DOCSLIB.ORG

UNIVERSITY of CALIFORNIA SAN DIEGO Observation of Higgs Boson

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
UNIVERSITY of CALIFORNIA SAN DIEGO Observation of Higgs Boson UNIVERSITY OF CALIFORNIA SAN DIEGO Observation of Higgs boson production in association with a top quark-antiquark pair in the diphoton decay channel A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by Samuel James May Committee in charge: Professor Avraham Yagil, Chair Professor Garrison Cottrell Professor Aneesh Manohar Professor Julian McAuley Professor Frank Würthwein 2020 Copyright Samuel James May, 2020 All rights reserved. The dissertation of Samuel James May is approved, and it is acceptable in quality and form for publication on microfilm and electronically: Chair University of California San Diego 2020 iii DEDICATION To my mom and dad, who have always encouraged my curiosity and supported my education. iv EPIGRAPH Sometimes science is more art than science. —Rick Sanchez v TABLE OF CONTENTS Signature Page . iii Dedication . iv Epigraph . v Table of Contents . vi List of Figures . ix List of Tables . xiii Acknowledgements . xiv Vita . xvii Abstract of the Dissertation . xviii Chapter 1 Introduction . 1 Chapter 2 Theory . 3 2.1 Introduction . 3 2.2 Quantum Field Theory . 5 2.2.1 Classical Field Theory . 5 2.2.2 Quantum Mechanics . 6 2.2.3 The Klein-Gordon Field . 6 2.2.4 Spinor & Vector Fields . 9 2.3 The Standard Model of Particle Physics . 10 2.3.1 Gauge Fields . 11 2.3.2 Quantum Electrodynamics . 12 2.3.3 Quantum Chromodynamics . 13 2.3.4 Spontaneous Symmetry Breaking & The Higgs Mechanism . 15 2.3.5 Electroweak Interactions . 18 2.3.6 Shortcomings of the Standard Model . 21 2.3.7 The Higgs Boson . 22 Chapter 3 Physics of Proton-Proton Collisions . 24 3.1 The Parton Model . 24 3.2 Proton-Proton Collisions . 25 3.2.1 Cross Sections . 25 3.2.2 Parton Showers, Hadronization, and Jets . 28 3.2.3 Underlying Event and Pileup . 29 3.3 Monte Carlo Simulation . 30 Chapter 4 Compact Muon Solenoid . 32 vi 4.1 The Large Hadron Collider . 32 4.2 The Compact Muon Solenoid Detector . 35 4.2.1 General Design Concepts . 36 4.2.2 Solenoid . 38 4.2.3 Tracker . 40 4.2.4 Electromagnetic Calorimeter . 42 4.2.5 Hadronic Calorimeter . 44 4.2.6 Muon System . 45 4.2.7 Trigger System . 47 4.3 Acknowledgements . 49 Chapter 5 Event Reconstruction and Selection . 50 5.1 Introduction . 50 5.2 The Particle Flow Algorithm . 50 5.3 Vertex Reconstruction . 52 5.4 Photon Reconstruction . 53 5.4.1 Variable Definitions . 54 5.4.2 Energy Scale & Resolution Corrections . 56 5.4.3 Shower Shape & Isolation Corrections . 59 5.4.4 Photon Identification BDT . 59 5.4.5 Selection Criteria . 60 5.5 Jet Reconstruction . 62 5.6 Lepton Reconstruction . 65 5.7 Missing Transverse Momentum Reconstruction . 66 5.8 Acknowledgements . 66 Chapter 6 t¯tH (H gg) Analysis . 68 6.1 Introduction! . 68 6.1.1 The Top Quark Yukawa Coupling . 68 6.1.2 Landscape of t¯tH Measurements . 70 6.2 Overview of Analysis Strategy . 70 6.2.1 The H gg Decay Mode . 70 6.2.2 Estimates! of Expected Sensitvity . 72 6.3 Preselection . 73 6.4 Background Description . 73 6.4.1 Challenges of MC Description . 74 6.4.2 Data-Driven Description of Multi-jet and g + jets Backgrounds . 74 6.5 Machine Learning Algorithms . 83 6.5.1 High-Level Features . 83 6.5.2 Deep Neural Networks for gg + jets and t¯t + gg Backgrounds . 85 6.5.3 Top Tagger BDT . 91 6.5.4 BDT-bkg . 94 6.6 Event Categorization . 97 6.7 Signal & Background Models . 98 6.7.1 Signal Models . 98 6.7.2 Background Models . 99 vii 6.8 Systematic Uncertainties . 100 6.8.1 Theoretical Uncertainties . 102 6.8.2 Experimental Uncertainties . 103 6.8.3 Impact of Systematic Uncertainties . 106 6.9 Results . 106 6.9.1 Statistical Analysis . 106 6.9.2 Cross Section, Signal Strength, & Significance . 110 6.9.3 CP Measurement . 112 6.10 Acknowledgements . 113 Chapter 7 Conclusion . 116 Appendix A Plots of input features to BDT-bkg . 