Diffractive z/gamma* -> mu+ mu- production with rapidity gap in proton-antiproton collisions at sqrt (s) = 1.96 TeV in teh D0 expirement

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(1)DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON COLLISIONS AT. √. s = 1.96 T eV. in the DØ EXPERIMENT. A Dissertation. Submitted to the Physics Department. of Universidad de los Andes for the degree of. Doctor of Physics. by. Luis Miguel Mendoza Navas, M.S. Dr. Carlos Avila, Director of Thesis. Department of Physics. Universidad de los Andes, BOGOTÁ - COLOMBIA. July 2007.

(2) c Copyright by. LUIS MIGUEL MENDOZA NAVAS. 2007. All rights reserved.

(3) To my wife Marcela and my little girl Luisa Alexandra. To my parents Orlando and Nubia. In memory to my best friend Alejandro Rueda.

(4) Contents 1 Theory 1.1 The Standard Model . . . . . . . . 1.2 Z 0 Bosons at the Tevatron . . . . . 1.3 Diffraction Phenomenology . . . . 1.3.1 Elastic Scattering . . . . . . 1.3.2 Hard Diffraction . . . . . . 1.3.3 Rapidity Gaps . . . . . . . 1.3.4 Rapidity Gap Survival . . . 1.3.5 Soft Color Interaction (SCI). . . . . . . . .. . . . . . . . .. 2 Experimental Apparatus 2.1 Fermilab Accelerator Complex . . . . 2.1.1 The Pre-accelerator . . . . . . 2.1.2 The Linac . . . . . . . . . . . . 2.1.3 The Booster . . . . . . . . . . . 2.1.4 The Main Injector . . . . . . . 2.1.5 The Antiproton Source . . . . 2.1.6 The Recycler . . . . . . . . . . 2.1.7 The Tevatron . . . . . . . . . . 2.1.8 Luminosity . . . . . . . . . . . 2.2 Interactions of Energetic Particles with 2.2.1 Electrons and Photons . . . . . 2.2.2 Muons . . . . . . . . . . . . . . 2.2.3 Hadronic Particles . . . . . . . 2.2.4 Neutrinos . . . . . . . . . . . . 2.3 The DØ Detector . . . . . . . . . . . 2.3.1 Coordinate System . . . . . . . 2.3.2 Luminosity Monitors . . . . . . 2.3.3 The Tracking System . . . . .. iii. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. 1 1 2 4 5 6 8 11 11. . . . . . . . . . . . . . . . . . .. 12 12 12 13 14 14 15 16 16 16 17 18 18 18 19 19 21 21 23.

(5) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.3.4 2.3.5 2.3.6 2.3.7. 2.3.8 2.3.9. The Silicon Microstrip Tracker (SMT) . . . . Central Fiber Tracker (CFT) . . . . . . . . . Solenoidal Magnet . . . . . . . . . . . . . . . Pre-shower Detectors . . . . . . . . . . . . . . The Calorimeter System . . . . . . . . . . . . The Inter-Cryostat Detectors . . . . . . . . . The Muon System . . . . . . . . . . . . . . . Toroidal Magnets . . . . . . . . . . . . . . . . Proportional Drift Tubes . . . . . . . . . . . Mini Drift Tubes . . . . . . . . . . . . . . . . Scintillation Counters . . . . . . . . . . . . . Shielding . . . . . . . . . . . . . . . . . . . . Forward Proton Detector (FPD) . . . . . . . Trigger System and Data Acquisition System Level 1 Trigger(L1) . . . . . . . . . . . . . . . Level 2 Trigger (L2) . . . . . . . . . . . . . . The Level 3 Trigger (L3) . . . . . . . . . . .. 3 Object Identification 3.1 Charged Tracks . . 3.2 Primary Vertex . . 3.3 Muons . . . . . . . 3.4 Electrons . . . . . 3.5 Jets . . . . . . . . 3.6 Missing ET (6ET ) .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. 23 25 26 26 27 31 31 33 33 33 33 34 35 36 37 37 38. . . . . . .. 39 39 39 40 42 44 45. 4 Measurement of the Production Cross Section of diffractive Z 0 /γ ∗ → µ+ µ− with Gap 46 4.1 Data Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.3 Trigger Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Z Diffractive Event Selection . . . . . . . . . . . . . . . . . . . . . . 53 4.4.1 Fraction of the Proton Momentum Loss . . . . . . . . . . . . 53 4.4.2 Gap Requirement . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4.3 Cell Energy Thresholds . . . . . . . . . . . . . . . . . . . . . 55 4.4.4 Choice of event kinematics . . . . . . . . . . . . . . . . . . . 61 4.5 Monte Carlo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.6 Background Subtraction Method . . . . . . . . . . . . . . . . . . . . 71 4.7 Diffractive Cross section for Z boson decaying in two muons . . . . . 81 4.7.1 Corrections to obtain the Cross Section . . . . . . . . . . . . 81. iv.

(6) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 4.8. Number of Events . . . . . . . . . . . . . . . . Integrated Luminosity . . . . . . . . . . . . . . Efficiency of Monte Carlo . . . . . . . . . . . . Other Efficiencies and backgrounds . . . . . . . 4.7.2 Systematic Errors . . . . . . . . . . . . . . . . Cell Energy Thresholds . . . . . . . . . . . . . Background . . . . . . . . . . . . . . . . . . . . Gap Size . . . . . . . . . . . . . . . . . . . . . Integrated Luminosity . . . . . . . . . . . . . . 4.7.3 Results for Diffractive Cross Section with Gap Fraction of Z bosons produced diffractively with gap from Z inclusive production . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . requirement . . . . . . . .. 82 82 82 82 83 83 84 84 85 85 85. 5 Summary 88 5.1 Comparison with Run I Results . . . . . . . . . . . . . . . . . . . . . 88 5.2 Comparison with Run II Results . . . . . . . . . . . . . . . . . . . . 89 5.3 Suggestions for future diffractive Z analyses . . . . . . . . . . . . . . 89 A Muon Quality Definitions. 91. B Trigger Names. 93. C Efficiencies and Corrections Factors for Inclusive Z boson tion C.1 Efficiency of isolation cuts εisol . . . . . . . . . . . . . . . . C.2 Efficiency of Opposite Sign Requirement and bb̄ Background C.3 Efficiency and Background for Cosmic Rays . . . . . . . . . C.4 Z/γ ∗ → τ + τ − Background . . . . . . . . . . . . . . . . . . . C.5 Background from W + Jets and Di-boson Events . . . . . . D The T42 and Hot Cell Killer Algorithms. v. Produc. . . . .. . . . . .. . . . . .. . . . . .. . . . . .. 94 94 94 97 99 100 101.

(7) List of Tables 1.1. 1.2 2.1. Schematic representation of the Standard Model: Constituents are doublets of quarks and leptons in three generations. Forces are mediated by gauge bosons . . . . . . . . . . . . . . . 2 Branching Ratios for Z boson decays. The invisible decays are presumed to be to neutrinos . . . . . . . . . . . . . . . . . . 3 Pseudorapidity coordinate |iη| in the calorimeter . . . . . . .. 29. Integrated Luminosity by trigger version . . . . . . . . . . . . Number of events - Z selection criteria . . . . . . . . . . . . . Convention of numbers used for cell energy thresholds . . . R Ldt in pb−1 by sub-versions . . . . . . . . . . . . . . . . . . . . Normalization constants for PYTHIA . . . . . . . . . . . . . . ξ reconstructed and ξ corrected, correction factors applied . Efficiencies and backgrounds taken from the inclusive Z → µ+ µ− cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Z Diffractive Cross Section by varying cell energy thresholds in 0.05 GeV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.9 Z Diffractive Cross Section by varying normalization constants for background in ±1σ . . . . . . . . . . . . . . . . . . . . 4.10 Z Diffractive Cross Section by varying gap size . . . . . . . . 4.11 Systematic Errors for fraction of Diffractive Z boson from Z inclusive production . . . . . . . . . . . . . . . . . . . . . . . .. 51 52 60 74 75 78. B.1 Description of trigger components used for trigger names .. 93. 4.1 4.2 4.3 4.4 4.5 4.6 4.7. vi. 83 83 84 85 86.

