Feasibility Study√ of a Measurement of pp¯ Total Cross-Section at s =1.96 TeV using the FPD Subdetector of DZero Experiment by Carolina Garc´ıa A thesis submitted in partial fulfillment of the requirements for the Degree of Master in Sciences - Physics Physics Department Universidad de los Andes Bogot´a D.C. - Colombia January 2007 Approved by: PhD., Carlos Avila.´ Dr.rer.nat., Bernardo G´omez. PhD., Carlos Quimbay. i Abstract A feasibility study of the total cross-section (σtot) for proton-antiproton collisions at √ center-of-mass energy ( s) of 1.96TeV has been developed. The study consists of changing the position of the FPD subdetector at DZero Experiment and obtaining the total cross-section from the Luminosity Independent Method using MonteCarlo simulations. The elastic events are analyzed separately from the inelastic events. The obtained results show cases with an uncertainty 50% lesser than 2mb, which is the uncertainty reported by real experiments. Hence, we found that the positions 10, 12 and 14σ,whereσ is the beam size, with an emitancia of =10π are optimal for the σtot measurement using the FPD. Additionally, we estimate an uncertainty of about 1.1mb for the total cross-section measurement when the FPD is located at the positions established in the data-store on February 2006, with a rate of background about 20% for the inelastic events. Resumen Se ha realizado un estudio de factibilidad para efectuar la medici´on de la secci´on-eficaz √ total (σtot) de las colisiones prot´on-antiprot´on, a energ´ıas de centro-de-masa ( s)de 1.96TeV. El estudio se efectua cambiando la posici´on del subdetector FPD del exper- imento DCero y obteniendo la secci´on-eficaz total a partir del Mtodo Independiente de la Luminosidad usando simulaciones de MonteCarlo. Los eventos el´asticos son estudiados independientemente de los inel´asticos. Los resultados obtenidos muestran casos con una incertidumbre 50% menor a los 2mb reportada por los experimentos reales. Se establece entonces que las posiciones 10, 12 y 14σ, donde σ es el ancho del haz, con una emitancia de =10π son ´optimas para la medici´on de σtot con el FPD. Adicionalmente se estima que con las posiciones establecidas para la toma-de-datos llevada a cabo en febrero de 2006, la medici´on de la secci´on-eficaz total que se obtenga con el FPD tendr´a una incertidumbre alrededor de 1.1mb con una tasa de background alrededor del 20% para los eventos inel´asticos. Acknowledgments Working in this dissertation and writing this document are a very complete and adorable experience in my life. And, as in the life, the experience and preceded work of others are necessary to achieve that you want (that is close or almost that you desire). Without the help of others (many people out of this paper) I never would have obtained that I started. First I would like to thank my Advisor professor Carlos Avila, not only for being my advisor and provide me the topic, also for his patience and comprehension of my work. I will always appreciate the opportunity provided by him; although we never found us in a class and he could have said -no- to my interest, he took the risk. I was fortunate enough to count on Luis Miguel. His constant and important support, in discussing the strategies to obtain results from D0gstart and its physics, is very grateful. The help of Jorge Molina with the Propagation Function and the email communica- tion is grateful as well. I am also deeply grateful to Santiago, because of his nice and punctual comments and questions at the end of this process and his first explanations when all began. Many thanks as well to Andres for reading a draft of this document and providing me an unsuspected force to face the final steps of this work. ii iii The financial support, for my Master and this project, from the Physics Department and the Faculty of Sciences at Universidad de los Andes are really appreciated. It has been a great pleasure and honor to study and work with the scientists listed above and the faculty, staff, and students at the Universidad de los Andes, where I constantly felt inspired by the intelligence and humanity surrounding me. I would specially like to thank Professor Bernardo Gomez for his always support and provide me the enthusiasm to continue the not easy way that I chose. I owe he more that I could express in a piece of paper. His support made all the difference in my academic career. Sources of support, joy, and laughter in my journey at Los Andes, that I would like to thank, are also: Angela, Angelita, Luisilla, CaroV, Magnis, Giova, Diana, Carlitos, Juan Andres, Nicolas and all the people of the FUT 2006. Last but not least, I am thankful to My Parents. Their sacrifices to ensure that I had a good education are appreciated as well as the freedom for choosing my path. Carolina Garcia Contents List of Figures vi List of Tables ix 1 Introduction 2 2 The Total Cross-Section Measurement 6 2.1 The Total Cross-Section (σtot)...................... 