LHC10e and LHC10f periods.

  65. 74 CHAPTER 3. DATA ANALYSIS 20 〉 2 T p LHC10e 〈 18 LHC10f 16 14 12 10 8 6 4 2 0 1 2 3 Multiplicity bin P T 2 � � Figure 3.29: variation in three multiplicity bins. 5 〉 T p LHC10e 〈 4.5 LHC10f 4 3.5 3 2.5 2 1.5 1 0.5 0 1 2 3 Multipliicity bin Figure 3.30: � P T � variation in three multiplicity bins. P T 2 � � For each period we can see an increasing trend both in the and in P T 2 � � the � P T � spectra. In particular we can see an increase of and � P T � between the first and the second bin, both in LHC10e and LHC10f periods, even if the size of the error bars does not allow a strong statement in this sense. Since the results (in each of the three multiplicity bins) are within

  66. 75 CHAPTER 3. DATA ANALYSIS errors, we decided to merge the two periods, in order to study the transverse momentum of the J/ ψ with a larger statistics. � We fitted the invariant mass spectra (obtained in P T and multiplicity 3.7.6 Full statistics analysis In this paragraph we’ll present the transverse momentum analysis based on � We divided the number of J/ ψ in each P T bin by the efficiency cor- the merged statistics of LHC10e and LHC10f periods. The procedure is very similar to that previously used. bins) with the Crystal Ball and the sum of two exponential functions � We plotted the number of J/ ψ versus P T and fitted these distributions (Figures 3.31, 3.32, 3.33). � We obtained the value of rection factors. In particular we considered the mean value of the correction factors of the LHC10e and LHC10f periods, showed in Fig- ure 3.17. (See Figure 3.34) P T 2 � � and � P T � (Tables 3.12, 3.13). Multiplicity interval c1 c2 x (2 . 542 ± 0 . 161) · 10 3 0 < N tracklets ≤ 10 3 . 419 ± 0 . 270 3 . 360 ± 0 . 274 (1 . 428 ± 0 . 129) · 10 3 10 < N tracklets ≤ 20 3 . 635 ± 0 . 489 3 . 078 ± 0 . 442 (9 . 271 ± 0 . 930) · 10 2 N tracklets > 20 3 . 846 ± 0 . 480 3 . 134 ± 0 . 396 Table 3.12: Full statistics analysis: parameters of the fit function. P T 2 � ( GeV/c ) 2 � Multiplicity interval � P T � ( GeV/c ) 7.75 ± 0 . 79 2 . 32 ± 0 . 12 0 < N tracklets ≤ 10 0 . 81 0 . 12 10.01 ± 1 . 54 2 . 64 ± 0 . 19 10 < N tracklets ≤ 20 1 . 37 0 . 17 10.63 ± 1 . 52 2 . 74 ± 0 . 19 N tracklets > 20 1 . 39 0 . 19 P T 2 � � Table 3.13: Full statistics analysis: and � P T � values.

  67. 76 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM Bin 1 ± dN/dM ± N = 410 29 Bin 2 N = 757 40 ψ J/ ψ J/ 3 10 3 10 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM Bin 3 Bin 4 ± N = 528 32 N = 319 24 ψ J/ ψ J/ 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ 2 µ µ 10 µ µ dN/dM dN/dM ± ± Bin 6 N = 100 15 Bin 5 N = 196 20 ψ ψ J/ J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ 2 µ 10 ± ± dN/dM dN/dM N = 86 14 Bin 8 N = 22 8 Bin 7 ψ ψ J/ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.31: Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the first multiplicity interval.

  68. 77 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM ± dN/dM ± Bin 1 Bin 2 N = 261 25 N = 426 34 ψ ψ J/ J/ 3 10 10 3 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 3 ± ± N = 409 29 Bin 4 N = 257 23 ψ ψ J/ J/ 10 2 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM ± 10 2 ± Bin 5 N = 176 18 Bin 6 N = 105 14 ψ ψ J/ J/ 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ 2 µ 10 dN/dM ± N = 93 14 Bin 7 ψ J/ 10 1 1.5 2 2.5 3 3.5 4 4.5 2 M (GeV/c ) µ µ Figure 3.32: Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c) in the second multiplicity interval. The fit in the last P T bin (8-10 GeV/c) failed due to the low statistic.