(8) List of Figures 1.1 1.2. 1.3 1.4. 1.5. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9. Z production and decay at the Tevatron . . . . . . . . . . . . . Illustrations for Diffractive Events: (a) Elastic scattering, (b) single diffractive dissociation, (c) double diffractive dissociation, and (d) double pomeron exchange . . . . . . . . . . Schematic view Diffractive Z production . . . . . . . . . . . . Rapidity distribution for diffractive events. There is a rapidity gap in the negative z axis. System X is the final state particles [7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z production (decaying leptonically) in a pp̄ collision with string topology (double-dashed lines) before (left) and after (right) a soft color exchange resulting in a rapidity gap . . . The accelerator chain at Fermilab . . . . . . . . . . . . . . . . . Schematic view of magnetron operation for the hydrogen ion source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Schematic drawing of Linac RF cavity . . . . . . . . . . . . . . Simplified drawing of anti-proton production with nickel target and lithium lens. . . . . . . . . . . . . . . . . . . . . . . . Total integrated luminosity delivered and recorded for Run II from April 2002 until Jul 2007 . . . . . . . . . . . . . . . . . Energy loss through ionization of muons in various energy regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Side view of the DØ detector for Run II . . . . . . . . . . . . Luminosity Monitor layout. The r − φ view is shown on the left, the r − z view of the two arrays is shown on the right. . The sketch on the left shows the diferentiation between inelastic collisions and beam halo. Expected z vertex distribution for inelastic collisions, centered at z = 0 cm, p halo centered at z = −140 cm, and p̄ halo centered at z = 140 cm (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii. 3. 4 7. 10. 11 13 14 14 15 17 19 20 22. 23.

(9) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.10 Schematic view of the DØ central tracking system . . . . . . 2.11 Schematic 3D view of the silicon vertex detector . . . . . . . 2.12 Cross section and layout geometry of CPS and FPS scintillator strips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 Isometric view of the central and two end calorimeters . . . 2.14 Schematic view of a portion of the DØ calorimeters showing the transverse and longitudinal segmentation pattern. The shading pattern indicates groups of cells ganged together for signal readout. The rays mark pseudorapidity intervals from the centre of the detector. . . . . . . . . . . . . . . . . . . 2.15 Projection of the calorimeter towers in the iη − layer plane . 2.16 Schematic view of a calorimeter cell. . . . . . . . . . . . . . . . 2.17 Schematic view of the muon system. . . . . . . . . . . . . . . . 2.18 View of the three drift chamber layers of the muon system. 2.19 View of the three scintillator layers of the muon system. . . 2.20 Schematic view of The Forward Proton Detector (FPD). Quadrupole Roman pot detectors are named P or A when placed on the p or p̄ side, respectively. Dipole pots, located on the p̄ side, are named D. . . . . . . . . . . . . . . . . . . . . . 2.21 Overview of the DØ trigger and data acquisition systems . 2.22 Schematic view of subdetectors with L1 and L2 trigger elements. Horizontal arrows indicate the direction of dataflow. 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14. Muon ηdet Distribution . . . . . . . . . . . . . . . . . . . . . . . . Muon pT Distribution . . . . . . . . . . . . . . . . . . . . . . . . . Di-Muon Invariant Mass . . . . . . . . . . . . . . . . . . . . . . . Pseudo-acolinearity Plot, the arrow indicates the cut applied in this variable . . . . . . . . . . . . . . . . . . . . . . . . . Events that pass dca cuts in CFT and SMT . . . . . . . . . . Events that pass isolation cuts . . . . . . . . . . . . . . . . . . . Acolinearity Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance Closest Approach Cut . . . . . . . . . . . . . . . . . . Di-Muon pT and Rapidity Distribution. Z boson candidates Reconstructed ξ in the p̄ side . . . . . . . . . . . . . . . . . . . . ξ contribution from di-muons in the pbar side . . . . . . . . . Number of primary vertices vs < ξ > . . . . . . . . . . . . . . . Primary vertex distribution - Before and After Diffractive cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fraction of antiproton momentum loss - Gap Requirement applied . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. viii. 24 24 27 28. 29 30 31 32 34 35. 36 37 38 47 48 48 49 49 50 51 52 52 54 55 56 56 57.

(10) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 4.15 Energy cell distribution for electromagnetic cells (Layers 1 to 7). Minimum bias, zero bias and emptybx sample. . . . . 58 4.16 Energy cell distribution for fine hadronic cells (Layers 11 to 14). Minimum bias, zero bias and empty BX sample . . . . . 58 4.17 ξ distributions - Physics signal and Noise for proton and antiproton side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.18 Sketch ξ distributions - Empty BX (Noise) and MinBias(signal) 60 4.19 Thresholds for EM and FH calorimeter cells. Blue Line corresponds to signal efficiency. Red Line correspond to noise rejection. x axis is explained in Table 4.3 . . . . . . . 60 4.20 Invariant Mass Distribution for Z boson candidates in the range 0.02 < ξ < 0.1. Plots have been fitted by using a gaussian and exponential decay distributions in all the Invariant Mass range .. P 4.21 ξpbar versus E for −36 < iη < −32. Before and After Gap Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.22 Single Diffractive signal at DØ . . . . . . . . . . . . . . . . . . . 4.23 ξpbar and Rapidity distributions for Events that pass kinematical cuts. Rapidity is obtained from the energy and longitudinal momentum of the muons . . . . . . . . . . . . . . 4.24 Single Diffractive events by POMWIG . . . . . . . . . . . . . . 4.25 Z invariant mass - POMWIG at generator Level . . . . . . . 4.26 ξpbar - POMWIG at generator Level . . . . . . . . . . . . . . . 4.27 η and pT distributions for muons from Z boson - POMWIG at generator level . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.28 η distribution for final state particles - POMWIG at generator level. The distribution shows that final particle states destroy the gap of most of diffractive events . . . . . . . . . . 4.29 π ± Energy distribution in the Gap region - POMWIG at generator level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.30 ξpbar - Events with two muons into |η| < 2 - POMWIG at generator Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.31 ξpbar - Geometrical Acceptance - POMWIG at generator Level 4.32 ξpbar and Rapidity Distribution - Events that pass all requirements - POMWIG at generator Level . . . . . . . . . . . 4.33 POMWIG plots after Full Simulation. pT and Rapidity distribution, dimuon mass and ξpbar . . . . . . . . . . . . . . . . . . P 4.34 E versus ξpbar - POMWIG events before and after gap requirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.35 ξpbar and Rapidity distributions for POMWIG events that pass all diffractive cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix. 62 63 64. 64 65 66 66 67. 68 68 69 69 70 71 72 72.

