Table Of ContentSpringer
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Byron P. Roe
Particle Physics at the
New Millennium
With 134 Figures
Including Nine in Color
, Springer
Byron P. Roe
Randall Lab, Dept. of Physics
University of Michigan
Ann Arbor, MI 49109
On the cover: A historic photograph of a neutrino interaction involving the weak
neutral current vN --> vX, seen in the large heavy-liquid bubble chamber Gargamelle
at CERN. See also page 182.
Library of Congress Cataloging-in-Publication Data
Roe, Byron P.
Particle physics at the new millennium/Byron P. Roe.
p. cm.
Includes bibliographical references and index.
ISBN 0-387-94615-2 (hardcover)
I. Particles (Nuclear physics) 2. Nuclear physics. I. Title.
QC793.2.R64 1996
539.7'2-dc20 95-44879
Printed on acid-free paper.
© 1996 Springer-Verlag New York, Inc.
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987654321
ISBN 0-387-94615-2 Springer-Verlag New York Berlin Heidelberg SPIN 10518233
Preface
The twentieth century has been a golden age of physics. The discoveries
of relativity and of quantum mechanics have been two philosophical revo
lutions, each of which has fundamentally changed humanity's view of the
world. Layer after layer has been peeled off the structure of matter, from
molecules to atoms to nuclei to neutrons and protons to quarks. The weak
and strong interactions have been discovered, and the weak interactions
have been found to be deeply intertwined with electromagnetism. The
weak, electromagnetic, and strong interactions have been found to obey a
profound symmetry, which only becomes apparent at very high energies.
The Standard Model has been developed, which essentially explains all
present data. Particle physics at the edge of the millennium stands on a
very high plateau.
Nonetheless, the Standard Model is known to be only a way station;
it cannot be complete. Some physicists believe that the great quest is
almost over and that early in the millennium the fundamental laws of
nature will be completely laid bare. Others suspect that there will be still
more revolutions, comparable to the development of quantum mechanics
and relativity, ahead of us.
This book is intended to provide physics graduate students with an
overview of the field at this splendid time. For experimental physicists,
this overview may be sufficient. Theorists may desire to supplement this
volume with a more theoretically inclined text such as the one by T.D.
Lee. [l[ The text by R.N. Cahn and G. Goldhaber [2J I. S recommended as an
excellent reprint volume, containing copies of many historically important
publications in this field.
There are, basically, two ways of approaching the subject, which can
be called the "top down" and "bottom up" methods. In the "top down"
method, one starts from the basic postulates of present theory and derives
the experimental phenomena. In the treatment of electromagnetism, this
corresponds to starting with Maxwell's equations and deriving the many
electromagnetic phenomena we see.
For particle physics, the author strongly prefers the "bottom up" ap
proach. In this approach, the basic postulates are constructed piece by
piece, and at each postulate the evidence driving one to that postulate is
given.
The present Standard Model is very beautiful and it might be right, if
certainly not complete. However, as we have seen many times in physics, a
beautiful present day theory may not survive, and a new theory then will
be built using fragments from the old one. In this situation it is essential
for a working physicist to have a clear idea of what evidence pushes what
conclusions.
The author has tried to introduce mainly the formalism needed to test
hypotheses and look at the data. The student should have had a course in
quantum mechanics and should be familiar with special relativity and with
matrix manipulations. A knowledge of elementary group theory would be
useful, but is not required. No other special knowledge is assumed.
Feynman diagrams are introduced to be used, for much of the book, only
in a qualitative (but still powerful!) way. However, in Chapter 12, the set
of rules needed to write down a matrix element from Feynman diagrams
and a Lagrangian is described and illustrated with several examples. Dirac
notation and relativistic quantum methods are introduced. This book in no
way substitutes for a course in relativistic quantum field theory. However, a
minimum number of concepts are introduced where needed to allow contact
with data.
For a one semester course, chapters 12-17 and perhaps chapters 2-3
could be omitted, or left for individual reading. If desired, sections 6.5,
6.6, 7.3, 7.13, 8.4, 9.5, 10.2, 10.3, and 11.7-11.14 could also be left out
without affecting the rest of the course.
The author wishes to thank Gail Hanson who taught from a preliminary
version of the text and provided the author with extremely valuable feed
back, including corrections, additional material, and exercises. In addition,
she read the final manuscript for errors.
The author also wishes to thank M. Veltman, R. Akhoury, J. Wells,
and W. Loinaz for their very great help in elucidating the extent to which
the form of the Standard Model is fixed by the need to avoid bad high
energy behavior. He wishes to thank y'-P. Yao for his help on a number of
theoretical questions, for his critical reading of Chapter 11 and his valuable
suggestions for improvements.
The author also wishes to thank B. Demkowski and R.C. Ball for their
enormous help in preparing the text.