  69. 78 CHAPTER 3. DATA ANALYSIS µ µ µ µ dN/dM Bin 1 ± dN/dM ± N = 147 21 Bin 2 N = 340 28 ψ ψ J/ J/ 3 10 3 10 2 10 2 10 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 3 ± ± Bin 4 N = 258 22 N = 204 20 ψ ψ J/ J/ 10 2 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ 2 µ 10 µ dN/dM dN/dM ± N = 119 15 ± Bin 5 Bin 6 N = 86 9 ψ J/ ψ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM ± dN/dM ± N = 72 12 Bin 8 Bin 7 N = 30 7 ψ J/ ψ J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 3.33: Invariant mass spectra and fits, for the full statistic (LCH10e + LHC10f), corresponding to 8 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c, 6-8 GeV/c, 8-10 GeV/c), in the third multiplicity interval.

  70. 79 CHAPTER 3. DATA ANALYSIS ψ Number of J/ ≤ 0 < N 10 tracklets 3 10 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T ψ Number of J/ ≤ 10 < N 20 tracklets 3 10 2 10 0 1 2 3 4 5 6 7 8 p (GeV/c) T ψ Number of J/ N > 20 3 tracklets 10 2 10 10 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 3.34: In these plots we show the number of J/ ψ in each P T bin, corrected for the efficiency effects, for the full statistic. The blue line is the results of the fit.

  71. 80 CHAPTER 3. DATA ANALYSIS Full statistics analysis: a summary In this paragraph I present a summary of the analysis on the complete P T 2 � � statistics. We show the and the � P T � dependence on multiplicity (Figures 3.35 and 3.36 respectively). 20 〉 2 T p 〈 18 LHC10e & LHC10f 16 14 12 10 8 6 4 2 0 1 2 3 Multiplicity bin P 2 � � Figure 3.35: variation in three multiplicity bins, full statistics analysis. T 4 〉 T p 〈 LHC10e & LHC10f 3.5 3 2.5 2 1.5 1 1 2 3 Multiplicity bin Figure 3.36: � P T � variation in three multiplicity bins, full statistics analysis.

  72. 81 CHAPTER 3. DATA ANALYSIS From the analysis of the merged data (coming from LHC10e and LHC10f � P T 2 � periods) we can see an increase of and � P T � . The variation is more ev- ident between the first and second multiplicity bin, while is less pronounced between the second and the third multiplicity bin. Such an increase trend was already seen in other ALICE analysis studying the evolution of P T of charged hadrons vs multiplicity (See Figure 3.37). Figure 3.37: � P T � variation as a function of charged multiplicity (from: “Transverse momentum analysis in pp at 900 GeV and 7 TeV”), by H. Appelsh¨ auser , Univ. Frankfurt.

  73. Chapter 4 Simulations 4.1 Introduction The aim of this chapter is to study the J/ ψ production through simulations, in order to test the Monte Carlo generators and to compare their outputs with the results of the analysis. The simulation work has been performed using Pythia as an external generator. We start with a brief introduction dedicated to the features of the generator, then we present the obtained results. We start by generating a minimum bias p-p collisions and comparing the multiplicity distributions with the experimental results. The production of the J/ ψ in Pythia is then studied both forcing J/ ψ production in each event and analyzing a very large sample of minimum bias Monte Carlo events. 4.2 The PYTHIA event generator Multiparticle production is one of the most characteristic feature of current high-energy-physics. Reliable event generators are very important for data analysis at the LHC because they are necessary to study detector require- ments, to predict event rates and to simulate possible backgrounds. One of the most used event generator is Pythia . It was born as a develop- ment of JETSET, the first member of the “Lund Monte Carlo” family [21]. Pythia was begun by members of the Lund theory group in 1978 [15], and has evolved since then. Pythia is largely based on original research, but also borrows many formulae and other knowledge from the literature. The 82

