Table Of ContentTexts and Monographs in Physics
Series Editors: R. Balian W. Beiglb6ck H. Grosse E. H. Lieb
N. Reshetikhin H. Spohn W Thirring
Springer
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New York
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Texts and Monographs in Physics
Series Editors: R. Balian W. Beiglb6ck H. Grosse E. H. Lieb
N. Reshetikhin H. Spohn W. Thirring
From Microphysics to Macrophysics Supersymmetric Methods in Quantum
I + II Methods and Applications of and Statistical Physics By G. Junker
Statistical Physics By R. Balian CP Violation Without Strangeness
Variational Methods in Mathematical Electric Dipole Moments of Particles,
Physics A Unified Approach Atoms, and Molecules
By P. Blanchard and E. Brtining By I. B. Khriplovich and S. K. Lamoreaux
Quantum Mechanics: Inverse Schrodinger Scattering
Foundations and Applications in Three Dimensions
3rd enlarged edition By A. Bohm By R. G. Newton
The Early Universe Scattering Theory of Waves
Facts and Fiction 3rd corrected and Particles 2nd edition
and enlarged edition By G. Borner By R. G. Newton
Operator Algebras and Quantum Quantum Entropy and Its Use
Statistical Mechanics I + II 2nd edition By M. Ohya and D. Petz
By O. Bratteli and D. W. Robinson
Generalized Coherent States
Geometry of the Standard Model and Their Applications
of Elementary Particles By A. Perelomov
By A. Derdzinski
Essential Relativity Special, General,
Scattering Theory of Classical and Cosmological Revised 2nd edition
and Quantum N-Particle Systems By W. Rindler
By J. Derezinski and C. Gerard
Path Integral Approach
Effective Lagrangians to Quantum Physics An Introduction
for the Standard Model 2nd printing By G. Roepstorff
By A. Dobado, A. G6mez-Nicola,
Finite Quantum Electrodynamics
A. L. Maroto and J. R. Pelaez
The Causal Approach 2nd edition
Quantum By G. Scharf
The Quantum Theory of Particles, Fields,
From Electrostatics to Optics
and Cosmology By E. Elbaz
A Concise Electrodynamics Course
Quantum Relativity By G. Scharf
A Synthesis of the Ideas of Einstein
The Mechanics and Thennodynamics
and Heisenberg
of Continuous Media By M. Silhavy
By D. R. Finkelstein
Large Scale Dynamics of Interacting
Quantum Mechanics I + II
Particles By H. Spohn
By A. Galindo and P. Pascual
The Theory of Quark and Gluon
The Elements of Mechanics
Interactions 2nd completely revised
By G. Gallavotti
and enlarged edition By F. J. Yndurrun
Local Quantum Physics
Relativistic Quantum Mechanics and
Fields, Particles, Algebras
Introduction to Field Theory
2nd revised and enlarged edition
By F. J. Yndurrun
ByR. Haag
Iosif B. Khriplovich
Steve K. Lamoreaux
CP Violation
Without Strangeness
Electric Dipole Moments
of Particles, Atoms, and Molecules
With 36 Figures
Springer
Iosif B. Khriplovich Steve K. Lamoreaux
Budker Institute of Nuclear Physics University of California
630090 Novosibirsk, Russia Los Alamos National Laboratory
Los Alamos, NM 87545, USA
Editors
Roger Balian Nicolai Reshetikhin
CEA Department of Mathematics
Service de Physique Theorique de Saclay University of California
F-91191 Gif-sur-Yvette, France Berkeley, CA 94720-3840, USA
Wolf Beiglb6ck Herbert Spohn
Institut flir Angewandte Mathematik Theoretische Physik
Universitat Heidelberg Ludwig-Maximilians-Universitat Miinchen
1m Neuenheimer Feld 294 TheresienstraBe 37
0-69120 Heidelberg, Germany 0-80333 Miinchen, Germany
Harald Grosse Walter Thirring
Institut fiir Theoretische Physik Institut flir Theoretische Physik
Universitat Wien Universitat Wien
Boltzmanngasse 5 Boltzmanngasse 5
A-I 090 Wien, Austria A-I 090 Wien, Austria
Elliott H. Lieb
Jadwin Hall
Princeton University, P. O. Box 708
Princeton, NJ 08544-0708, USA
Library of Congress Cataloging-in-Publication Data. Khriplovich, 1. B. (Iosif Bentsionovich)
CP violation without strangeness: electric dipole moments of particles, atoms, and molecules IIosif
B. Khriplovich, Steve K. Lamoreaux. p. em. - (Texts and monographs in physics, ISSN 0172-5998)
Includes bibliographical references and index. 1. CP violation
(Nuclear physics) 2. Time reversal. 3. Dipole moments. I. Lamoreaux, Steve Keith. II. Title.