(11) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 4.36 Z kinematical Variables - PYTHIA. pT and Rapidity ditribution, Di-muon mass and ξpbar distribution . . . . . . . . . . 4.37 ξpbar and Rapidity distributions for PYTHIA events that pass all diffractive cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.38 ξpbar non diffractive cuts DATA and PYTHIA . . . . . . . . . 4.39 Kinematical variables (pT , Invariant Mass and Rapidity) for Di-muon Candidates. PYTHIA (yellow) and Data . . . . . . 4.40 ξpbar Distribution SIGNAL and Background . . . . . . . . . . 4.41 ξpbar Distribution - Diffractive Candidates and POMWIG . . 4.42 ∆ξ (Left) and ξreco versus ξgen (Right). The 2D plot is fitted to a polynomial function to correct the ξreco to the ξgen . . . 4.43 ∆ξ (Left) and ξcorr versus ξgen (Right). The 2D plot is fitted to the linear function, the slope is about 1, it shows the correspondence one by one between both variables . . . . . . 4.44 dσ/dξ diffractive candidates and POMWIG. The mean value by bin corresponds to the ξ corrected. (See Table 4.6) . . . 4.45 Rapidity Distribution SIGNAL and Background . . . . . . . 4.46 dσ/dy Diffractive Candidates and POMWIG . . . . . . . . . .. 73 73 75 76 76 77 78. 79 80 80 81. C.1 Distribution of Mµµ for events exclusively rejected by the isolation cuts. Blue shaded histogram: Expected shape and size of Mµµ for signal events rejected by the isolation cuts . . 95 C.2 Distribution of Mµµ for the events exclusively rejected by the requirement that the two muons be oppositely charged. 96 C.3 Distribution of Mµµ for events with two isolated muons. The distributions are normalized to the same number of events in the region Mµµ > 50 GeV . . . . . . . . . . . . . . . . . . . . . 96 C.4 ∆tA versus ∆αµµ for events that have passed all cuts but that on ∆αµµ . The red arrow indicates the position of the cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 C.5 Speed of muon pair in candidate events as if they were one muon transversing the detector . . . . . . . . . . . . . . . . . . 98 C.6 Distribution of Mµµ for the events rejected by the cosmic muons (dca or ∆αµµ ) . . . . . . . . . . . . . . . . . . . . . . . . . 99 C.7 Distribution of dca for one muon track versus dca for the other muon track for events that fail the dca cut but have passed all other cuts, with the additional requirement that all four isolation cuts pass. (a) For events where both tracks have SMT hits. (b) For events where at least one track has no SMT hits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100. x.

(12) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. D.1 Cube definition surrounding a candidate hot cell in η × φ plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102. xi.

(13) Acknowledgements I would like to express my deep sense of gratitude to my thesis advisor Professor Carlos Avila, for his guidance, constant support and encouragement all through my research career at Universidad de los Andes. I thank him for everything I learnt from him. I thank the Faculty of Science of Universidad de los Andes for the financial support through research seed projects. Working within a big collaboration is not possible without the help of many people. Sincere thanks to all DØ people for their help during my work and stay at Fermilab. I also want to thank the Fermilab beams division for the efforts in delivering high luminosity at the two collisions point in the Tevatron. Thanks to COLCIENCIAS for providing financial support during my studies. Initially, through the program ”CREDITOS CONDONABLES DOCTORADOS NACIONALES” and later through the research project number 1205-05-13624. I want to thank the staff of the department of physics of Universidad de los Andes for their permanent collaboration and support. I would like to thank Dr. Andrew Brandt and Dr. Duncan Brown from the University of Texas at Arligton for their support and guidance when I was at Fermilab. Special thanks to Dr. Bernardo Gomez. His great educational and human qualities are a model to follow. To all my friends. I prefer to thank them personally because I guess that many of them will not read this dissertation.. xii.

(14) Abstract. Measurements of the inclusive diffractive Z → µ+ µ− cross section with an as√ sociated rapidity gap for Mµµ > 40 GeV at s = 1.96 T eV and fraction of Z bosons produced diffractively with gap to Z inclusive production are presented. The measurements are performed using a data sample corresponding to an integrated luminosity of 820 pb−1 , collected with the DØ detector at the Tevatron, between 2003 to 2006. A total of 39955 di-muons events are selected and final results are: gap ∗ + − σDif f × Br(Z/γ → µ µ ) = 4.09 ± 0.64(stat.) ± 0.88(syst.) ± 0.27(lumi.) pb. and, gap RDiff = 1.92 ± 0.30(stat.) ± 0.41(syst.) ± 0.12(lumi) %. In adition, dσ/dξ and dσ/dy distributions for the Diffractive Z sample are presented and compared with a diffractive montecarlo (POMWIG). A reasonable agreement is obtained in this comparison, which indicates that the quark Pomeron modeled by POMWIG describes the data appropiately..

(15) Chapter 1. Theory 1.1. The Standard Model. Elementary particle physics deals basically with the study of the ultimate constituents of matter and the nature of the interactions between them. It is well known that everyday life is properly described by Newton laws of classical mechanics. But for objects that travel at speeds comparable to the speed of light, c, the classical rules need to be modified by special relativity; furthermore, for objects that are very small (roughly at the subatomic level), classical mechanics is superseded by quantum mechanics. As elementary particles are both fast and small their description falls under the domain of the quantum field theory. In the present state of our knowledge leptons and quarks are considered to be the elementary constituents of matter. Together with the four fundamental interactions (the strong, electromagnetic, weak and gravitational forces) they represent the basic ingredients for a description of the physical world. The Standard Model describes the interaction between quarks and leptons by means of two mathematical models: Quantum Chromodynamics QCD and the Electroweak Theory [1], [2], [3]. QCD, which is based on the SU(3) group, accounts for the strong interaction; the Electroweak Theory which successfully unifies the electromagnetic and weak interactions, is based on a group structure of SU (2)L × U (1). The fundamental particles considered by the Standard Model are fermions and bosons. The fermions are quarks or leptons with spin 21 , that are considered to be the constituents of matter. The bosons have spin 1 and are responsible for mediating the strong and electroweak forces. The model considers the existence of six electrically charged quarks (Up, Down, 1.

(16) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Charm, Strange, Top and Bottom) paired in three generations as shown in Table 1.1. The existence of all the quarks has been experimentally verified. Quarks u, c, t d, s, b. Charge + 23 − 13. Leptons νe , νµ , ντ e− , µ− , τ −. Charge 0 −1. Interaction EM Weak Strong. Gauge Bosons photon (γ) W ±, Z 0 gluons (g). Table 1.1: Schematic representation of the Standard Model: Constituents are doublets of quarks and leptons in three generations. Forces are mediated by gauge bosons Each quark has an additional degree of freedom called color, and labeled Red, Green or Blue. Quarks can only exist in color singlet states and thus can not be isolated. Quarks bound in color singlet states form the hadrons which are found in nature. As the quarks carry electric and color charges, they are subject to both strong and electroweak forces. The second group of fermions are the leptons which also appear paired in three families (see Table 1.1). The electron (e− ),muon (µ− )and tau (τ − ) are massive particles which carry a negative electric charge e = 1.6 × 10−19 C and thus are subject to electroweak forces. These leptons are paired with three neutrinos which are light (mν < 2 eV ) electrically neutral particles that only experience weak interactions. The gauge bosons are responsible for mediating the fundamental forces. The coupling constants describing the strength of these forces are all dimensionless. The strong force which acts between particles carrying color is mediated by eight gluons. Gluons are electrically neutral bosons that carry color charge and therefore undergo self-interactions. The photon γ and the three intermediate vector bosons W ± and Z 0 mediate the electroweak force. The model also predicts the existence of a neutral scalar Higgs boson which is a remnant of the mechanism that breaks the SU (2) × U (1) symmetry and generates the W and Z boson masses. So far no experimental evidence exists for the Higgs boson.. 1.2. Z 0 Bosons at the Tevatron. At the Tevatron, Z bosons are predominantly produced by annhilation of a quarkantiquark pair (the Drell-Yan process [4]): q q̄ → Z. Figure (1.1) shows this process for a Z, which will decay to a pair of muons. The cross section for such processes, pp̄ → Z 0 , can be written in the factorised form: 2.