  74. 83 CHAPTER 4. SIMULATIONS Pythia program can be used to generate high-energy-physics “events”, i.e. sets of outgoing particles produced in the interactions between two incom- ing particles (in our case p-p). In fact, the output of an event generator, should be in the form of “events”, with the same average behaviour and the same fluctuations as real data. In Pythia , Monte Carlo techniques are used to select all relevant variables according to the desired probability distribu- � MSEL: this switch allow the user to select between full user control and tions, and thereby ensure randomness in the final events. In this work we used Pythia 6.4.1 version (the most used version at the moment). The Pythia program allows the user to change a wide number of param- eters. Although it is not possible to give a detailed description of these � MSUB: this array is to be set when MSEL=0, to choose which subset parameters in this work (for further reading see the Pythia manual [15]), we now present a list of flags, used to “switch-on” some processes. some preprogrammed alternatives. MSEL=0 means full user control and the desired subprocesses have to be switched-on in MSUB. � CKIN: this flag is used to force some kinematic cuts. For example of subprocesses include in the generation. The ISUB is the process code number (for example ISUB=86 is the J/ ψ production from the fusion of two gluons: g+g → J/ ψ +g). When MSUB(ISUB)=0 the subprocess ISUB is excluded, conversely when MSUB(ISUB)=1 the subprocess ISUB is included. CKIN(3) is used to set up the lower P T range value, while CKIN(4) defines the upper P T generated value. The Pythia program is written in FORTRAN language and it is also in- terfaced with the AliROOT framework. The interface between Aliroot and Pythia is provided by two classes: AliGenPythia and AliDecayerPythia . The first is used to handle the particle production mechanism, the second one to manage particle decays. We actually used this interface to initialize the generator (instead of modify the original Pythia code). This choice allows us to simulate in a more efficient way (because both generation and reconstruction are performed in the same analysis framework).

  75. 84 CHAPTER 4. SIMULATIONS 4.2.1 The Configuration file (Config.C) * gener = new AliGenPythia( − 1) ; The heart of simulation is the Config.C file. This configuration file contains both GEANT parameters (in order to simulate the interactions between particles and the sub-detector materials), and the interface to the external generator. In the following we present a few lines of the code we used to set up the event generator. AliGenPythia gener − > SetMomentumRange (0 , 999999.) ; gener − > SetThetaRange ( 0 . , 180.) ; gener − > SetYRange ( − 12. ,12.) ; gener − > SetPtRange (0 ,1000.) ; gener − > SetProcess (kPyMb) ; gener − > SetEnergyCMS (7000) ; gener − > SetOrigin (0 ,0 ,0) ; gener − > SetSigma (0 ,0 ,5.3) ; gener − > SetCutVertexZ ( 3 . ) ; gener − > SetForceDecay ( kAll ) ; gener − > I n i t () ; The code can be modified in order to set-up the allowed range for kinematic variables such as momentum, rapidity, energy, etc. The range of gener- ated kinematic variables (such momentum, theta, rapidity) is usually quite wide, to ensure that the generation is performed on a kinematic range wider than that covered by the detectors. The most important lines allows us to set a specific production method (SetProcess) and the decay mechanism (SetForceDecay) . In reference to the previous example, the code was used to simulate minimum bias events (kPyMb), without forcing any particular decay channel (kAll). 4.2.2 Event generation and reconstruction The complete process can be summarized in the following five points: 1. Event generation ( Pythia 6); 2. Tracking through the apparatus (AliROOT); 3. Detector simulation (GEANT 3,4 and AliROOT);

  76. 85 CHAPTER 4. SIMULATIONS 4. Event Reconstruction (AliROOT); 5. Physics Analysis (ROOT). After the Config.C is modified to fit user’s requests, the simulation can ac- tually start. The primary p-p interaction is simulated by Pythia . The produced particles are also saved internally, to keep track of the produc- tion history. Each particle is then transported into the detectors: the point where energy is deposited together with the amount of such energy con- stitutes a “hit”. The hits contain also information about the particle that generated them. At the next step the detector information is taken into account. The hits are “dis–integrated”: the information on the parent track is lost and the spatial position is translated into the corresponding detector readout element (strips, pad, etc.), thus generating the digits. The digits are eventually converted in raw-data, which are stored in binary format. The reconstruction chain can then start, allowing the creation of track can- didates. The final ouput is an Event Summary Data (ESD), a .ROOT file containing the output of the reconstruction for physics studies. In our case, in order to decrease the simulation’s time we reconstructed tracks only in the Muon Spectrometer and in the Silicon Pixel Detector. � MSUB (92): single diffraction (AB → XB). 4.3 Minimum bias simulations � MSUB (93): single diffraction (AB → AX). The first objective is the production of a minimum bias sample, in order to study the multiplicity distribution without forcing any particular physics � MSUB (94): double diffraction. process. We used the default kPyMb process, which enables the following � MSUB (95): low-p T production. sub-processes: In addition we didn’t force any particular decay, using the kAll option. Anyway, the set of initialization parameters contained in the default set of processes is not accurate enough to ensure a good agreement with the