7 2.2 σtot MeasurementTechniques...................... 7 2.2.1 TheLuminosityIndependentMethod(LIM).......... 9 2.3 Physical Quantities Involved in LIM for this Feasibility Study .... 10 3 Accelerator Description 12 3.1TheTevatronatFermilab........................ 13 3.2ParticleBeamsandPhaseSpace..................... 16 3.2.1 Transversalphasespacedynamics................ 17 3.2.2 Beam Emittance ........................ 18 3.2.3 Longitudinalphasespacedynamics............... 19 3.3ParametersfortheTevatron....................... 20 3.3.1 LuminosityintheTevatron................... 20 4 Detector Description 23 4.1TheDØDetector............................. 24 4.2TheForwardProtonDetector(FPD)atDØ.............. 32 iv CONTENTS v 4.2.1 TheRomanpotsoftheFPD................... 33 4.2.2 TheEffectiveLengthsofFPD.................. 34 4.2.3 TevatronTimingandElasticEventsintheFPD........ 36 4.2.4 High β Store........................... 38 4.3TheLuminosityMonitors(LM)atDØ................. 39 4.4CoordinateSystemfortheFPD..................... 40 5 Physical Processes Involved in a pp¯ Collision 42 5.1MainDiffractiveProcesses........................ 44 5.2Kinematicsoftwo-bodyprocesses.................... 47 5.3DifferentialElasticCross-SectionRemark................ 48 5.4Definitionsofusefulvariables...................... 49 6 Simulation Description 52 6.1ClassificationofEventsStrategy..................... 52 6.2MonteCarloStudyofElasticEvents................... 54 6.2.1 DistributionoftheTransferredMomentum........... 56 6.2.2 Calculation of the Geometrical Acceptance of the FPD . 59 6.2.3 FiducialCuts........................... 62 6.3SimulationStudyofInelasticEvents.................. 63 6.3.1 BeamPipeEffectViewusingPYTHIAandGEANT4..... 65 6.4TheTotalCross-SectionUncertainty.................. 69 7 Inelastic Acceptance Simulation Results 71 7.1 Acceptance of LM for Each Process . ................. 72 7.2 Single Diffractive FPD Acceptance Changing Positions . ...... 74 7.3 Pots located at high β Store....................... 77 8 Statistical Errors for σtot,pp¯ Simulation Results 81 8.1TablesofFits............................... 81 8.2Tableofeachtermuncertaintycontribution.............. 84 8.3Totalcross-sectionuncertaintyresults.................. 86 CONTENTS vi 8.4Changingemittance............................ 87 8.5 High-β-Storeresults........................... 90 √ 9 Systematic Errors for σtot,pp¯ at s =1.96TeV Results 92 10 Background Analysis and Results 95 10.1MultipleInteractions........................... 95 10.2HaloBackground............................. 97 11 Conclusions 102 Bibliography 105 A The FPD Elastic Dispersion Function 107 A.1 Input parameters . ............................ 107 A.2Obtainingthefinalpositioninthedetectors.............. 109 A.3Theoutputdistribution......................... 110 B The FPD Propagator Function 112 B.1 Input Parameters . ............................ 112 B.2OutputAdjustment............................ 113 C Computation Tools 115 C.1NotesofusingDØgstar.......................... 115 C.1.1CARDFILES........................... 117 C.2NotesofusingPOMWIG......................... 118 C.3NotesofusingPYTHIA......................... 119 C.4NotesofusingGeant4.......................... 120 List of Figures 1.1 Fit from experimental data of the pp¯ totalcrosssection........ 3 3.1 The Tevatron accelerator chain at Fermilab. .............. 13 3.2Exampleoflongitudinalalignment.................... 19 4.1TheDØDetectorcomponents...................... 24 4.2SchematicidentificationofparticlesintheDØDetector........ 25 4.3SMTdetectorlayout............................ 26 4.4CalorimeteratDØDetector. ...................... 28 4.5MuonSystematDØDetector. ..................... 30 4.6TheForwardProtonDetector....................... 33 4.7FibersplanesfortheForwardProtonDetector............. 34 4.8TimingintheFPD............................. 36 4.9PositionoftheLuminosityMonitors(LM)atDØDetector...... 39 4.10TheLuminosityMonitor.......................... 40 4.11DØCoordinateSystem.......................... 41 4.12FPDcoordinatesystem ......................... 41 5.1SchematicViewofanElasticprocess. ................. 44 5.2SchematicViewofSingleDiffractiveSoftProcess............ 45 5.3SchematicViewofSingleDiffractiveHardProcess........... 45 5.4SchematicViewofDouble-DiffractiveProcess. ............ 46 5.5SchematicViewofDoublePomeronExchangeProcess......... 46 vii LIST OF FIGURES viii 6.1SingleDiffractiveProcessCandidate.................. 53 6.2DoublePomeronExchangeProcessCandidate. ............ 55 6.3Rangeforthefitintheblockfunction.................. 56 6.4Distributionsoftheexpectedtransferredmomentum........