(17) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. +. µ. q Ζ. 0. −. µ. q. Figure 1.1: Z production and decay at the Tevatron. σ=. X i,j. fi x1 , µ2F. . ⊗. P Ci,j. . Q2 x1 x2 s, 2 µF. . ⊗ f¯j x2 , µ2F ,. (1.1). where Q2 is the scale of the hard process, s is the square of the center of mass Q2 P energy of the pp̄ system, Ci,j x1 x2 s, µ2 are the coefficient functions describing F the hard processes, qi q̄j → Z, and fi x1 , µ2F and f¯j x2 , µ2F are the PDFs1 of the proton and antiproton respectively. The coefficient functions can be calculated from first principles whereas the PDFs must be taken from fits to experimental data. The partons inside the hadrons that do not participate in the hard interaction will generally interact softly. This part of the process is known as the underlying event. The Z 0 boson is unstable and decays to a pair of fermions; the branching ratio for the decays [5] are shown in Table 1.2 for the Z bosons. decay channel e+ e− µ+ µ− τ +τ − invisible hadrons. branching ratio (%) 3.363 ± 0.004 3.366 ± 0.007 3.370 ± 0.008 20.00 ± 0.06 69.91 ± 0.06. Table 1.2: Branching Ratios for Z boson decays. The invisible decays are presumed to be to neutrinos In the DØ collaboration, the Z boson decay channels studied correspond to the lepton channels (e+ e− , µ+ µ− ) because they are experimentally the easiest to 1. PDFs: Parton Distribution Functions. 3.

(18) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. identify. Both channels require charged tracks identified by the tracking system and in the case of the electron channel, two isolated electrons in the calorimeter. For the muon channel must have identified two muons by the muon system. The muon channel is used in this analysis. The Z mass boson is about 91 GeV , however when the Z invariant mass is reconstructed a gaussian distribution is obtained. This is due to the uncertainty principle of quantum mechanics that allows the production of a virtual Z 0 with higher or lower mass. However, the probability for virtual Z 0 production drops quickly when the mass differs from 91 GeV , this effect is quantified in terms of the width of the gaussian distribution. This also related to the lifetime of a particle. Particles with long lifetime have small fluctuations in mass and therefore small widths. The Z 0 has a width of around 2.5 GeV [6], corresponding to a lifetime of around 10−24 s in the rest frame. Other sources of background correspond to QCD processes like hadrons with content of b quark, τ lepton and γ ∗ , which have the same decay channel (electron or muon channel).. 1.3. Diffraction Phenomenology. Hadronic diffraction is generally defined as a reaction in which no quantum numbers are exchanged between particles colliding at high energies [7]. The exchanged object between the colliding particles which carries the quantum numbers of the vacuum is referred as the pomeron and will be denoted by IP . There are two classes of Diffractive events in pp̄ collisions: elastic scattering and diffractive dissociation. Diffractive dissociation can be subdivided in: single diffractive dissociation, double diffractive dissociation and double pomeron exchange. Diffractive process are shown schematically in Figure (1.2). (a). (b) a. a. (c) a. a. IP. (d). a. Xa. a. a IP. IP. IP. X IP. b. b. b. Xb. b. Xb. b. b. Figure 1.2: Illustrations for Diffractive Events: (a) Elastic scattering, (b) single diffractive dissociation, (c) double diffractive dissociation, and (d) double pomeron exchange. 4.

(19) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. • Elastic scattering: both incoming particles remain intact from the collision. a+b →a+b. (1.2). • Single diffractive dissociation: one of the incoming particles is scattered by losing a small momentum fraction while the other dissociates into a cluster of final state particles. a + b → a + Xb. (1.3). where Xb corresponds to the final state particles with the quantum numbers of the (b) particle. • Double diffractive dissociation: each incoming particle dissociates into a cluster of final state particles with the same quantum numbers as the incoming particle. a + b → Xa + Xb. (1.4). • Double pomeron exchange: both particles are scattered by losing a small momentum fraction and a cluster of particles X with the quantum numbers of the vacuum is produced. a+b→a+X +b. 1.3.1. (1.5). Elastic Scattering. Elastic scattering can be explained by using the classical theory of diffraction of light. In optics the intensity of the light scattered off an absorbing disk, which is a close analogy to an absorbing hadron as a function of the scattering angle θ is given by (2J1 (x))2 r2 2 2 I = ≈ 1− k θ (1.6) I0 x 4 where J1 (x) is the first order Bessel function, r is the radius of the absorbing disk, θ is the scattering angle of the light, k is the wave number of the photons, and x = kr sin θ ≈ krθ at small angles. In quantum mechanics is obtained similar diffraction patterns when interaction particles are described. Diffraction is an intrinsic property of the propagation of probability waves and a consecuence of the principle of superposition for probability amplitudes. The differential cross section for hadron-hadron elastic scattering at small angles can be described in a similar way by: 5.

(20) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. . dσ dt. . = elastic. dσ dt. t=0. ebt ≈ 1 − b(pθ)2 ,. (1.7). where p is the momentum of the incident hadron scattered at the angle θ, and t = −(pf − pi )2 is the four-momentum transfer squared. The slope parameter b is related to the radius of the absorbing disk by b = r 2 /4. For a target proton of radius ≈ 1/mπ , where mπ is the pion mass, b ≈ 13 GeV −2 . This slope agrees with the measured values of the slope parameter for pp, pp̄ elastic scattering at high energies [8].. 1.3.2. Hard Diffraction. According to Regge theory, at high energies, small-t processes are well described by single-pomeron exchange [9]. Although this description is phenomenologically successful, there is not yet understanding of the nature of the Pomeron (IP ) under the fundamental quantum field theory of the strong interaction. In QCD, interactions between hadrons arise through the interactions of their quark and gluon components. Quarks and gluons experience and transmit strong forces. It is known that the strong interactions of quarks and gluons occur due to the quantum characteristic called color carried by them. Only colored particles can emit or absorb a gluon. Because of color, gluons can couple directly to other gluons whereas photons cannot couple to each other. A fundamental aspect of QCD is asymptotic freedom [10]. This feature accounts for the tendency of hadrons to behave like collections of pointlike constituents, also called partons, when they are probed at short distances, and determines the applicability of the perturbation expansion formalism in the calculation of observables in parton-parton scattering. The most crucial consequence of strong forces is color confinement, which means that neither quarks nor gluons can appear in isolation. They can only exist within colorless (color singlet) composite hadrons. Since diffractive processes involve a strong interaction, it is natural to ask whether the pomeron can be understood as an object composed of partons. Hadron interactions proceeding through the exchange of a particular combination of quarks and gluons that preserve the quantum numbers of the initial hadron states lead to either elastic scattering of the initial hadrons, or to diffraction dissociation of one (single diffraction dissociation) or both (double diffraction dissociation) hadrons in the final state into multi-hadron systems. Until recently, there has not been much overlap between Regge theory and perturbative QCD. Diffraction, which is intimately connected with confinement, 6.

(21) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. since it displays the basic property of hadrons behaving as objects of finite size and definite quantum numbers, is concentrated at small momentum transfers and appears as a large distance phenomenon, dominated by nonperturbative effects. Hence, it is not calculable by perturbative QCD. In order to probe the Pomeron structure function in a hard scattering process, Ingelman and Schlein [11] suggested that if the Pomeron has a partonic structure it should manifest in diffractive scattering through the appearance of jets, or heavy quarks [12], or W and Z bosons [13]. The diffractive cross section Z production is based on extending the concept of factorization to hard pomeron-hadron collisions by treating the pomeron flux factor as a flux of particle-like pomerons with a unique partonic structure. In this model the diffraction dissociation process proceeds in two steps. In the first step, a pomeron is emitted from the (anti)proton with a small squared momentum transfer t = −(pf − pi )2 , and with a forward momentum fraction ξ = 1 − pf /pi smaller than 0.1. In the second step, this pomeron interacts with a parton (quark or gluon) in the (anti)proton in a large momentum transfer process between the constituent partons producing a Z boson. Diffractive Z production is shown schematically in Figure (1.3).. t. p. p ξ. P. Z. 0. µ+ µ−. X. p. Figure 1.3: Schematic view Diffractive Z production. 7.