  77. 86 CHAPTER 4. SIMULATIONS data. For this reason we have considered a fine “tune” of our generator. We have used a Pythia tune described in the “ ATLAS Monte Carlo tune for MC09 production ” [16]. The aim is to tune the parameters of Pythia using recent set of data at lower energies. As an example, very recent sets of parton density function (PDFs) were used. The simulation work has been performed using the INFN Turin computing center: we produced and reconstructed 5 × 10 5 events. The total amount of computing time was about two weeks. 4.3.1 Multiplicity distributions In Figure 4.1 we present the generated multiplicity distribution: we only consider charged primary particles. A pseudorapidity cut of | η | ≤ 1 has also been applied to approximately match the acceptance of the SPD. The mean value of this distribution is also presented. MC Charged particles mult ch dN/d  η  ≤ 1,charged & primary 4 10 〈 〉 ± N = 11.23 0.02 ch 3 10 2 10 10 1 20 40 60 80 100 N ch Figure 4.1: Generated multiplicity distribution with Atlas tuning. We can now show (Figure 4.2) the reconstructed multiplicity distributions obtained in the Silicon Pixel Detector. The blue line is the simulated mul- tiplicity distribution, while the red line refers to datas (from the LHC10e period). We recall that the charged multiplicity was estimated as the num- ber of tracklets associated to the reconstructed vertex (See Section 3.6).

  78. 87 CHAPTER 4. SIMULATIONS -1 10 〈 〉 ± N = 8.90 0.01 trackets 〈 〉 ± N = 8.98 0.01 -2 10 trackets -3 10 -4 10 -5 10 LHC10e datas -6 10 Atlas MC09 tuning -7 10 20 40 60 80 100 N trackets Figure 4.2: Reconstructed multiplicity distribution. Figure 4.3: Reconstructed and generated multiplicity distribution: the area corresponding to | η | ≤ 1 is highlight in red. We can see an asymmetry in the reconstructed distribution due to the detector efficiency losses. This figure was taken from the “Multiplicity analysis and dN/d η reconstruction with the silicon pixel detector ”, by Maria Nicassio, Terzo Convegno Nazionale sulla Fisica di ALICE Frascati (Italy) - November 12-14, 2007.

  79. 88 CHAPTER 4. SIMULATIONS As we can see from Figure 4.2, there is a good agreement between data and simulations. This agreement can also be found in the mean values. We can see that the mean value of the generated multiplicity distribution ( N ch = 11 . 23 ± 0 . 02) is greater than the reconstructed mean value ( N tracklets = 8 . 98 ± 0 . 01). This effect is caused by the fact that we are not able to � Direct production (where gluon fusion give raise to a bound c¯ reconstruct all generated particles, due to acceptance limitations of the SPD (see Figure 4.3). 4.4 J/ ψ production in Pythia � Decays of b-mesons and baryons. In Pythia one may distinguish between two main sources of J/ ψ production. c pair). Higher-lying states, like the χ c ones, are also produced and may sub- sequently decay to J/ ψ . � J/ ψ production method: “kPyJpsi” . In our simulation we have only taken into account direct production, which is dominant. At the generator level we used the option called kPyJpsi : this method gen- erates one J/ ψ per event. Moreover, in order to increase the reconstructed � J/ ψ decay method: “kPyJpsiDiMuon” . event statistics, we decided to force the J/ ψ decay into a muon pair using the option KJpsiDiMuon . In summary: g+g → J/ ψ +g J/ ψ → µ + µ − We used these settings to produce a sample of 10 5 events, using the INFN Turin computing center. 4.4.1 Multiplicity distributions for events containing a J/ ψ In Figures 4.4 and 4.5 respectively, we present the generated and recon- structed multiplicity distributions. Mean values are also reported. Also

  80. 89 CHAPTER 4. SIMULATIONS in this case we can see a decrease of the mean value in the reconstructed distribution, due to acceptance effects. ch 4 10 dN/d  η  ≤ 1,charged & primary 〈 〉 ± N = 14.1 0.1 ch 3 10 2 10 10 1 0 10 20 30 40 50 60 70 80 N ch Figure 4.4: Generated multiplicity using kPyJpsi production method. 4 10 〈 〉 ± N = 13.4 0.1 trackets 3 10 2 10 10 1 10 20 30 40 50 60 70 80 N trackets Figure 4.5: Reconstructed multiplicity in the SPD using kPyJpsi production method. 4.4.2 Comparison between data and simulation: multiplicity In order to test the reliability of Pythia we now present the comparison be- tween the multiplicity distributions obtained from data (already presented

