Contemporary Physics Based on Lectures at the University of Maryland College Park Editor-in-ChieJ Edward F. Redish (University of Maryland, College Park)
Editorial Board (At the University of Maryland, College Park) Alex J. Dragt Richard A. F errell Oscar W. Greenberg Richard E. Prange Philip G. Roos Guarang Y odh Contemporary Physics
R.N. Mohapatra: Unification and Supersymmetry: The Frontiers of Quark-Lepton Physics R.E. Prange and S.M. Girvin (eds.): The Quantum Hall Effect Rabindra N. Mohapatra
Unification and Supersymmetry
The Frontiers of Quark-Lepton Physics
With 49 Illustrations
Springer Science+Business Media, LLC Rabindra N. Mohapatra Department of Physics and Astronomy University of Maryland College Park, MD 20742 U.S.A.
Editor in Chief Edward F. Redish Department of Physics and Astronomy University of Maryland College Park, MD 20742 U.S.A.
Library of Congress Cataloging in Publication Data Mohapatra, R. N. (Rabindra Nath) Uni/kation and supersymmetry. (Contemporary physics) Includes bibliographies and index. 1. Grand unified theories (Nuclear physics) 2. Supersymmetry. 3. Particles (Nuclear physics) I. Title. 11. Series: Contemporary physics (New York, N.Y.) QC794.6.G7M64 1986 530.1 86-1814
© 1986 by Springer Science+Business Media New York Originally published by Springer-Verlag New York Inc. in 1986 Softcover reprint of the hardcover 1st edition 1986 All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer Science+Business Media, LLC
The use of general descriptive names, trade names, trademarks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely byanyone.
Typeset by Asco Trade Typesetting Ltd., Hong Kong.
9 8 7 6 5 4 3 2 1 ISBN 978-1-4757-1930-7 ISBN 978-1-4757-1928-4 (eBook) DOI 10.1007/978-1-4757-1928-4 To Manju, Pramit and Sanjit Preface
The theoretical understanding of elementary particle interactions has under gone a revolutionary change during the past one and a half decades. The spontaneously broken gauge theories, which in the 1970s emerged as a prime candidate for the description of electro-weak (as weIl as strong) interactions, have been confirmed by the discovery of neutral weak currents as weIl as the w- and Z-bosons. We now have a field theory of electro-weak interactions at energy scales below 100 GeV-the Glashow-Weinberg-Salam theory. It is a renormalizable theory which enables us to do calculations without en countering unnecessary divergences. The burning question now is: Wh at lies ahead at the next level of unification? As we head into the era of supercolliders and ultrahigh energy machines to answer this question, many ap,pealing possi bilities exist: left-right symmetry, technicolor, compositeness, grand unifica ti on, supersymmetry, supergravity, Kaluza-Klein models, and most recently superstrings that even unify gravity along with other interactions. Experi ments will decide if any one or any combination of these is to be relevant in the description of physics at the higher energies. As an outcome of our con fidence in the possible scenerios for elementary particle physics, we have seen our understanding of the early uni verse improve significantly. Such questions as the origin of matter, the creation of galaxies, and the puzzle of the cosmic horizon are beginning to receive plausible answers in teqns of new ideas in particle physics. Although a final solution is far from being at hand, reason able theoretical frameworks for carrying out intelligent discussions have been constructed. Even such difficult questions as the "birth" and "death" of the universe have been discussed. This book, based on advanced graduate courses offered by me at CCNY (City College of New Y ork) and in Maryland, attempts to capture these exciting developments in a coherent chapter-by-chapter account, in the hope viii Preface
that the frontiers of our understanding (or lack of it) in this exciting field of science can be clearly defined for students as weIl as beginning researchers. The emphasis has been on physical, rather than technical and calculational, aspects although some necessary techniques have been included at various points. Extensive references are provided to original works, which the readers are urged to consult in order to become more proficient in the techniques. The prerequisites for this book are an advanced course in quantum field theory (such as a knowledge of Feynman diagrams, the renormalization pro gram, CaIlan~Symanzik equations, etc.), group theory (Lie groups at the level of the books by Gilmore or Georgi), basic particle theory such as the quark model, weak interaction and general symmetry principles (at the level of the books by Marshak, Riazuddin and Ryan or by Commins), and familiarity with spontaneously broken gauge theories (at the level of the books by J. C. Taylor or Chris Quigg). The book is divided into two parts: the first eight chapters deal with the introduction to gauge theories, and their applications to standard SU(2)L x U(l) x SU(3)c models and possible extensions involving left~right symmetry, technicolor, composite models, quarks and leptons, strong and weak CP-violation and grand unification. In the last eight chapters, we discuss global and local supersymmetry, its application to particle interac tions, and the possibilities beyond N = 1 supergravity. Interesting recent developments in the area of superstrings are only touched on but, unfor tunately, could not be discussed as extensively as they ought to be. I would like to acknowledge many graduate students at CCNY and in Maryland over the past seven years, as weIl as colleagues at both places who attended the lectures, and helped to sharpen the focus of presentation by their comments. I am grateful to many of my colleagues and collaborators for generously sharing with me their insight into physics. I wish to thank E. F. Redish for suggesting that I compile the lectures into book form, and C. S. Liu and the members of the editorial board of this lecture se ries for their support at many crucial stages in the production of this book. FinaIly, I wish to thank Mrs. Rachel Olexa for her careful and prompt typing of the manu script, and J. Carr for reading several chapters and suggesting language improvements. I wish to acknowledge the support ofthe U.S. National Science Foundation during the time this book was written.
