Elementary Particles and Their Interactions

Transcription

1 Elementary Particles and Their Interactions

2 Springer-Verlag Berlin Heidelberg GmbH

3 Quang Ho-Kim Xuan-Yem Pham Elementary Particles and Their Interactions Concepts and Phenomena With 116 Figures, 36 Tables, Numerous Examples, and 102 Problems with Selected Solutions, Springer

4 Professor Quang Ho-Kim Physics Department Universite Laval Ste-Foy, QC Canada GIK 7P 4 qhokim@phy.ulaval.ca Professor Xuan-Yem Pham Directeur de recherche au CNRS Universites Paris VI et VII Laboratoire de Physique Theorique et Hautes Energies Tour 16, ler Etage, 4 Place Jussieu F Paris Cedex 05, France pham@lpthe.jussieu.fr ISBN DOI / ISBN (ebook) Library of Congress Cataloging-in-Publication Data Ho-Kim, Q. (Quang), Elementary particles and their interactions: concepts and phenomena / Quang Ho-Kim, Xuan-Yem Pham. p. cm. Includes bibliographical references and index. ISBN (alk. paper) 1. Particles (Nuclear physics) 2.. Nuclear reactions. I. Pham, Xuân-yem. II. Tide. QC H '2.-dc CIP This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifica1ly the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 11)98 Softcover reprint of the hardcover ISt edition 11)98 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by Fa. Steingraeber, Heidelberg Cover design: design & production GmbH, Heidelberg SPIN / o - Printed on acid-free paper

5 To our families

6 Preface The last few decades have seen major advances in the physics of elementary particles. New generations of particle accelerators and detectors have come into operation, and have successfully contributed to improving the quantity and quality of data on diverse interaction processes and to the discoveries of whole new families of particles. At the same time, important new ideas have emerged in quantum field theory, culminating in the developments of theories for the weak and strong interactions to complement quantum electrodynamics, the theory of the electromagnetic force. The simplest of the new theories that are at the same time mathematically consistent and physically successful constitute what is known as the standard model of the fundamental interactions. This book is an attempt to present these remarkable advances at an elementary level, making them accessible to students familiar with quantum mechanics, special relativity, and classical electrodynamics. The main content of the book is roughly divided into two parts; one on theories to lay the foundation and the other on further developments of concepts and descriptions of phenomena to prepare the student for more advanced work. After a brief overview of the subject and a presentation of some basic ideas, two chapters which deal mostly with relativistic one-body wave equations, quantization of fields, and Lorentz invariance follow. In the spirit of the practical approach taken in this book, a heuristic derivation of the Feynman rules is given in the fourth chapter, where the student is shown how to calculate cross-sections and decay rates at the lowest order. The following chapter contains a discussion on discrete symmetries and the concept of symmetry breaking. Isospin is introduced next as the simplest example of internal symmetries in order to ease the reader into the notion of unitary groups in general and of SU(3) in particular, which is discussed next together with the recent discoveries of new particles. The next two chapters present the standard model of the fundamental interactions. We make contact with experiments in subsequent chapters with detailed studies of some fundamental electroweak processes, such as the deep inelastic leptonnucleon scattering, the CP violation in the neutral K mesons, the neutrino oscillations and the related problem of the solar neutrino deficit, and finally, the T lepton decay, which touch upon many aspects of weak interactions. The very high precision of the data that is now attained in some of these processes requires a careful examination of higher-order effects. This leads to a detailed

7 VIII Preface study of one-loop QCD corrections to weak intera~tions. The next chapter demonstrates the remarkable property of asymptotic freedom of quantum chromodynamics and introduces the powerful concept of the renormalization group which plays a central role in many phenomena. The heavy flavors of quarks, which pose new questions on several aspects of interactions and could open windows on the 'new' physics, form the subject of a separate chapter. We close with a review of the present status of the standard model and, briefly, of its extensions. Selected solutions to problems are given. Finally, important formulas are collected in an Appendix for convenient reference. In writing this book we have constantly borne in mind the beginning student learning the subject for the first time. For this reason we have avoided a presentation of the formalism based either on canonical quantization or path integral methods. We have adopted instead a decidedly more practical approach based on perturbative field theory. Many particle phenomena may thus be described in detail early in the book, and the student, in turn, can carry out actual calculations. The importance of the physical point of view is further emphasized by the many examples found throughout the book. The first part of the book gives the student the basic (and some extra) material needed to follow the arguments leading to the standard model and to understand the physics that flows from it. The second part is an attempt to reflect recent advances in experimental particle physics (such as neutrino oscillations, B meson physics, and precision tests of electroweak processes). These topics are selected mainly on the strength of their lasting intrinsic value or because they bring out some novel physics. Whatever the motivations, we introduce all topics at an elementary level, work out the calculations in detail, and carry the development to the point where the reader can start deepening his or her own understanding through a meaningful independent study. We owe thanks to our teachers, students, and colleagues for the physics they have taught us. Many have helped us in our present project. We are in particular grateful to Pierre Fayet, Michel Gourdin, Chi-Sing Lam, Serguey Petcov, and Pham Tri-Nang for reading parts of the book and for making judicious comments and suggestions. Thanks are also due to Dr. Hans K6lsch, our editor at Springer for a pleasant and fruitful collaboration. One of us (QHK) acknowledges with gratitude the financial support given by the Natural Sciences and Engineering Research Council of Canada and the gracious hospitality extended to him by the Laboratoire de Physique Theorique et Hautes Energies (Universite Paris VI et Universite Paris VII) and the Laboratoire de Physique Theorique et Modelisation (Universite Cergy-Pontoise). Finally, we are greatly indebted to our families, to whom this work is dedicated, for their support and encouragement throughout the writing of this book. Paris 1998 Q. Ho-Kim & X- Y. Pham