(22) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. According to the factorization, the diffractive Z cross section can be expressed as: dσ(p̄IP → Z + X) dσ(pp̄ → p + Z + X) = fIP/p (xIP , t) dxIP dtdx1 dx2 dx1 dx2. (1.8). where fIP/p (xIP , t) is the pomeron flux factor, it gives the probability that the →Z+X) is the pomeron-antiproton (anti)proton emits a pomeron [11] and dσ(p̄IP dx1 dx2 cross section. The pomeron-antiproton cross section can be defined as:. dσ(p̄IP → Z + X) = fq/IP (x1 )fq/p̄ (x2 )σ̂(q q̄ → Z) dx1 dx2. (1.9). where fq/IP (x1 ) and fq/p̄ (x2 ) correspond to the parton structure functions of the Pomeron and antiproton respectively and σ̂(q q̄ → Z) is the elemental q q̄ cross →Z+X) sections that contribute to the diffractive Z production. dσ(p̄IP is based on a dx1 dx2 quark structure of the Pomeron because the diffractive Z production is dominated by Leading Order (LO) process. Bruni and Ingelman predicted the fraction of Z bosons produced diffractively from Z inclusive production [13]. For a quark-dominated pomeron the observable diffractive Z boson production of the total Z cross section in lepton decays is: Zdif f ractive → l+ l− ∼ 15% Zall → l+ l−. (1.10). where l+ l− correspond to the lepton channels e, µ. Experimental results (DØ [66] and CDF [14]) showed big differences to the values predicted by Bruni-Ingelman for the fraction of W/Z bosons producted diffractively from W/Z inclusive production. Experimental results probe that hard diffraction cannot be explained under the factorization scheme.. 1.3.3. Rapidity Gaps. Experimentally, diffractive events can be identified either by detecting the intact particle directly using forward proton detectors or by tagging events with a rapidity gap. Although the DØ detector has forward proton detectors, they will be not used in this analysis. The rapidity gap is used as signal for diffractive events. In hadron collisions, Rapidity (y) is associated to the longitudinal momentum of the final states particles. It’s defined as: y=. 1 E + pz ln 2 E − pz 8. (1.11).

(23) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. where E and pz are the energy and the longitudinal momentum respectively. For massless particles one has E ≈ |~ p| and the rapidity is directly related with the polar angle θ measured with respect to the z axis. Rapidity can be rewritten as: 1 y ≈ ln 2. . 1 + cos θ 1 − cos θ. . = − ln tan. θ =η 2. (1.12). where η is called pseudorapidity. In high energies, the variables rapidity and pseudorapidity are used interchangeably. The maximum values for rapidities in both sides ocurr when the particles no exchange four-momentum between them (pT = 0). The rapidities y+ and y− of the particles measured in their center of mass system are,. y± ≈ ± ln. √. s , m. (1.13). where y± is for the particle running in the positive (negative) z direction. For nondiffractive events in which both incoming particles dissociate into a system X, the maximum and minimum rapidities of the system X are given by yxmax. √ s , ≈ ln m. yxmin. √ s ≈ − ln m. (1.14). where m is the mass of the final state particles. Taking a look in single diffractive events with a intact particle in the negative z direction when is scattered quasielastically (pT ≈ 0), the minimum rapidity for the leading particle is defined as, √ √ s(1 − ξ) s ≈ − ln . (1.15) yleading,min ≈ − ln m m The maximum rapidity of the system X is the same as that in non-diffractive events, √ s . (1.16) yX,max ≈ ln m The minimum rapidity of the system X corresponds to a particle with longitudinal √ momentun pz ≈ ξ · s/2 √ sξ yX,min ≈ − ln . (1.17) m Therefore, the rapidity region without particles, called a rapidity gap, between the quasielastically scattering leading particle and the system X is: 9.

(24) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. ∆ygap = yX,min − yleading,min ≈ − ln ξ.. (1.18). Figure (1.4) shows the rapidity distribution for final state particles in diffractive events.. Figure 1.4: Rapidity distribution for diffractive events. There is a rapidity gap in the negative z axis. System X is the final state particles [7]. According to the scaling law proposed by R. P. Feynman [15], the longitudinal distribution of final state particles is, dN ∼ ρ, dy. (1.19). where the particle density ρ is approximately constant over the phase space available for the dissociation products. In terms of rapidity intervals ∆y between final state particles, the distribution obtained from Poisson fluctuations is given by dN ≈ e−ρ∆y . d∆y. (1.20). Thus, in non-diffractive events, rapidity gaps are exponentially suppressed. In diffractive events, the distribution of rapidity intervals between the leading particle and the system X behaves as dN ≈ constant. d∆y. (1.21). Therefore, diffractive dissociation is often defined as events containing large rapidity gaps in the final state which are not exponentially suppressed [7].. 10.

(25) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 1.3.4. Rapidity Gap Survival. The Rapidity Gap Survival (RGS) is associated to diffractive events where the gap is destroyed due to multiple interactions between the spectactor partons from the interaction [16]. According to some phenomenological models, RGS causes the factorization breakdown because the diffractive signature is spoiled. In these models, predictions based on the factorization scheme have to be multiplied by a function called rapidity gap survival probability [18], which represents the probability that no additional soft parton is exchanged between the colliding hadrons. Bjorken √ estimated that the survival probability is < S 2 >≈ 0.05 − 0.1 at s = 1.8 T eV and √ found that < S 2 > decreases with increasing s, since the interactions between the particle remnants become stronger and tend to destroy the gap. This fact explains why the diffractive to non-diffractive ratio predictions based on HERA √ data ( s = 630 GeV ) is 10 times greater that the values obtained in the Tevatron √ in Run I at s = 1.8 T eV .. 1.3.5. Soft Color Interaction (SCI). Given the conceptual problems of the Pomeron Model and the impossibility to cover all aspects by a pQCD treatment (factorization breakdown), Soft Color Interaction (SCI) arise as a single simple model that describes all final states, with or without gaps [19]. The SCI model is formulated on a parton basis, with soft color exchange between quarks and gluons, the basic assumption is that the soft color exchange changes the topology of the confining color force fields given by the perturbative QCD interaction (including remnants of initial hadrons). Figure (1.5) shows an illustration of Diffractive Z production by using Soft Color Interaction model. p. p. q q. 11 00 00 11 00 11 q. Z. q q. q q. 11 00 00 11 00 11 q. µ−. Z. q. µ+. q. µ− µ+ gap. p. 11 00 00 11 00 11. q q. qq. p. 11 00 00 11 00 11. q q. qq. Figure 1.5: Z production (decaying leptonically) in a pp̄ collision with string topology (double-dashed lines) before (left) and after (right) a soft color exchange resulting in a rapidity gap. 11.

(26) Chapter 2. Experimental Apparatus This analysis involves a collection of data taken in the DØ detector, using beams of protons and antiprotons with a center of mass energy of 1.96 T eV . The source of these beams is an accelerator complex at Fermilab. This chapter gives a brief overview of the accelerator chain and the DØ detector.. 2.1. Fermilab Accelerator Complex. Before protons and antiprotons collide in the DØ detector, they have to pass through a sequence of seven accelerators [20]. A Cockcroft-Walton pre-accelerator, a linear accelerator (Linac) and a synchrotron (Booster) that provides a source of 8 GeV protons. The Antiproton source is composed by the Debuncher and the Accumulator. The Main Injector has two functions: It serves as the final boosting stage before injecting protons and antiprotons into the Tevatron and it also provides energetic protons which are needed in the antiproton source. Figure (2.1) shows a schematic view of the Fermilab accelerator chain.. 2.1.1. The Pre-accelerator. The Pre-accelerator produces negatively charged hydrogen ions (H − ) with an energy of 750 keV . Hydrogen gas (H2 ) enters a magnetron surface-plasma source (See Figure (2.2)). The electrons are separated from the Hydrogen atoms due to the electric field between the anode (positively charged) and the cathode (negatively charged) creating a plasma. Cesium vapor is used in order to reduce the work function of the cathode by helping to the separation of electrons from the metal surface. The positively charged hydrogen ions are moved to the cathode where they will collect extra electrons. Due to this, negatively charged hydrogen ions (H − ) are created. The H − are extracted through the anode aperture with an electric field of 12.