111. Series. QC793.3.V5K47 1997 539.7'25-dc21 97-28480
ISSN 0172-5998
ISBN-13: 978-3-642-64577-8 e-ISBN-13: 978-3-642-60838-4
DOl: 10.1007/978-3-642-60838-4
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© Springer-Verlag Berlin Heidelberg 1997
Softcover reprint of the hardcover 1s t edition 1997
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Preface
Electric dipole moments (EDMs) have interested physicists since 1950, when
it was first suggested that there was no experimental evidence that nuclear
forces are symmetric under parity (P) transformation. This question was
regarded as speculative because the existence of an EDM, in addition to P
violation, requires a violation of time-reversal (T) symmetry.
In 1964 it was discovered that the invariance under CP transformation,
which combines charge conjugation (C) with parity, is violated in K-meson
decays. This provided a new incentive for EDM searches. Since the combined
operations of CPT are expected to leave a system invariant, breakdown of CP
invariance should be accompanied by a violation of time-reversal symmetry.
Thus there is a reason to expect that EDMs should exist at some level. The
original neutron EDM experiments were later supplemented with checks of T
invariance in atoms and molecules. These investigations are pursued now by
many groups. Over the years, the upper limit on the neutron EDM has been
improved by seven orders of magnitude, and the upper limit on the electron
EDM obtained in atomic experiments is even more strict.
Even without the discovery of the effects sought, the neutron and atomic
experiments have ruled out most models of C P violation suggested to explain
the effects in K-meson decays; in fact, one could argue that the neutron
EDM measurement has ruled out more theoretical models than any other
experiment in the history of physics. As to the mechanism of C P violation
incorporated in the standard model of electroweak interactions, which is most
popular at present, the prediction for the neutron EDM is six orders of mag
nitude below the present experimental bound. The gap for the electron EDM
in this model is much larger.
But does this mean that the experiments discussed in this book are of
no serious interest for the elementary particle physics, that they are nothing
but mere exercises in precision spectroscopy? Just the opposite. It means
that these experiments now, at the present level of accuracy, are extremely
sensitive to possible new physics beyond the standard model, physics to which
the kaon decays are insensitive. These experiments have been described as
"the poor man's high-energy physics" [1], insofar as they are typically done by
relatively small collaborations (less than 10 participants), with a relatively
VI Preface
small budget. They certainly provide valuable information complementary to
the more traditional high-energy experiments.
It is essential that there are no fundamental restrictions to the accuracy
that can be obtained in a precision spectroscopy experiment, barring counting
statistics and systematic effects. Of course, at any given time, any specific
experiment runs into technical limitations, but over the last fifty years for
example, the limit on the neutron EDM has been reduced by nearly two
orders of magnitude per decade. It is interesting to note that, at each stage
of the progress, the technical difficulties were enormous and certainly the
maximum sensitivity, given the state of the art, was achieved. Nonetheless,
after each stage new ideas would arise, and experimentalists had the courage
and support to put those ideas into practice; taken together with the great
theoretical progress in regard to interpretation of the experiments, the study
of EDMs has been, and will remain, a fruitful and exciting subject.
We believe that this circumstance is by itself a good reason to write
a book on the subject. Besides, we hope that the wide-ranging collection
of physical problems presented here will be useful for advanced studies of
various branches of physics.
It is impossible to list here all those who generously shared with us their
knowledge and understanding of the subject. However, we cannot help men
tioning some persons whose collaboration has influenced so much the content
of this book: R.S. Conti, V.V. Flambaum, E.N. Fortson, R. Golub, B.R.
Heckel, V.M. Khatsymovsky, J.M. Pendlebury, M.E. Pospelov, N.F. Ramsey,
O.P. Sushkov, A.I. Vainshtein, A.S. Yelkhovsky, and A.R. Zhitnitsky. We owe
special thanks to D.P. DeMille for critical comments on the manuscript. To
our friends, those whose names are given here and those who we could not
mention, we owe our deep and sincere gratitude.