118 Appendix B Observed Diphoton Mass Distributions . 134 Bibliography . 137 viii LIST OF FIGURES Figure 3.1: Parton distribution functions for the proton, shown for Q2 = 10 GeV (left) and Q2 = 104 GeV (right), as calculated by the MSTW group. The width of each band indicates the 68% C.L. Taken from [102]. 26 Figure 3.2: Cross sections for typical processes of interest in pp collision experiments, shown as a function of the center-of-mass energy, ps. Taken from [20]. 27 2 Figure 3.3: The strong coupling constant as of QCD as a function of Q . Different colored lines correspond to various renormalization schemes. Taken from [62]. 28 Figure 3.4: Schematic of a hadron-hadron collision. Taken from [90]. 30 Figure 4.1: Mean number of interactions per bunch crossing recorded by the CMS detector during Run 2 of the LHC. Taken from [51]. 34 Figure 4.2: Total luminosity delivered by the LHC (blue) and total luminosity recorded by the CMS detector (yellow) during Run 2 of the LHC. Taken from [51]. 35 Figure 4.3: Schematic of the various components of the CMS detector. Taken from [33]. 36 Figure 4.4: Depiction of a transverse slice of the CMS detector, along with trajectories of particles of different types. Taken from [42]. 39 Figure 4.5: Comparison of tracker performance before and after the upgrade to the pixel detector, performed in between the 2016 and 2017 data-taking periods. Taken from [14]. 40 Figure 4.6: Schematic of the CMS tracker from a cross-sectional viewpoint. TIB, TOB, TID, and TEC represent the tracker inner barrel, tracker outer barrel, tracker inner disk, and tracker endcap components, respectively. Taken from [33]. 41 Figure 4.7: The material budget for the CMS tracker shown for both the characteristic radiation lengths of electromagnetic interactions (left) and the characteristic nuclear interaction lengths of hadronic interactions (right), with the contributions of each of the tracker subcomponents shown individually. Taken from [37]. 42 Figure 4.8: Tracking efficiency as a function of pT for muons (left), charged pions (middle), and electrons (right), shown separately for the barrel (black), transition region (blue), and endcap (red). Taken from [37]. ..
Load more

Recommended publications
  • Arxiv:2012.15102V2 [Hep-Ph] 13 May 2021 T > Tc
    Confinement of Fermions in Tachyon Matter at Finite Temperature Adamu Issifu,1, ∗ Julio C.M. Rocha,1, y and Francisco A. Brito1, 2, z 1Departamento de F´ısica, Universidade Federal da Para´ıba, Caixa Postal 5008, 58051-970 Jo~aoPessoa, Para´ıba, Brazil 2Departamento de F´ısica, Universidade Federal de Campina Grande Caixa Postal 10071, 58429-900 Campina Grande, Para´ıba, Brazil We study a phenomenological model that mimics the characteristics of QCD theory at finite temperature. The model involves fermions coupled with a modified Abelian gauge field in a tachyon matter. It reproduces some important QCD features such as, confinement, deconfinement, chiral symmetry and quark-gluon-plasma (QGP) phase transitions. The study may shed light on both light and heavy quark potentials and their string tensions. Flux-tube and Cornell potentials are developed depending on the regime under consideration. Other confining properties such as scalar glueball mass, gluon mass, glueball-meson mixing states, gluon and chiral condensates are exploited as well. The study is focused on two possible regimes, the ultraviolet (UV) and the infrared (IR) regimes. I. INTRODUCTION Confinement of heavy quark states QQ¯ is an important subject in both theoretical and experimental study of high temperature QCD matter and quark-gluon-plasma phase (QGP) [1]. The production of heavy quarkonia such as the fundamental state ofcc ¯ in the Relativistic Heavy Iron Collider (RHIC) [2] and the Large Hadron Collider (LHC) [3] provides basics for the study of QGP. Lattice QCD simulations of quarkonium at finite temperature indicates that J= may persists even at T = 1:5Tc [4] i.e.