(27) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Figure 2.1: The accelerator chain at Fermilab. 18 kV applied by the extractor plate. Free electrons are separated of the H − ions by means of the perpendicular magnetic field to the electric field that curves their trajectories. A Cockcroft-Walton Generator is used to further accelerate the H − ions to an energy of 750 keV . The Cockcroft-Walton Generator produces a 750 kV potential difference by charging capacitors in parallel from an AC voltage source and discharging them in series, via diodes. The H − ions leave of the Cockcroft-Walton device and travel through a transfer line. Before entering the Linac the continuous stream of H − ions passes through a single gap radio frequency (RF) cavity which bunches the beam at the RF frequency of the Linac (201.24 M Hz).. 2.1.2. The Linac. The Linac (Fig. 2.3) uses RF cavities to accelerate bunches H − ions to an energy of 400 M eV coming from pre-accelerator. The RF cavities are contained within of five steel tanks which hold a sequence of drift tubes separated from each other by gaps. In order to accelerate H − ions, the cavities are designed in such a way that particles traveling in the gaps experience an acceleration, while particles traveling in the drift tubes are shielded from the RF. Bunches H − ions leave to the Linac with an energy of 400 M eV and they are transferred to the Booster.. 13.

(28) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Figure 2.2: Schematic view of magnetron operation for the hydrogen ion source. Figure 2.3: Schematic drawing of Linac RF cavity. 2.1.3. The Booster. The Booster is a synchotron composed of a sequence of dipoles and quadrupoles magnets and 17 RF cavities arranged in a circle with a diameter of 151 m. The Booster receives negatively charged H − ions coming from the Linac where they are merged with protons (H + ions) circulating previously in the Booster with the help of dipole magnets. The electrons are removed from the H − ions by passing the combined beam through a carbon foil. Once the Booster is filled with proton bunches, these are accelerated up to 8 GeV over the course of 20000 turns and transferred to the Main Injector. A detailed technical description of the Booster can be found in [22].. 2.1.4. The Main Injector. The Main Injector is a synchroton with a diameter of 1 km. It accelerates protons (coming from the Booster) and antiprotons (coming from the Antiproton source) from 8 GeV to 150 GeV before to the injecting them into the Tevatron. Also, The Main Injector accelerates protons to an energy of 120 GeV that are directed toward a target for antiproton production. 14.

(29) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.1.5. The Antiproton Source. Antiprotons are produced by bombarding a production target with a high energy protom beam. It consists of three major components [23]: the Target Station, the Debuncher, and the Accumulator. In the Target Station protons with an energy of 120 GeV coming from the Main Injector strike a Nickel target. The collision produces a shower of secondary particles (including antiprotons) with a large spread in angles and particle momentum. The beam is focused and positively charged particles are removed by means of Lithium lens and bending magnets (Fig. 2.4).. Lithium Lens. All sorts of stuff. +. 7 cm Nickel Target. Antiprotons 650 kA. Bend Magnet. Figure 2.4: Simplified drawing of anti-proton production with nickel target and lithium lens. A process called stochastic cooling [24] is used in both the Debuncher and the Accumulator to reduce the spread in momentum and position of the antiprotons. Antiprotons are then stored in the Accumulator. The process is inherently inefficient, for every 105 protons that hit the Nickel target, only about 1 or 2 antiprotons (The pbar production efficiency is about 15 × 10−6 ) can be gathered. Therefore the Accumulator stores antiprotons until a sufficient amount has been generated to be transferred into the Main Injector. The Accumulator must be capable of storing antiprotons over many hours. The performance of the antiproton source greatly affects the quality and duration of stores in the Tevatron. The low pbar production efficiency has an deep impact over the collected luminosity. At the moment, the ratio of antiprotons and protons per bunch crossing is of 1 to 5. Tevatron efforts are oriented to obtain a ratio of 1 to 1 between antiprotons and protons to increase the luminosity.. 15.

(30) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.1.6. The Recycler. The Recycler [25] is a 3.3 km storage ring composed of gradient magnets and quadrupoles. The Recycler has three functions: Collect remnant antiprotons at the end of Tevatron Collider stores (typically 80% of the number injected into the Tevatron) to be re-cooled and re-used. The Recycler acts as a post-Accumulator cooler ring, since the antiproton production rate decreases as the beam current in the Accumulator ring rises above a certain level. In addition, the permanent magnets in the Recycler reduce the probability of unexpected losses of the antiprotons.. 2.1.7. The Tevatron. The Tevatron is the final stage to the accelerator chains. It accelerates to protons and antiprotons coming from Main Injector up to 980 GeV , leading to a center of mass energy of 1.96 T eV in the collision point. 36 bunches of protons and 36 bunches of anti-protons are loaded in the opposite direction which results in a time interval of 396 ns between two consecutive collision. The Tevatron uses superconducting magnets at low temperatures provided by cryogenic liquid helium, which bend and focus the particle beam to collide at two crossing points: BØ (CDF detector) and DØ detector.. 2.1.8. Luminosity. Fermilab accelerators chain bring protons and antiprotons to an energy of 980 GeV for collisions at a rate high enough to study a big diversity of processes, and increase the precision of already known processes. The rate of collisions is calculated by the energy and density of particles in the proton and antiproton bunches. The unit of measurement used to described the scattering cross section of these bunches is called barn (1 b = 10−24 cm2 ). The rate at which the effective cross sectional area of the proton or antiproton bunch is being bombarded is the luminosity. Luminosity is given in units of cm−2 · s−1 In Run I, the instantaneous luminosity reached 20× 1030 cm2 ·s−1 , DØ detector collected an integrated luminosity of 120 pb−1 over four years. During this period, there were 6×6 bunches of protons and antiprotons circling the accelerator. For Run II, with the new bunches structure of protons and antiprotons (36×36) by circling at the Tevatron, the instantaneous luminosity has reached peaks of 171×1030 cm2 ·s−1 . Figure (2.5) shows the integrated luminosity for Run II from April 2002 until july 2007. The integrated luminosity expected to be deliver by the Tevatron from 2007 to 2009 is about 5 f b−1 . 16.

(31) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Figure 2.5: Total integrated luminosity delivered and recorded for Run II from April 2002 until Jul 2007. 2.2. Interactions of Energetic Particles with Matter. The main method used to detect and measure the properties of particles is to look for the position and energy deposited as those particles pass through a layer of material. In the DØ detector the relevant particles to analyze are electrons, muons, hadronic particles and neutrinos. The interaction of these particles with detector subsystems results in energy loss which can be detected and measured. Position of the particles are measured with tracking detectors. Usually, the tracking systems are embedded in a magnetic field to measure the particle momentum with high precision. Calorimeters fully absorb the particles and their showers, and thus their energy, in the process of measurement. The interactions of the different types of particles with the DØ detector are described below.. 17.