Novosibirsk, Russia I.B. Khriplovich
Los Alamos, New Mexico, USA S.K. Lamoreaux
May 1997
Contents
1. Introduction.............................................. 1
1.1 Overview of C P Violation Without Strangeness . . . . . . . . . . . . 1
1.2 The Neutron Electric Dipole Moment:
Early History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Molecular Electric Dipole Moments
and C P Violation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 T-Odd Effects Without CP Violation. . . . . . . . . . . . . . . . . . . . . 5
l.4.1 Can an Unstable Particle Have a Dipole Moment? . . . . 5
1.4.2 Spurious EDM Effect Due to Nuclear Anapole Moment 7
2. Kinematics of Discrete Symmetries . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 CPT Theorem: Intuitive Approach .. . . . . . . . . . . . . . . . . . . . . . 9
2.2 T-Even and T-Odd Electromagnetic Multipole Moments .... 11
2.3 General Structure of Four-Fermion Operators. . . . . . . . . . . . .. 15
3. General Features of EDM Experiments............ . . .. . .. 19
3.1 Interaction of an EDM with an Electric Field. . . . . . . . . . . . .. 19
3.1.1 Sensitivity Limit Due to the Uncertainty Principle. . .. 20
3.1.2 Ramsey's Method of Separated Oscillatory Fields. . . .. 23
3.1.3 Linewidth and Sensitivity
with Separated Oscillatory Fields. . . . . . . . . . . . . . . . . .. 25
3.2 Ground State Optical Pumping
and Detection of Atomic Polarization . . . . . . . . . . . . . . . . . . . .. 25
3.2.1 Atomic Spin Magnetometers.. .. . . . . . . . . . . . . . . . . . .. 27
3.3 Electric Fields and Coherence Times in Various Systems. . . .. 31
3.3.1 Electric Fields in Vacuum. . . . . . . . . . . . . . . . . . . . . . . .. 31
3.3.2 Electric Fields in Gases ..................... . . . . .. 33
3.3.3 Electric Fields in Liquids. . . . . . . . . . . . . . . . . . . . . . . . .. 33
3.3.4 Electric Fields in Solids. . . . . . . . . . . . . . . . . . . . . . . . . .. 33
3.3.5 Coherence Times for Various Systems. . . . . . . . . . . . . .. 34
3.4 Magnetic Field Control and Generation .............. . . . .. 35
3.4.1 Field Stability and Homogeneity Requirements. . . . . .. 35
3.4.2 Magnetic Shields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 36
3.4.3 Field Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 40
VIII Contents
3.5 Systematic Effects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 42
3.5.1 Leakage Current Effects. . . . . . . . . . . . . . . . . . . . . . . . . .. 43
3.5.2 Problems Related to Polarizability
and Electric Quadrupole Moments. . . . . . . . . . . . . . . . .. 44
3.5.3 The v x E Problem .............................. 45
4. The Search for the Neutron EDM ..... ............ .... . .. 53
4.1 Properties of the Neutron ............................... 53
4.2 Interaction of Neutrons with Matter. . . . . . . . . . . . . . . . . . . . .. 55
4.2.1 Neutron Polarization. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.2.2 Production and Moderation of Neutrons. . . . . . . . . . . .. 63
4.2.3 Transport of Cold Neutrons. . . . . . . . . . . . . . . . . . . . . . .. 64
4.3 Neutron Beam EDM Experiments . . . . . . . . . . . . . . . . . . . . . . .. 65
4.3.1 The Oak Ridge Experiment of 1950. . . . . . . . . . . . . . . .. 65
4.3.2 The Oak Ridge Experiment of 1967 . . . . . . . . . . . . . . . .. 68
4.3.3 The Crystal Scattering Experiment of 1967 . . . . . . . . .. 69
4.3.4 Pendellosung Fringes. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 73
4.3.5 Neutron Beam Experiments, 1968-1973 .. . . . . . . . . . .. 75
4.3.6 The Institut Laue-Langevin (ILL) Experiment of 1977 77
4.4 Ultracold Neutrons .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
4.4.1 Sources of Ultracold Neutrons. . . . . . . . . . . . . . . . . . . . .. 80
4.5 Neutron EDM Measurements
with Stored Ultracold Neutrons ......... . . . . . . . . . . . . . . . .. 81
4.5.1 Present Limits for the Neutron EDM ............... 81
4.5.2 Stored UCN EDM Experiment
at the Institut Laue-Langevin. . . . . . . . . . . . . . . . . . . . .. 81
4.5.3 UCN EDM Experiment at the VVR-M Reactor,
Petersburg Nuclear Physics Institute. . . . . . . . . . . . . . .. 88
4.5.4 The 199Hg Comagnetometer UeN Experiment. . . . . .. 91
4.6 The Future: Superftuid He Neutron EDM
with a 3He Comagnetometer . . . . . . . . .. . . . . . . . . . . . . . . . . . .. 95