College Park RABINDRA N. MOHAPATRA March, 1986 Contents
CHAPTER 1 Important Basic Concepts in Partic1e Physics ...... 1.1. Introduction...... 1 1.2. Symmetries and Currents ...... 3 1.3. Local Symmetries and Yang-Mills Fields...... 7 1.4. Quantum Chromodynamic Theory of Strong Interactions: An Application ofYang-Mills Theories...... 10 1.5. Hidden Symmetries ofWeak Interactions...... 13 References ...... 17
CHAPTER 2 Spontaneous Symmetry Breaking, Nambu-Goldstone Bosons, and the Riggs Mechanism...... 20 2.1. Symmetries and Their Realizations ...... 20 2.2. Nambu-Goldstone Bosons for an Arbitrary Nonabelian Group...... 23 2.3. Some Properties of Nambu-Goldstone Bosons...... 25 2.4. Phenomenology of Massless and Near-Massless Spin 0 Bosons ...... 27 2.5. . The Higgs-Kibble Mechanism in Gauge Theories ...... 29 2.6. Group Theory of the Higgs Phenomenon ...... 32 2.7. Renormalizability and Triangle Anomalies...... 33 References ...... 34
CHAPTER 3 The SU(2)L x U(l) Model...... 36 3.1. The SU(2)L x U(I) Model ofGlashow, Weinberg, and Salam ...... 36 3.2. Neutral Current Interactions ...... 40 3.3. Masses and Decay Properties of W- and Z-Bosons...... 45 3.4. Fermion Masses and Mixing ...... 50 x Contents
3.5. Higher Order Induced Flavor-Changing Neutral Current Effects . . . . . 52 3.6. The Higgs Bosons ...... 55 3.7. SU(2)L x U(I) Model with Two Higgs Doublets...... 58 3.8. Beyond the Standard Model...... 60 References ...... 63
CHAPTER 4 CP-Violation: Weak and Strong...... 65 4.1. CP-Violation in Weak Interactions ...... 65 4.2. CP-Violation in Gauge Models: Generalities ...... 68 4.3. The Kobayashi-Maskawa Model...... 70 4.4. Left-Right Symmetric Models ofCP-Violation...... 74 4.5. The Higgs Exchange Models ...... 81 4.6. Strong CP-Violation and the 8-Problem...... 83 4.7. Other Solutions to the Strong CP-Problem ...... 87 4.8. Summary...... 89 References ...... 90
CHAPTER 5 Grand Unifieation and the SU(5) Model...... 92 5.1. The Hypothesis of Grand Unification ...... 92 5.2. SU(N) Grand Uniiication ...... 93 5.3. Sin 2 8w in Grand Unified Theories (GUT) ...... 94 5.4. SU(5)...... 94 5.5. Grand Unification Mass Scale and Sin2 8w at Low Energies ...... 100 5.6. Detailed Predictions ofthe SU(5) Model for Proton Decay and Uncertainties in the Predictions ...... 103 5.7. Some Other Aspects ofthe SU(5) Model...... 109 References ...... 114
CHAPTER 6 Left-Right Symmetrie Models ofWeak Interaetions...... 116 6.1. Why Left-Right Symmetry? ...... 116 6.2. The Model, Symmetry Breaking, and Gauge Boson Masses...... 118 6.3. Limits on mw• from Charged Current Weak Interactions ...... 122 6.4. Properties of Neutrinos and Lepton Number Violating Processes. . . . . 128 6.5. Baryon Number Nonconservation and Higher Unification ...... 139 6.6. Sin 2 8w and the Scale of Partial Unification...... 145 6.7. Conclusions...... 147 References ...... 147
CHAPTER 7 S0(10) Grand Unifieation ...... 151 7.1. Introduction...... 151 7.2. SO(2N) in an SU(N) Basis ...... 152 7.3. Fermion Masses and the "Charge Conjugation" Operator...... 154 7.4. Symmetry Breaking Patterns and Intermediate Mass Scales ...... 159 7.5. Decoupling Parity and SU(2)R Breaking Scales ...... 162 References ...... 164 Contents xi