    [Show full text]
  • Supersymmetric and Conformal Features of Hadron Physics
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 16 October 2018 doi:10.20944/preprints201810.0364.v1 Peer-reviewed version available at Universe 2018, 4, 120; doi:10.3390/universe4110120 Supersymmetric and Conformal Features of Hadron Physics Stanley J. Brodsky1;a 1SLAC National Accelerator Center, Stanford University Stanford, California Abstract. The QCD Lagrangian is based on quark and gluonic fields – not squarks nor gluinos. However, one can show that its hadronic eigensolutions conform to a repre- sentation of superconformal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spec- troscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The predictions from light-front holography and superconformal algebra can also be extended to mesons, baryons, and tetraquarks with strange, charm and bottom quarks. The pion qq¯ eigenstate has zero mass for mq = 0: A key tool is the remarkable observation of de Alfaro, Fubini, and Furlan (dAFF) which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale κ appears which determines universal Regge slopes, hadron masses in the absence of the Higgs coupling. One also 2 −Q2=4κ2 predicts the form of the nonperturbative QCD running coupling: αs(Q ) / e , in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions.
    [Show full text]
  • Arxiv:1910.11245V1 [Hep-Ph] 24 Oct 2019 Inclusion of a Magnetic field Can Affect This Result Since the Magnetic field Contribute to the Charge Screening
    Magnetic Field Effect in the Fine-Structure Constant and Electron Dynamical Mass E. J. Ferrer1 and A. Sanchez2 1Dept. of Physics and Astronomy, Univ. of Texas Rio Grande Valley, 1201 West University Dr., Edinburg, TX 78539 and CUNY-Graduate Center, New York 10314, USA 2Facultad de Ciencias, Universidad Nacional Aut´onomade M´exico, Apartado Postal 50-542, Ciudad de M´exico 04510, Mexico. We investigate the effect of an applied constant and uniform magnetic field in the fine-structure constant of massive and massless QED. In massive QED, it is shown that a strong magnetic field removes the so called Landau pole and that the fine-structure constant becomes anisotropic having different values along and transverse to the field direction. Contrary to other results in the literature, we find that the anisotropic fine-structure constant always decreases with the field. We also study the effect of the running of the coupling constant with the magnetic field on the electron mass. We find that in both cases of massive and massless QED, the electron dynamical mass always decreases with the magnetic field, what can be interpreted as an inverse magnetic catalysis effect. PACS numbers: 11.30.Rd, 12.20.-m, 03.75.Hh, 03.70.+k I. INTRODUCTION The effect of magnetic fields on the different properties of quantum particles has always attracted great interest [1]. At present, it has been reinforced by the fact that there is the capability to generate very strong magnetic fields in non-central heavy ion collisions, and because of the discovery of strongly magnetized compact stars, which have been named magnetars.
    [Show full text]
  • Thermodynamics of Generalizations of Quantum Chromodynamics
    Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics by Daniel C. Hackett B.A., University of Virginia, 2012 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics 2019 This thesis entitled: Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics written by Daniel C. Hackett has been approved for the Department of Physics Prof. Thomas DeGrand Prof. Ethan Neil Prof. Anna Hasenfratz Prof. Paul Romatschke Prof. Markus Pflaum Date The final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. iii Hackett, Daniel C. (Ph.D., Physics) Fantastic Gauge Theories and Where to Find Them: Thermodynamics of Generalizations of Quantum Chromodynamics Thesis directed by Prof. Thomas DeGrand Over the past few decades, lattice gauge theory has been successfully employed to study the finite-temperature phase structure of quantum chromodynamics (QCD), the theory of the strong force. While this endeavor is well-established, QCD is only one strongly-coupled quantum field theory in a larger family of similar theories. Using the lattice toolkit originally invented to investigate QCD, we have begun exploring the phase structures of these cousins of QCD. This thesis focuses on generalizations of QCD with multiple different species of fermions charged under distinct representations of the gauge group. I present the results of the first-ever lattice study of the thermodynamics of one such theory, as well as an analytic calculation which predicts the order of the phase transition for all such theories.