4.6.1 The Production of UCN in Superftuid 4He. . . . . . . . . .. 95
4.6.2 Superftuid 4He Neutron EDM Search
with a 3He Comagnetometer ....................... 100
4.6.3 Dressed Spin Magnetometry ....................... 102
4.6.4 Analysis of the Dressed Spin System
and Systematic Effects ............................ 104
4.7 Comparison of Experimental Techniques ................... 105
5. Theoretical Predictions for Neutron
and Electron Dipole Moments ............................ 107
e
5.1 The CP-Violating Term
in Quantum Chromodynamics ........................... 108
5.2 Predictions of the Standard Model
for Dipole Moments ..................................... 111
Contents IX
5.3 Spontaneous CP Violation in the Higgs Sector ............. 112
5.4 Phenomenological Approach ............................. 116
6. EDM Experiments
with Paramagnetic Atoms ................................ 119
6.1 The Shielding Problem .................................. 119
6.2 Enhancement of the Electron EDM
in Paramagnetic Atoms ................................. 121
6.3 Overview of Paramagnetic Atom Experiments .............. 122
6.4 The Cs EDM Experiment ............................... 124
6.5 The TI EDM Experiment ................................ 126
6.6 Future Prospects for Improving
the Electron EDM Limit ................................ 133
6.7 EDM Limits of Some Other Elementary Particles ........... 135
6.7.1 The Proton ...................................... 135
6.7.2 The Neutrino .................................... 135
6.7.3 The Muon ....................................... 135
6.7.4 The AO Hyperon ................................. 136
6.7.5 The T Lepton .................................... 136
7. EDM Experiments with Diamagnetic Atoms .............. 137
7.1 Shielding in the ISO System .............................. 137
7.2 The 129Xe EDM Experiment ............................. 139
7.3 The 199Hg EDM Experiment ............................. 142
7.4 3He - 129Xe Comparison ................................ 147
8. Atomic Calculations ...................................... 149
8.1 Wave Function of an Outer Electron
at Short Distances ...................................... 149
8.2 The Electron EDM in Paramagnetic Heavy Atoms .......... 152
8.3 CP-Odd Electron-Nucleon Interaction .................... 155
8.3.1 CP-Odd Mixing of Atomic Levels .................. 156
8.3.2 Paramagnetic Atoms .............................. 157
8.3.3 Diamagnetic Atoms ............................... 159
8.3.4 Summary of the Constants k1,2,3 .............•..... 162
8.4 Electron EDM in Diamagnetic Atoms ..................... 164
8.5 CP-Odd Nuclear Moments .............................. 167
8.5.1 The Schiff Moment ............................... 167
8.5.2 Magnetic Quadrupole Moment ..................... 172
9. T Violation in Molecules .................................. 177
9.1 Enhancement of an Applied Field
by a Polar Molecule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
9.2 TIF Beam Experiments ................................. 179
9.3 What Have We Learned from the TIF Experiment? ......... 183
X Contents
9.4 Paramagnetic Molecules ................................. 185
9.5 What Will Be Gained from Experiments
with Paramagnetic Molecules? ........................... 186
10. CP-Odd Nuclear Forces .................................. 189
10.1 CP-Odd Mixing of Opposite-Parity Nuclear Levels ......... 189
10.2 Nuclear Moments
Induced by T- and P-Odd Potentials ...................... 192
10.3 Enhancement Mechanisms for T- and P-Odd Nuclear Multi-
poles .................................................. 195
10.4 Theoretical Predictions and Implications .................. 198
11. What Do We Really Know About T-Odd,
but P-Even Interactions? ................................. 203
11.1 Long-Range Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
11.2 TOPE Fermion-Fermion Interactions.
One-Loop Approach .................................... 205
11.3 TOPE Fermion-Fermion Interactions.
Two-Loop Approach .................................... 207
11.4 Conclusions on TOPE eN and N N Interactions ............ 211
11.5 T-Odd /3 Decay Constants ............................... 213
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Index ......................................................... 227