(32) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.2.1. Electrons and Photons. Electrons passing through matter loose their energy primarily through ionization and bremsstrahlung. Bremsstrahlung is the dominant process, the critical energy can be expressed as [26]: 800 M eV, Z + 1.2 Z corresponds to the atomic number of the medium EC =. (2.1). The emitted photons produce electron-positron pairs, which in turn emit photons. The resulting shower of electrons and photons grows until the energy of the electrons falls below the critical energy. Below to the critical energy, electrons interact mainly by ionization. The mean distance over which an electron loses all but 1/e of its energy is called the radiation length X0 [26]. X0 =. 716.4 A √ g · cm−2 , Z(Z + 1) ln (287/ Z). (2.2). where A is the atomic mass of the medium in g · mol−1 .. 2.2.2. Muons. Muons interact through bremsstrahlung at a much lower rate than electrons due to their larger mass. They lose energy primarily through ionization, however, the critical energy for muons is of the order of several hundreds of GeV. Muons at the Tevatron have energies of the order of GeV, and hence are minimum ionizing particles, also called MIP. They deposit only minimal energy in the detector and leave it essentially unperturbed, in contrast to all other particles (with the exception of neutrinos). Figure (2.6) shows the energy loss per unit of material for muons in various energy regimes [26].. 2.2.3. Hadronic Particles. Hadronic particles collide inelastically with the nuclei of the detector elements, producing secondary hadronic particles like pions and kaons. These secondary hadrons interact in turn with the near nuclei producing a hadronic shower in the calorimeter. The distance that the hadronic shower is propagated depend on the nuclear interaction length (λI ), which is dependently of the material density and atomic mass, but it is roughly independent of the energy. 18.

(33) Stopping power [MeV cm2/g]. DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. µ+ on Cu µ−. 10. LindhardScharff. 100. Bethe-Bloch. Radiative. AndersonZiegler. Eµc Radiative losses. Radiative Minimum effects ionisation reach 1%. Nuclear losses. Without δ 1 0.001. 0.01. 0.1. 1. 0.1. 1. 10. 100. [MeV/c]. 10. βγ. 1. 100. 1000. 10 4. 10. 100. 1. [GeV/c] Muon momentum. 10 5. 10 6. 10. 100. [TeV/c]. Figure 2.6: Energy loss through ionization of muons in various energy regimes. λI ≈ 35A1/3 g · cm2. (2.3). Hadronic showers are much longer than electromagnetic showers when are compared with the same initial energy. Therefore, hadronic calorimeters are much longer than electromagnetic calorimeters.. 2.2.4. Neutrinos. Being uncharged leptons, neutrinos interact only weakly via W and Z boson exchange, making their energy loss negligible and their direct detection impossible at DØ. Their presence can be inferred, however, from transverse momentum conservation requirements.. 2.3. The DØ Detector. The DØ detector [27] is a huge device used to study subatomic particles resulting √ from pp̄ collisions at s = 1.96 T eV . The detector is oriented primarily to probe the Standard Model of particle physics. Precision measurements W and Z bosons, observation of the top quark, studies of b-quark hadrons, testing of perturbative QCD, and the search for the new physics beyond to the standard model. The DØ detector can be divided into three main subdetectors: The Tracking System, the Calorimeter and the Muon spectrometer. 19.

(34) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. The tracking system records precisely the angles of charged particles, it is surrounded by a magnetic field that bends the charged tracks trajectories to measure their transverse momentum. The tracking system went upgraded for Run II, the silicon microstrip tracker and a scintillation fiber-tracker within a 2 T solenoid magnet were installed. The Calorimeter measures the energy of electromagnetic and hadronic showers, it is composed by uranium/liquid-argon cells, the calorimeter system was not upgraded for Run II. The muon spectrometer measures the momentum of muons. In the forward muon system, proportional drift chambers have been replaced by mini drift tubes and trigger scintillation counters. In the central region, scintillation counters have been added for improved muon triggering. In adition, Forward proton detector is also added for the study of diffractive physics. A side view of the upgraded DØ detector is shown in (Fig. 2.7).. Figure 2.7: Side view of the DØ detector for Run II. 20.

(35) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. 2.3.1. Coordinate System. The DØ detector is centered at the pp̄ collision point. This point is the origin of the different system coordinates defined for the detector. The cartesian coordinate system used for the DØ detector is right-handed with the z axis parallel to the direction of the beam such that the protons go in the positive z direction. The y axis is then vertical, and the x axis points towards the center of the accelerator ring. A cylindrical coordinate system (r, φ, z) is defined because the DØ detector has cylindrical symmetry around z axis (beamline). With r=. p. x2 + y 2 ,. and,. φ = arctan. y x. (azimuthal angle). (2.4). Another useful coordinate used in the detector is associated with the polar angle θ 1 , this variable is called pseudorapidity, it is defined as: . θ η = − ln tan . (2.5) 2 z The rapidity (y) is defined as, y = 21 ln E+p E−pz , where E and pz are the energy and longitudinal momentum of the particle respectively. At high energies, the momentum of a particle is much larger than its mass (p ≫ m); therefore, E 2 ≃ p2 and pz = p cos θ ≃ E cos θ. Using these approximations y ≈ η. The coordinates system commonly used in the DØ detector is a combination of cylindrical and spherical coordinates: (z, η, φ). The z coordinate is used to determine the event vertex location along the beam pipe. The azimuthal angle φ is measured in the perpendicular plane to z and η replaces to the polar angle. Furthermore, intervals in η are Lorentz invariant under boosts parallel to the z-axis. Depending on the choice of the origin of the coordinate system, the coordinates are called as physics coordinates when the origin is the reconstructed vertex of the interaction (φ and η), or detector coordinates (φdet and ηdet ) when the origin is chosen to be the center of the DØ detector.. 2.3.2. Luminosity Monitors. The Luminosity monitors [28] consists of two arrays of twenty-four plastic scintillation counters with photomultiplier readout. A schematic drawing of the system is shown (Fig. 2.8). The arrays are located on the inside faces of the end-cap 1. θ = arccos. „. √. z x2 +y 2 +z 2. «. 21.

(36) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. calorimeters at z = ±140 cm. The counters are 15 cm long and cover the pseudorapidity range 2.7 < |ηdet | < 4.4.. Figure 2.8: Luminosity Monitor layout. The r − φ view is shown on the left, the r − z view of the two arrays is shown on the right. The main purpose of the Luminosity Monitors (LM) is to make an accurate determination of luminosity at the DØ interaction region [29]. The instantaneous luminosity is measured from the average number of inelastic collisions per beam crossing N̄LM detected by the LM, and determined as:. L=. f N̄LM , σLM. (2.6). where f is the beam crossing frequency and σLM is the effective cross section [81] for the luminosity monitors taking into account the acceptances and efficiency of the LM detector [29] . Usually, N̄LM is greater than one, so, it is important to take into account multiple pp̄ collisions in the same bunch crossing. This is done by counting the fraction of bunch crossings with no collisions and using Poisson statistics to obtain N̄LM . In order to measure the instantaneous luminosity exactly, it is necessary to distinguish pp̄ interactions from the beam halo. The beam halo is produced by early hits in the luminosity monitors. In order to exclude this background, time-offlight measurements of particles traveling at small angles with respect to the beams are done. The z coordinate of the interaction vertex is calculated from the difference of time-of-flight: (t− − t+ )/2, where t+ and t− are the times-of-flight measured for particles hitting the LM detectors placed at ±140 cm. pp̄ collisions are selected by requiring |z| < 100 cm because the colissions are produced in a range of ±30 cm respect to detector center. Beam halo particles traveling in the ±z direction will have z ≈ ∓140 cm and don’t pass the |z| < 100 cm requirement (see Fig. 2.9).. 22.