    [Show full text]
  • Exploring the Fundamental Properties of Matter with an Electron-Ion Collider
    Exploring the fundamental properties of matter with an Electron-Ion Collider Jianwei Qiu Theory Center, Jefferson Lab Acknowledgement: Much of the physics presented here are based on the work of EIC White Paper Writing Committee put together by BNL and JLab managements, … Eternal Questions People have long asked Where did we come from? The Big Bang theory? What is the world made of? Basic building blocks? What holds it together? Fundamental forces? Where are we going to? The future? Where did we come from? Can we go back in time or recreate the condition of early universe? Going back in time? Expansion of the universe Little Bang in the Laboratory Create a matter (QGP) with similar temperature and energy density BNL - RHIC CERN - LHC Gold - Gold Lead - Lead Relativistic heavy-ion collisions – the little bang q A virtual Journey of Visible Matter: Lorentz Near Quark-gluon Seen contraction collision plasma Hadronization Freeze-out in the detector q Discoveries – Properties of QGP: ² A nearly perfect quantum fluid – NOT a gas! at 4 trillion degrees Celsius, Not, at 10-5 K like 6Li q Questions: ² How the observed particles were emerged (after collision)? Properties of ² Does the initial condition matter (before collision)? visible matter What the world is made of? Human is only a tiny part of the universe But, human is exploring the whole universe! What hold it together? q Science and technology: Particle & Nuclear Physics Nucleon: Proton, or Neutron Nucleon – building block of all atomic matter q Our understanding of the nucleon evolves 1970s
    [Show full text]
  • Color Symmetry and Quark Confinement
    COLOR SYMMETRY AND QUARK CONFINEMENT Proceedings of the TWELFTH�ENCONTRE DE MORIOND. I 2�. Flaine - Haute-Savoie (France) March 6-March 18, 1977 VOL III COLOR SYMMETRY AND QUARK CONFINEMENT edited by TRAN THANH VAN SPONSORED BY INSTITUT NATIONAL DE PHYSIQUE NUCLEAIRE • ET DE PHYSIQUE DES PARTICULES • COMMISSARIAT A L'ENERGIE ATOMIQUE 3 The " Color Symmetry and Quark Confinement ,, Session was organ ized by G. KANE and TRAN THANH VAN J. With the active collaboration of M. CHANOWITZ ...... ___, \. (/ Permanent SecrCtariat . Rencontre de Moriond Laboratoire de Physique Theoriquc B<."ttiment Universite de Paris-Sud 211 - ORSA Y (France) 91405 Tel. 941-73-72 - 941-73-66 4 FOREWORD The Xllth Rencontre de Moriond has devoted a two-day session to the problem of Color Symmetry and Quark Confinement. The talks given at that session are collected in this book with an added pedagogical introduction. It is hoped that this book will be useful to learn about color and how it can be tested experimentally. The review papers summarize the current situation at April-May 1977. I wish to thank all the contributors for the ir efforts in making the ir papers as pedagogical as possible. TRAN THANH VAN J. 5 CONTENTS G. KANE Pedagogi.cal introduction to color calculations 9 CHANOWITZ Color and experiments M. 25 O.W. GREENBERG Unbound color 51 J.D. JACK SON Hadronic wid ths in charmonium 75 J. KRIPFGANZ Parton mode l structure from a confining theory 89 C. �IGG Dilepton production in hadron-hadron collisions and .the "factor of three" from color 93 M.