8 Contents 1 Particles and Interactions: An Overview A Preview Particles Leptons Quarks Hadrons Interactions Symmetries Physical Units Problems Suggestions for Further Reading 16 2 Boson Fields Lorentz Symmetry Lorentz 'Transformations Tensor Algebra Tensor Fields Scalar Fields Space-Time 'Translation of a Scalar Field Lorentz 'Transformation of a Scalar Field Vector Fields The Klein-Gordon Equation Free-Particle Solutions Particle Probability Second Quantization Operator Algebra Physical Significance of the Fock Operators Quantized Vector Fields Massive Vector Fields The Maxwell Equations Quantization of the Electromagnetic Field Field Energy and Momentum The Action The Euler-Lagrange Equation Conserved Current

9 X Contents Problems.... Suggestions for Further Reading Fermion Fields The Dirac Equation Lorentz Symmetry Covariance of the Dirac Equation Spin of the Dirac Field : Bilinear Covariants Free-Particle Solutions Normalized Spinors Completeness Relations Helicities The Lagrangian for a Free Dirac Particle Quantization of the Dirac Field Spins and Statistics Dirac Field Observables Fock Space Zero-Mass Fermions Problems Suggestions for Further Reading 88 4 Collisions and Decays Interaction Representation The Three Pictures Time Evolution in the Interaction Picture The S-matrix Cross-Sections and Decay Rates General Formulas Two-Body Reaction to Two-Body Final States Decay Rates Interaction Models Decay Modes of Scalar Particles Neutral Decay Mode Charged Decay Mode Pion Scattering The Scalar Boson Propagator Scattering Processes Summary and Generalization

10 Contents XI 4.6 Electron-Proton Scattering....'... " The Electromagnetic Interaction Electron-Proton Scattering Cross-Section Electron-Positron Annihilation Compton Scattering Problems Suggestions for Further Reading Discrete Symmetries Parity Parity in Quantum Mechanics Parity in Field Theories Parity and Interactions Time Inversion Time Inversion in Quantum Mechanics Time Inversion in Field Theories T and Interactions Charge Conjugation Additive Quantum Numbers Charge Conjugation in Field Theories Interactions The CPT Theorem Implications of CPT Invariance C, P, T, and CPT Problems Suggestions for Further Reading Hadrons and Isospin Charge Symmetry and Charge Independence Nucleon Field in Isospin Space Pion Field in Isospin Space G-Parity Nucleon and Pion Fields Other Unflavored Hadrons Isospin of Strange Particles Isospin Violations Electromagnetic Interactions Weak Interactions Problems Suggestions for Further Reading

11 XII Contents 7 Quarks and SU(;J) Symmetry Isospin: SU(2) Symmetry Hypercharge: SU(3) Symmetry The Fundamental Representation Higher-Dimensional Representations Physical Significance of F3 and Fa x 3* Equal Mesons x 3 x 3 Equal Baryons Mass Splitting of the Hadron Multiplets Baryons Mesons Including Spin: SU(6) Mesons Baryons Application: Magnetic Moments of Hadrons The Color of Quarks The New Particles J/'I/J and Charm The Tau Lepton From Bottom to Top Problems Suggestions for Further Reading Gauge Field Theories Symmetries and Interactions Abelian Gauge Invariance Non-Abelian Gauge Invariance Quantum Chromo dynamics Spontaneous Breaking of Global Symmetries The Basic Idea Breakdown of Discrete Symmetry Breakdown of Abelian Symmetry Breakdown of Non-Abelian Symmetry Spontaneous Breaking of Local Symmetries Abelian Symmetry Non-Abelian Symmetry Problems.' Suggestions for Further Reading The Standard Model of the Electroweak Interaction The Weak Interaction Before the Gauge Theories Gauge-Invariant Model of One-Lepton Family Global Symmetry Gauge Invariance