  81. 90 CHAPTER 4. SIMULATIONS in section 3.6.2) and simulation (with the kPyJpsi method previously pre- sented). In particular we used the data multiplicity distribution obtained with side window option number 5 (See 3.6.3). counts Side band #5 Data (LHC10e) -1 10 Simulation 〈 〉 ± N = 16.1 0.3 tracklets -2 10 〈 〉 ± N = 13.4 0.1 tracklets -3 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 4.6: Comparison between simulated (using the Pythia method kPyJpsi ) and LHC10e multiplicity distribution. counts Side band #5 Data (LHC10f) -1 10 Simulation 〈 〉 ± N = 15.8 0.4 10 -2 tracklets 〈 〉 ± N = 13.4 0.1 tracklets -3 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 4.7: Comparison between simulated (using the Pythia method kPyJpsi ) and LHC10f multiplicity distribution. From Figures 4.6 and 4.7 we can see that the shapes of the simulated mul- tiplicity distributions (associated to the J/ ψ production) are quite different from those of the experimental data. The main difference, in the simulation distributions, is the absence of the tail at high multiplicity and a steeper

  82. 91 CHAPTER 4. SIMULATIONS decrease at low multiplicity. From these results we can assert that the mul- tiplicity distribution associated to the J/ ψ production is not well reproduced by Pythia , when we force the production of the J/ ψ with the kPyJpsi set- ting. For this reason, we concluded that the kPyJpsi setting cannot be used to obtain realistic results for the J/ ψ production. 4.5 Analysis of the LHC10f6a production J/ ψ production with Pythia can also be studied by considering large sam- ples of minimum bias events. In this way the production is not explicity forced but, since the J/ ψ production cross section is very low ( ∼ 10 − 6 ) with respect to minimum bias p-p cross section, the simulation sample must contain > 10 8 events. Such a production requires a lot of time and computing resources and, ob- viously, cannot be performed neither in local mode nor using a private com- puting center (like the INFN Turin farm). The only way is to analyze a Grid production: using the Monalisa page (see 3.2) dedicated to the MonteCarlo production cycles, we found a promising sample of about 1 . 72 · 10 8 mini- mum bias events. This sample, LHC10f6a , was produced with Pythia and corrensponds to our requests (p-p collisions at the energy of √ s = 7 TeV). 4.5.1 The analysis of the LHC10f6a production The analysis of the LHC10f6a production has been performed using the Grid. This kind of analysis is necessary because it is not possible to run the � Allow using all existing types of input data to be processed (ESD, analysis tasks in local mode (due to the very high amount of data). The analysis on the Grid is managed by a plugin. The purpose of the plugin is to allow running transparently in AliEn (the Grid framework developed � Generate XML (eXtensible Markup Language) collections correspond- by ALICE) the same user analysis that runs on the local PC. The plugin provides the following functionality to hide the complexity of the underlying Grid for users, for example: AOD files). ing to requested runs.

  83. � Copy all needed files in user’s AliEn space and submit the job auto- � Start an alien shell to allow inspecting the job status. 92 CHAPTER 4. SIMULATIONS matically. The first step required, in order to analyze the Grid production, is the con- figuration of the analysis task and the plugin: this work has been performed in local mode. Afterwards, using the plugin, we submitted analysis jobs on the Grid. Using Monalisa Agent we monitored the analysis process. At the end of the analysis output files were stored in AliEn directories. The output files were finally merged, in order to obtain only one file containing the full statistics. The resulting output file has been analyzed in local mode, using ROOT macros. This work required about two weeks to be done and, at the end, we were able to analyze the 94% of the total statistic (about 1 . 72 · 10 8 events). The remaining 6% of the statistics was lost due to Grid errors (sometimes jobs gone in a non-working node and we could not resubmit them). 4.5.2 Invariant mass spectrum In Figure 4.8 we present the reconstructed invariant mass spectrum for op- posite sign dimuons for the LHC10f6a production. µ µ dN/dM 3 10 2 10 10 1 0 1 2 3 4 5 6 7 8 9 10 2 M (GeV/c ) µ µ Figure 4.8: Invariant mass spectrum for opposite sign dimuons for the LHC10f6a production.