    [Show full text]
  • The Confinement Problem in Lattice Gauge Theory
    The Confinement Problem in Lattice Gauge Theory J. Greensite 1,2 1Physics and Astronomy Department San Francisco State University San Francisco, CA 94132 USA 2Theory Group, Lawrence Berkeley National Laboratory Berkeley, CA 94720 USA February 1, 2008 Abstract I review investigations of the quark confinement mechanism that have been carried out in the framework of SU(N) lattice gauge theory. The special role of ZN center symmetry is emphasized. 1 Introduction When the quark model of hadrons was first introduced by Gell-Mann and Zweig in 1964, an obvious question was “where are the quarks?”. At the time, one could respond that the arXiv:hep-lat/0301023v2 5 Mar 2003 quark model was simply a useful scheme for classifying hadrons, and the notion of quarks as actual particles need not be taken seriously. But the absence of isolated quark states became a much more urgent issue with the successes of the quark-parton model, and the introduction, in 1972, of quantum chromodynamics as a fundamental theory of hadronic physics [1]. It was then necessary to suppose that, somehow or other, the dynamics of the gluon sector of QCD contrives to eliminate free quark states from the spectrum. Today almost no one seriously doubts that quantum chromodynamics confines quarks. Following many theoretical suggestions in the late 1970’s about how quark confinement might come about, it was finally the computer simulations of QCD, initiated by Creutz [2] in 1980, that persuaded most skeptics. Quark confinement is now an old and familiar idea, routinely incorporated into the standard model and all its proposed extensions, and the focus of particle phenomenology shifted long ago to other issues.
    [Show full text]
  • Pos(LC2019)030
    Color Confinement and Supersymmetric Properties of Hadron Physics from Light-Front Holography Stanley J. Brodsky∗y PoS(LC2019)030 Stanford Linear Accelerator Center, Stanford University, Stanford, CA, 94309 E-mail: [email protected] I review applications of superconformal algebra, light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense – the QCD Lagrangian is based on quark and gluonic fields – not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconfor- mal algebra, reflecting the underlying conformal symmetry of chiral QCD. The eigensolutions of superconformal algebra provide a unified Regge spectroscopy of meson, baryon, and tetraquarks of the same parity and twist as equal-mass members of the same 4-plet representation with a universal Regge slope. The pion qq¯ eigenstate is composite but yet has zero mass for mq = 0: Light-Front Holography also predicts the form of the nonperturbative QCD running coupling: 2 2 2 as(Q ) ∝ exp Q =4k , in agreement with the effective charge determined from measurements − of the Bjorken sum rule. One also obtains viable predictions for tests of hadron dynamics such as spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combined approach of light-front holography and su- perconformal algebra also provides insight into the origin of the QCD mass scale and color con- finement. A key tool is the dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action.
    [Show full text]
  • Luca Lista Statistical Methods for Data Analysis in Particle Physics Lecture Notes in Physics
    Lecture Notes in Physics 909 Luca Lista Statistical Methods for Data Analysis in Particle Physics Lecture Notes in Physics Volume 909 Founding Editors W. Beiglböck J. Ehlers K. Hepp H. Weidenmüller Editorial Board M. Bartelmann, Heidelberg, Germany B.-G. Englert, Singapore, Singapore P. Hänggi, Augsburg, Germany M. Hjorth-Jensen, Oslo, Norway R.A.L. Jones, Sheffield, UK M. Lewenstein, Barcelona, Spain H. von Löhneysen, Karlsruhe, Germany J.-M. Raimond, Paris, France A. Rubio, Donostia, San Sebastian, Spain S. Theisen, Potsdam, Germany D. Vollhardt, Augsburg, Germany J.D. Wells, Ann Arbor, USA G.P. Zank, Huntsville, USA The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new devel- opments in physics research and teaching-quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic for- mats, the electronic archive being available at springerlink.com.