CHAPTER 8 Technicolor and Compositeness...... 165 8.1. Why Compositeness? ...... 165 8.2. Technicolor and Electro-Weak Symmetry Breaking ...... 166 8.3. Techni-composite Pseudo-Goldstone Bosons...... 169 8.4. Fermion Masses...... 171 8.5. Composite Quarks and Leptons...... 173 8.6. Light Quarks and Leptons and 't Hooft Anomaly Matching ...... 176 8.7. Examples of't Hooft Anomaly Matching...... 178 8.8. Some Dynamical Constraints on Composite Models...... 181 8.9. Other Aspects of Composite Models...... 182 References ...... 185
CHAPTER 9 Global Supersymmetry ...... 187 9.1. Supersymmetry...... 187 9.2. A Supersymmetric Field Theory...... 188 9.3. Two-Component Notation...... 191 9.4. Superfields...... 193 9.5. Vector and Chiral Superfields...... 196 References...... 201
CHAPTER 10 Field Theories withGlobal Supersymmetry ...... 202 10.1. Supersymmetry Action...... 202 10.2. Supersymmetric Gauge Invariant Lagrangian ...... 206 10.3. Feynman Rules for Supersymmetric Theories...... 207 10.4. Allowed Soft Breaking Terms...... 212 References ...... 213
CHAPTER 11 Broken Supersymmetry and Application to Particle Physics...... 214 11.1. Spontaneous Breaking of Supersymmetry...... 214 11.2. Supersymmetric Analog of the Goldberger-Treiman Relation...... 216 11.3. D-Type Breaking of Supersymmetry ...... 217 11.4. O'Raifeartaigh Mechanism or F-Type Breaking of Supersymmetry . .. 219 11.5. A Mass Formula for Supersymmetric Theories and the Need for Soft Breaking ...... 221 References ...... 223
CHAPTER 12 Phenomenology of Supersymmetric Models...... 224 12.1. Supersymmetric Extension ofthe Standard Model...... 224 12.2. Constraints on the Masses of Superparticles...... 231 12.3. Other EtTects of Superparticles ...... 240 References ...... 243 xii Contents
CHAPTER 13 Supersymmetrie Grand Unification...... 246 13.1. The Supersymmetrie SU(5)...... 246 13.2. Proton Decay in the Supersymmetry SU(5) Model...... 249 13.3. Inverse Hierarchy Alternative...... 251 References ...... 253
CHAPTER 14 Local Supersymmetry (N = 1)...... 255 14.1. Connection Between Local Supersymmetry and Gravity ...... 255 14.2. Rarita-Schwinger Formulation ofthe Massless Spin 3/2 Field ...... 257 14.3. Elementary General Relativity ...... 258 14.4. N = 1 Supergravity Lagrangian...... 260 14.5. Group Theory ofGravity and Supergravity Theories...... 262 14.6. Local Conformal Symmetry and Gravity ...... 266 14.7. Conformal Supergravity and Matter Couplings...... 268 14.8. Matter Couplings and the Scalar Potential in Supergravity ...... 273 14.9. Super-Higgs Effect ...... 277 14.10. Different Formulations of Supergravity...... 278 References ...... 279
CHAPTER 15 Application of Supergravity (N = 1) to Particle Physics...... 280 15.1. Effective Lagrangian from Supergravity ...... 280 15.2. The Polonyi Model for Supersymmetry Breaking ...... 282 15.3. Electro-Weak Symmetry Breaking and Supergravity ...... 285 15.4. Grand Unification and N = 1 Supergravity ...... 288 References...... 291
CHAPTER 16 Beyond N = 1 Supergravity...... 292 16.1. Beyond Supergravity ...... 292 16.2. Extended Supersymmetries (N = 2) ...... 293 16.3. Supersymmetries with N > 2 ...... 295 16.4. Higher Dimensional Supergravity Theories ...... 297 16.5. d = 10 Super-Yang-Mills Theory ...... 300 References ...... 303
Index...... 307 " .... Where tireless striving stretches its arms towards perfection:
Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit, .... "
GITANJALI, RABINDRA NATH TAGORE