12 Contents XIII Spontaneous Symmetry Breaking Feynman Rules for One-Lepton Family Including u and d Quarks Multigeneration Model The GIM Mechanism Classification Scheme for Fermions Fermion Families and the CKM Matrix Summary and Extensions Problems Suggestions for Further Reading Electron-Nucleon Scattering Electromagnetic and Weak Form Factors Analyticity and Dispersion Relation Exclusive Reaction: Elastic Scattering Inclusive Reaction: Deep Inelastic Scattering Structure Functions Bjorken Scaling and the Feynman Quark Parton Problems Suggestions for Further Reading Neutral K Mesons and CP Violation The Two Neutral K Mesons Strangeness Oscillations Regeneration of Kg Calculation of!:j..m CP Violation General Formalism Model-Independent Analysis of KL ' The Superweak Scenario Calculations of E and E' in the Standard Model The Gluonic Penguin and IE'/EI Problems Suggestions for Further Reading The Neutrinos On the Neutrino Masses General Properties Dirac or Majorana Neutrino? Lepton Mixing Oscillations in the Vacuum Oscillations in Matter Index of Refraction, Effective Mass The MSW Effect

13 XIV Contents Adiabaticity Neutral Currents by Neutrino Scattering Neutral Currents, Why Not? :Neutrino-Electron Scattering Neutrino-Nucleon Elastic Scattering Neutrino-Nucleon Deep Inelastic Collision Deep Inelastic Cross-Section Quarks as Partons Problems Suggestions for Further Reading Muon and Tau Lepton Decays Weak Decays: Classification and Generalities Leptonic Modes Leptonic Branching Ratio Parity Violation. Energy Spectrum Angular Distribution. Decay Rate Semileptonic Decays The One-Pion Mode: r- -+ V T + 71" The 2n-Pion Mode and CVC The Method of Spectral Functions The Three-Pion Mode Spectral Functions of Quark Pairs 470 Problems Suggestions for Further Reading One-Loop QCD Corrections Vertex Function Quark Self-Energy Mass and Field Renormalization Renormalized Form Factor Ffen(q2) Important Consequence of Mass Renormalization 14.4 Virtual GIuon Contributions Real Gluon Contributions Infrared Divergence Three-Particle Phase Space Bremsstrahlung Rate 14.6 Final Result Problems.... Suggestions for Further Reading Asymptotic Freedom in QCD Running Coupling Constant Vacuum Polarization

14 Contents XV Dressed and Renormalized Photon Propagator Vertex Renormalization Renormalized Vacuum Polarization llren(q2) Physical Effects of ITren(q) The Renormalization Group The Callan-Symanzik Equation Calculation of the (3- and 'Y-Functions Running Coupling from the Renormalization Group Solution of the Renormalization Group Equation One-Loop Computation of the QCD (3-Function...., Quark Self-Energy Counterterm Zq Quark-Gluon Vertex Counterterm ZI Gluon Self-Energy Counterterm Zglu The Running QCD Coupling Ghosts The Faddeev-Popov Gauge-Fixing Method Ghosts and Unitarity. 541 Problems Suggestions for Further Reading Heavy Flavors QCD Renormalization of Weak Interactions Corrections to Single Currents Corrections to Product of Currents Renormalization Group Improvement The AI = 1/2 in Strangeness Hadronic Decays Heavy Flavor Symmetry Basic Physical Pictures Elements of Heavy Quark Effective Theory (HQET) Inclusive Decays General Formalism Inclusive Semileptonic Decay: B -+ e- + ve + Xc Inclusive Nonleptonic Decay: B -+ Hadrons Exclusive Decays Form Factors in Bi3 Decays Semileptonic Decay Rates Two-Body Hadronic Decays CP Violation in B Mesons Bo-if Mixing CP Asymmetries in Neutral B Meson Decays Problems Suggestions for F\lrther Reading

15 XVI Contents 17 Status and Perspectives of the Standard Model Production and Decay of the Higgs Boson Why Go Beyond the Standard Model? The Stl'!Jldard Model as an Effective Theory Problems with the Standard Model Renormalization Group Equation Analysis Supersymmetry and Technicolor. 611 Problems Suggestions for Further Reading Selected Solutions Appendix: Useful Formulas A.l Relativistic Quantum Mechanics A.2 Cross-Sections and Decay Rates A.3 Phase Space and Loop Integrals A.4 Feynman Rules A.5 Parameters of the Standard Model Index