  84. 93 CHAPTER 4. SIMULATIONS We have fitted the invariant mass spectrum with the Crystal Ball function, in order to get the number of the J/ ψ . The result of the fit is showed in Figure 4.9, and in Table 4.1. µ µ dN/dM ± 3 N = 209 30 10 ψ J/ 2 10 10 1 1.5 2 2.5 3 3.5 4 4.5 2 M (GeV/c ) µ µ Figure 4.9: Fit of the invariant mass spectrum with the Crystal Ball func- tion. M J/ψ (GeV/ c 2 ) Γ J/ψ (MeV/ c 2 ) Dimuon events N J/ψ S/B 50275 209 ± 30 3.074 ± 0.016 92.035 ± 0.703 0.53 Table 4.1: Results of the invariant mass fits. It is interesting to see if the J/ ψ cross section, that can be extracted from the simulations, is similar to the one measured by ALICE. The integrated cross section of the J/ ψ , in the decay channel J/ψ → µ + µ − ( BR ( J/ψ ) → µ + µ − = 0 . 058), is given by the equation: N J/ψ J/ψ → µ + µ − � � σ J/ψ · BR = � Ldt · Acc J/ψ � where N J/ψ = 209 is the J/ ψ yield, Ldt is the integrated luminosity (de- fined here as the ratio between the number of minimum bias event and the

  85. 94 CHAPTER 4. SIMULATIONS minimum bias cross section N MB /σ MB ), and Acc J/ψ = 0 . 329 is the accep- tance. 209 σ J/ψ = = (4 . 13 ± 0 . 62) µb 0 . 329 · 1 . 61 · 10 8 · 0 . 058 62 In comparison the ALICE result is: σ J/ψ = (7 . 25 ± 0 . 29( stat ) ± 0 . 98( syst )) µb We see that the J/ ψ production cross section in Pythia agrees, within a factor of 2, with the ALICE measurement [18]. We also tried to understand the origin of the produced J/ ψ and, in particu- lar, to determine the fraction due to B-decays. Test was made to check the quality of our this assumption. We analyzed the entire stack (the stack is the container for the produced particles, created by the Monte Carlo gener- ator) in order to understand the relationship of the J /ψ . More specifically we scanned the stack (using the PDG code) since we found a J /ψ : when a J /ψ was found we increased a counter. Then we ask for the J /ψ ’s mother, and increased another counter if the mother is a b meson. At the end of this analysis, on a sample of 1 . 4706 · 10 7 events, we found 9703 J /ψ and 546 of them came from the decay of a b meson. In summary we found that about 5 % of the J /ψ are produced in B-decays. Again this is in agreement, within a factor of 2, with measurements from the LHCb experiment [19], performed in the same y-range of ALICE. 4.5.3 Multiplicity study In this paragraph we present the multiplicity study for the LHC10f6a pro- duction, comparing the simulated distributions to those obtained from ex- perimental data. Minimum bias multiplicity distributions The first step is the study of the minimum bias reconstructed multiplic- ity in the SPD. In Figure 4.10 we present the recostructed multiplicity for LHC10f6a production, superimposed to the LHC10e multiplicity and to the minimum bias Atlas Tune simulation (See: 4.3.1).

  86. 95 CHAPTER 4. SIMULATIONS -1 10 -2 10 -3 10 -4 10 -5 10 〈 〉 ± N = 8.90 0.01 -6 10 tracklets LHC10e data 〈 〉 ± N = 8.98 0.01 -7 10 tracklets Atlas Tune 〈 〉 ± N = 7.48 0.15 -8 10 tracklets LHC10f6a 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 4.10: The multiplicity distributions coming from: the LHC10e pe- riod, the minimum bias simulation with the Atlas tuning and the LHC10fa production. Mean values of the distributions are presented. From the previous figure we can see that the LHC10f6a multiplicity distri- bution slightly differs (expecially in the interval 0 < N tracklets ≤ 30 ) from LHC10e data and the Atlas tune simulation. However, it reproduces the essential features of the data. Multiplicity distributions associated to the J/ ψ production As we already explained in the paragraph 3.6 we can use the side windows technique to obtain the multiplicity associated to the J/ ψ production. counts Side window #5 LHC10e data -1 10 LHC10f6a simulation 〈 〉 ± N = 16.1 0.3 ch -2 10 〈 〉 ± N = 18.2 1.3 ch -3 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 4.11: Comparison between LHC10f6a and LHC10e multiplicity dis- tributions.