Contents
Preface. ..................................................... v
1. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. ......... .......... ...... ..... ..... ... .. .. 1
1.2 The Fundamental Particles and Forces, Fermions,
Bosons ........ ....................... ................. 1
1.2 a. The Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 b. The Interactions ................................ 3
1.2 c. Comments on Particles and Forces ............... 4
1.2 d. Some Common, Strongly Interacting Particles ... 5
1.3 Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Conventions and Units ................................ 9
1.5 Mandelstam Variables-s, t, U ........................... 10
1.6 Feynman Diagrams .................................... 11
1. 7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 16
2. Electromagnetic Interactions Used for Detection of
Charged Particles .......................................... 19
2.1 Rutherford Scattering ................................. 19
2.2 Multiple Scattering .................................... 25
2.3 Bremsstrahlung. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 27
2.4 Conversion of , -Rays to e+e- Pairs .................... 32
2.5 Direct Pair Production ................................ 33
2.6 Cherenkov Radiation .................................. 33
2.7 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35
3. Particle Accelerators and Detectors .... .................. 37
3.1 Particle Accelerators ....... .................. ......... 37
3.2 Present High-Energy Accelerators ................... ... 38
3.2 a. U.S. Accelerators ................................ 38
3.2 b. Accelerators in Western Europe ....... ... ....... 41
3.2 c. Accelerators Elsewhere .......................... 43
3.3 A Quick Survey of Some Major Types of Detectors ..... 44
3.3 a. Detectors Measuring Ionization ......... ......... 45
3.3 b. Other Types of Particle Detectors ............... 48
3.3 c. Calorimeters ........ ............. ..... .......... 51
3.4 Exercises. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 54
4. Invariance, Symmetries, and Conserved Quantities ..... 57
4.1 Preliminary Discussion ................................ 57
4.1 a. Invariance Formalisms .............. .. ........... 57
4.1 b. Conserved Electromagnetic Current ............. 58
4.2 Translation Invariance .......... .......... ... .. ........ 59
4.3 Rotation Invariance ................................... 60
4.4 Time Invariance ....................................... 61
4.5 Parity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.6 Time Reversal Invariance .............................. 63
4.6 a. Detailed Balance ......... ..... .. ................ 63
4.7 Illustration of Uses of Invariance Principles: Pions ..... 64
4.7 a. Pion Spin ....................................... 65
4.7 b. Pion Intrinsic Parity ............... ............. 67
4.8 Charge Conservation .................................. 70
4.9 Gauge Invariance ............ .......................... 71
4.10 Charge Conjugation ................................... 73
4.11 Illustration of Charge Conjugation:
Particle-Anti-Particle Pairs ........................... 75
4.12 P, C, and T. Who Is Invariant Under What? .......... 76
4.13 Isotopic Spin Invariance ............................... 77
Contents ix
4.13 a. The Two-Nucleon System and Multinucleons 78
4.14 Illustration of I-Spin Considerations: Pions and
the Pion Nucleon System .............................. 79
4.15 Further Use of I-Spin: Nucleon-Anti-Nucleon Pairs .... 82
4.16 Electromagnetism and Isotopic Spin ............ ....... 83
4.17 G-Parity .................... ........................ .. 84
4.18 Strangeness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
°
4.18 a. K and -K=-= <) Decays. ... .......................... 87
o
4.18 b.Ko-K Oscillations ............................. 89
4.18 c. C P Violation ................................... 90
4.19 Exercises .............................................. 93
5. Hadron-Hadron Scattering ................................ 97
5.1 Wave Optics Discussion of Hadron Scattering ...... .... 97
5.2 Breit-Wigner Resonance Formula ......... ......... .... 100
5.3 S-Matrix, Phase Space, and Dalitz Plots ............... 103
5.4 Exercises .......................................... .... 108
6. The Quark Model .......................................... 110
6.1 Introduction .. ......................................... 110
6.2 Baryons ............................................... 113
6.3 Mesons ........................................... ..... 120
6.4 Simple Model Relations ... .......... ................... 123
6.5 Mass Relations ..................................... ... 125
6.6 Baryon Magnetic Moments ............................ 128
6.7 Heavy Quarks ...................................... ... 129
6.8 Color .................................................. 138
6.9 Free Quarks ..................... ...................... 143
6.10 Exercises ............................. ................. 144
7. Weak Interactions ... .... ... ................................ 147
7.1 Brief Outline of Dirac Theory .................. ........ 147
7.1 a. Second Quantization ............................ 151
7.2 Nuclear ,a-Decay ....................................... 153
7.2 a. Parity Considerations ............... ............ 153
7.2 b. Nuclear ,a-Decay Summary ...................... 155
7.3 Kurie Plots; Neutrino Mass Limits ..................... 159
7.4 Zero Mass Neutrinos ................................... 161
7.5 Evaluating Matrix Elements; Traces ................... 163
7.6 7r -+ l + /J Decay .............................. ......... 165
7.7 Further Weak Interaction Results; Several Neutrinos;
Current-Current? ..................................... 168
7.8 Muon Decay ...... .. ................................... 171
7.9 Conserved Vector Current (CVC) ..................... . 174
7.10 Strangeness-Changing Weak Decays ............ ....... 178
7.10 a. Cabibbo Hypothesis ............................. 178
7.10 b.Non-Leptonic Weak Interactions ................. 179
7.11 Neutral Currents ...................................... 180
7.12 Generalized Cabibbo Theory:
The Cabibbo-Kobayashi-Maskawa Matrix 184
7.13 Penguin Diagrams; Applications to 6.1 = 1/2 and
to CP Violation ....................................... 187
7.14 Intermediate Bosons ................................... 188
7.15 Neutrino Oscillations .................................. 189
7.16 Exercises .............................................. 192
8. Elastic and Inelastic Scattering ........................... 196
8.1 Electron-Muon Elastic Scattering ...................... 197
8.2 Muon Pair Production in e+e- Annihilation ........... 199
8.3 Electron-Proton Elastic Scattering ..................... 200
8.4 Geometrical Interpretation of Form Factors ............ 203
8.5 Electron-Proton Inelastic Scattering ................... 204
8.6 Inelastic Charged Current v-p Scattering .............. 206
8.7 Form Factors in the Quark-Parton Picture ............. 208
8.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 225