    [Show full text]
  • Arxiv:1312.5000V2 [Hep-Ex] 30 Dec 2013
    1 Mass distributions marginalized over per-event errors a b 2 D. Mart´ınezSantos , F. Dupertuis a 3 NIKHEF and VU University Amsterdam, Amsterdam, The Netherlands b 4 Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 5 Abstract 6 We present generalizations of the Crystal Ball function to describe mass peaks 7 in which the per-event mass resolution is unknown and marginalized over. The 8 presented probability density functions are tested using a series of toy MC sam- 9 ples generated with Pythia and smeared with different amounts of multiple 10 scattering and for different detector resolutions. 11 Keywords: statistics, invariant mass peaks 12 1. Introduction A very common probability density function (p:d:f:) used to fit the mass peak of a resonance in experimental particle physics is the so-called Crystal Ball (CB) function [1{3]: 8 2 − 1 ( m−µ ) m−µ <>e 2 σ , if > −a p(m) / σ (1) > m−µ n :A B − σ , otherwise 13 where m is the free variable (the measured mass), µ is the most probable value 14 (the resonance mass), σ the resolution, a is called the transition point and n the arXiv:1312.5000v2 [hep-ex] 30 Dec 2013 15 power-law exponent. A and B are calculated by imposing the continuity of the 16 function and its derivative at the transition point a. This function consists of a 17 Gaussian core, that models the detector resolution, with a tail on the left-hand 18 side that parametrizes the effect of photon radiation by the final state particles 19 in the decay.
    [Show full text]
  • Quantum Mechanics Quantum Field Theory(QFT)
    Quantum Mechanics_quantum field theory(QFT) In theoretical physics, quantum field theory(QFT) is a theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles incondensed matter physics. A QFT treats particles as excited states of an underlying physical field, so these are called field quanta. For example, Quantum electrodynamics (QED) has one electron field and one photon field;Quantum chromodynamics (QCD) has one field for each type of quark; and, in condensed matter, there is an atomic displacement field that gives rise to phonon particles. Edward Witten describes QFT as "by far" the most difficult theory in modern physics.[1] In QFT, quantum mechanical interactions between particles are described by interaction terms between the corresponding underlying fields. QFT interaction terms are similar in spirit to those between charges with electric and magnetic fields in Maxwell's equations. However, unlike the classical fields of Maxwell's theory, fields in QFT generally exist in quantum superpositions of states and are subject to the laws of quantum mechanics. Quantum mechanical systems have a fixed number of particles, with each particle having a finite number of degrees of freedom. In contrast, the excited states of a QFT can represent any number of particles. This makes quantum field theories especially useful for describing systems where the particle count/number may change over time, a crucial feature of relativistic dynamics. Because the fields are continuous quantities over space, there exist excited states with arbitrarily large numbers of particles in them, providing QFT systems with an effectively infinite number of degrees of freedom.
    [Show full text]
  • Crystal Ball® 7.2.2 User Manual T Corporationand Other U.S
    Crystal Ball® 7.2.2 User Manual This manual, and the software described in it, are furnished under license and may only be used or copied in accordance with the terms of the license agreement. Information in this document is provided for informational purposes only, is subject to change without notice, and does not represent a commitment as to merchantability or fitness for a particular purpose by Decisioneering, Inc. No part of this manual may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, for any purpose without the express written permission of Decisioneering, Inc. Written, designed, and published in the United States of America. To purchase additional copies of this document, contact the Technical Services or Sales Department at the address below: Decisioneering, Inc. 1515 Arapahoe St., Suite 1311 Denver, Colorado, USA 80202 Phone: +1 303-534-1515 Toll-free sales: 1-800-289-2550 Fax: 1-303-534-4818 © 1988-2006, Decisioneering, Inc. Decisioneering® is a registered trademark of Decisioneering, Inc. Crystal Ball® is a registered trademark of Decisioneering, Inc. CB Predictor™ is a trademark of Decisioneering, Inc. OptQuest® is a registered trademark of Optimization Technologies, Inc. Microsoft® is a registered trademark of Microsoft Corporation in the U.S. and other countries. FLEXlm™ is a trademark of Macrovision Corporation. Chart FX® is a registered trademark of Software FX, Inc. is a registered trademark of Frontline Systems, Inc. Other product names mentioned herein may be trademarks and/or registered trademarks of the respective holders. MAN-CBUM 070202-2 6/15/06 Contents Welcome to Crystal Ball® Who should use this program ...................................................................1 What you will need ....................................................................................1 About the Crystal Ball documentation set ................................................2 Conventions used in this manual ...................................................................
    [Show full text]