  87. 96 CHAPTER 4. SIMULATIONS counts Side window #5 LHC10f data -1 10 LHC10f6a simulation 〈 〉 ± N = 15.8 0.4 ch -2 10 〈 〉 ± N = 18.2 1.3 ch -3 10 0 10 20 30 40 50 60 70 80 90 N tracklets Figure 4.12: Comparison between LHC10f6a and LHC10f multiplicity dis- tributions. In Figures 4.11 and 4.12 I present the multiplicity distributions for the LHC10f6a production, superimposed to the distributions obtained from the analysis of the LHC10e and LHC10f periods obtained using the side win- dows number 5. From this study we can see that the simulated multiplicity distributions (from the LHC10f6a production) are rather quite similar to those obtained with experimental data (LHC10e and LHC10f periods), even if they tend to have a slightly larger multiplicity. However, in some cases we can see a difference in the mean values, between data and simulation. 4.5.4 Transverse momentum study Another interesting study that can be performed with this Monte Carlo sample is the determination of the transverse momentum of the J/ ψ . Un- fortunately, due to the low statistics, only a study integrated over charged multiplicity can be performed. We extracted the invariant mass spectra from the same P T intervals used to analyze data and then we fitted them with the Crystal Ball function (Figure 4.13). Actually, due to low statistic, the fit in the last two P T bins failed, and therefore no results is shown for P T > 6 GeV/c . We fitted the P T spectrum with the function described in Section 3.7.4. The result of the fit is presented in Figure 4.14, while P T 2 � � the and � P T � are summarized in Table 4.2 and compared with the corresponding values from real data.

  88. 97 CHAPTER 4. SIMULATIONS µ µ µ µ ± dN/dM Bin 1 N = 37 11 dN/dM Bin 2 ± N = 51 15 ψ J/ ψ 10 3 J/ 2 10 10 2 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 3 ± ± N = 76 15 Bin 4 N = 45 11 ψ J/ ψ 10 2 J/ 10 10 1 1 1.5 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ µ µ µ µ dN/dM dN/dM Bin 5 ± ± Bin 6 N = 14 7 N = 6 4 ψ ψ J/ J/ 10 10 1 1 2 2.5 3 3.5 4 4.5 1.5 2 2.5 3 3.5 4 4.5 2 2 M (GeV/c ) M (GeV/c ) µ µ µ µ Figure 4.13: Invariant mass spectra and fits, for the LHC10f6a production, corresponding to 6 P T bins (0-1 GeV/c, 1-2 GeV/c, 2-3 GeV/c, 3-4 GeV/c, 4-5 GeV/c, 5-6 GeV/c)

  89. 98 CHAPTER 4. SIMULATIONS ψ Number of J/ 2 10 10 1 0 1 2 3 4 5 6 7 8 9 10 p (GeV/c) T Figure 4.14: Fit of the P T spectrum, for the LHC10f6a production. P T 2 � ( GeV/c ) 2 � Period � P T � ( GeV/c ) 7.25 ± 2 . 75 2 . 39 ± 0 . 43 LHC10f6a (simulation) 2 . 80 0 . 45 8.53 ± 0 . 82 2 . 42 ± 0 . 11 LHC10e (data) 0 . 79 0 . 10 8.56 ± 0 . 68 2 . 43 ± 0 . 10 LHC10f (data) 0 . 72 0 . 10 Table 4.2: Transverse momentum analysis without multiplicity cuts. From these results we can see, within the errors, an acceptable agreement be- tween the simulated (LHC10f6a) and the experimental data. We can finally compare the results coming from the analysis of the LHC10f6a production to those obtained with LHC10e and LHC10f data using multiplicity bins. The superimposed band on the Figures 4.15 and 4.16 shows the result extracted from the LHC10f6a simulation.

  90. 99 CHAPTER 4. SIMULATIONS 20 〉 2 T p 〈 18 LHC10e & LHC10f 16 14 12 10 8 6 4 2 0 1 2 3 Multiplicity bin Figure 4.15: Comparison between LHC10e data and LHC10f6a production. 4 〉 T p 〈 LHC10e & LHC10f 3.5 3 2.5 2 1.5 1 1 2 3 Multiplicity bin Figure 4.16: Comparison between LHC10f data and LHC10f6a production.

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