(37) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Functions: Gaussian (sigma) 0.15. 0.10. proton halo. anti-proton. 0.05. proton. inelastic collision. 0.00 -180. south. -90. 0. 90. 180. north. Figure 2.9: The sketch on the left shows the diferentiation between inelastic collisions and beam halo. Expected z vertex distribution for inelastic collisions, centered at z = 0 cm, p halo centered at z = −140 cm, and p̄ halo centered at z = 140 cm (right).. 2.3.3. The Tracking System. The Tracking System consists of the silicon microstrip tracker (SMT) and the central fiber tracker (CFT) surrounded by a solenoidal magnet. Combined SMT and CFT information, provide excellent tracking performance. The track momentum resolution is σpT /p2T ∼ 0.2%, with track reconstruction efficiency of more than 95%. The DØ central tracking system is shown in (Fig. 2.10). The Silicon Microstrip Tracker (SMT) The Silicon Microstrip Tracker (SMT) is the most internal system in the DØ detector [27]. It provides tracking and vertexing for a range in |η| ∼ 4 by giving full coverage to the muon system and covering a great part of the calorimeter. The SMT has a design of barrel modules interspersed with disks in the central region and assemblies of disks in the forward regions such that tracks are generally perpendicular to detector surfaces for all η. The barrel detectors primarily measure the r − φ coordinate and the disk detectors measure r − z as well as r − φ. Thus, vertices for particles at high η are reconstructed in three dimensions by the disks, and vertices of particles at small values of η are determined using the barrels and central fiber tracker. Figure (2.11) shows a schematic of the SMT. The detector has six barrels in the central region. Each barrel has four silicon readout layers. The silicon modules installed in the barrels are called ladders. Layers 1 and 2 have twelve ladders each; layers 3 and 4 have twenty-four ladders each, for a total of 432 ladders. Each barrel is capped at high |z| with a disk of 23.

(38) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Figure 2.10: Schematic view of the DØ central tracking system. Figure 2.11: Schematic 3D view of the silicon vertex detector. twelve double-sided wedge detectors, called as F-disk. In the far forward regions, two large-diameter disks called H-disks, provide tracking at high |η|. Twenty-four 24.

(39) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. full wedges, each consisting of two back-to-back single-sided wedges, are mounted on each H-disk. There are 144 F-wedges and 96 full H-wedges in the tracker; each side of a wedge (upstream and downstream) is read out independently [30]. The SMT uses a combination of single-sided (SS), double-sided (DS), and doublesided double-metal (DSDM) sensors. Disk sensors are trapezoids with readout strips arranged parallel to the long edge of the devices. This provides an efective 30◦ stereo angle for the double-sided F-disks. A wedge for the H-disks consists of a pair of single-sided half-wedges mounted back-to-back, giving an efective stereo angle of 15◦ . Charged particles passing through the 300 µm wafers of n − type silicon of the SMT produces pairs of electrons and holes. The charge is collected by strips of p-type or n+ -type silicon. The separation between these strips is normally 50 − 150 µm. Central Fiber Tracker (CFT) The CFT consists of scintillating fibers [31] mounted on eight concentric support cylinders and occupies the radial space from 20 to 52 cm from the center of the beampipe. To accommodate the forward SMT H-disks, the two innermost cylinders are 1.66 m long; the outer six cylinders are 2.52 m long. The outer cylinder provides coverage for |η| < 1.62. Each cylinder supports one doublet layer of fibers oriented along the beam direction and a second doublet layer at a stereo angle of alternating +3◦ and −3◦ . The two layers of fibers are offset by half a fiber width to provide full coverage. The small fiber diameter gives the CFT a cluster resolution of about 100 µm per doublet layer. Light production in the fibers is a multistep process. When a charged particle traverses one of the fibers, the scintillator emits light at λ = 340 nm through a rapid fluorescence decay. A wave-shifting dye absorbs the light at λ = 340 nm and emits it at λ = 530 nm. The light is then transmitted by total internal reflexion to the end of the scintillating fibers, where the light is transfered through an optical connection to clear ber waveguides of identical diameter which are 7.8 to 11.9 m long. The light is only observed from one end of each scintillating fiber. The opposite end of each of the scintillating fibers is mirrored by sputtering with an aluminum coating that provides a reflectivity of 85 to 90 %. The clear fiber waveguides carry the scintillation light to visible light photon counters (VLPCs), which convert it to an electronic pulse which is read out. The visible light photon counters are situated in a liquid Helium cryostat and operate at a temperature of 9 K. They detect photons with a quantum efficiency 25.

(40) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. of 85% and provide charge of about 30 to 60 k electrons per photon. A minimum ionizing particle creates an average of eight photo-electrons per layer, depending on the angle between the scintillating fiber and the particle trajectory.. 2.3.4. Solenoidal Magnet. The superconducting solenoidal magnet was included [32] for Run II. It is housed within the central calorimeter’s cryostat region, between the CFT and the preshower detectors. It produces a magnetic field of 2.0 T uniform in η and φ. The Lorentz force bends the trajectory of charged particles. Thus, within the magnetic field, together with the CFT and SMT, a measurement of the track momentum is possible from the measurement of the radius of curvature of the tracks.. 2.3.5. Pre-shower Detectors. The pre-shower detectors [34] are used to correct the electromagnetic energy measurement of the central and end calorimeters for losses in the solenoid. The basic principle is to introduce some material before the pre-shower detectors to induce electromagnetic, but not hadronic, shower formation. Then, with sufficient detector resolution, it is possible to separate electromagnetic objects from hadrons. Preshower scintillators are triangular shaped (Fig. 2.12). This arranges scintillator layers without creating any dead space and thereby improves the accuracy of position measurements. The center of each scintillator carries a wavelength-shifting fiber which collects the light created by passing charged particles. The light is transmitted via clear fibers to VLPCs for readout. The Central Preshower Detector (CPS) is located in the 5 cm gap between the solenoid and the central calorimeter, covering the region |η| < 1.3 (See Fig. 2.10). It consist of a layer of lead radiator which has a thickness corresponding to approximately one radiation-length (X0 ), followed by three layers of triangular scintillator strips. The scintillating layers are arranged in an axial-u-v geometry, with a u stereo angle of 23.8◦ and a v stereo angle of 24◦ . Each layer has a total number of 2560 readout channels. The two Forward Preshower Detectors (FPS) are attached to the faces of the end calorimeters and cover a region of 1.5 < |η| < 2.5 (See Fig. 2.10). Each detector consists of an upstream double layer of scintillator strips (minimum ionizing particle layers, or MIP layers), followed by a lead-stainless-steel absorber layer and another double layer of scintillator strips behind it (shower layers).. 26.

(41) DIFFRACTIVE Z/γ ∗ → µ+ µ− PRODUCTION WITH RAPIDITY GAP IN PROTON - ANTIPROTON √ COLLISIONS AT s = 1.96 T eV in the DØ EXPERIMENT. Figure 2.12: Cross section and layout geometry of CPS and FPS scintillator strips.. 2.3.6. The Calorimeter System. The calorimeter system was designed to measure the energy of electrons, photons, jets and neutrinos by inducing them to produce electromagnetic and hadronic showers. The calorimeter system is segmented longitudinally into electromagnetic and hadronic calorimeters. The electromagnetic calorimeter measures the energy of electrons and photons. The hadronic calorimeter measures the energy of hadrons as they interact with the material of the calorimeter. Muons only deposit a small amount of energy due to ionization. Neutrinos deposit no energy in the detector, but the absence of energy deposition results in a momentum imbalance in the transverse plane. The imbalance is called missing transverse energy (6ET ). The calorimeter consists of a central calorimeter (CC) covering roughly |ηdet | < 1, two end calorimeters (EC) extending the coverage to |ηdet | ≈ 5 and an intercryostat detector (ICD). These parts are shown in (Fig. 2.13). The central and end calorimeters are subdivided into three layers: the electromagnetic (EM) layer which is designed to measure electrons, positrons and photons, known collectively as electromagnetic (EM) objects, the electromagnetic section has 4 layers. The fine (FH) and coarse (CH) hadronic layers measure hadronic showers of particles. Fine hadronic calorimeter (FH) has 2 to 4 layers, and the coarse hadronic section (CH) has 1 to 3 layers. Each layer is divided into small units called cells. The readout cells are arranged 27.