Table Of ContentCP Violation
Editor
L. WOLFENSTEIN
Department of Physics, Carnegie Mellon University
Pittsburgh, Pennsylvania 15213-3890, USA
St
1989
NORTH-HOLLAND
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CP violation / Lincoln Wolfenstein, editor.
p. cm. — (Current physics ; 5)
Includes bibliographical references.
ISBN 0-444-88081-X. — ISBN 0-444-88114-X (pbk.)
1. CP violation (Nuclear physics) I. Wolfenstein, Lincoln.
II. Ser ies.
QC793.3.V5C6 1988b
539.7—dc20 89-23278
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Preface
In 1964, it was discovered by an experiment on K° decay that CP invariance was violated in
nature. From an analysis of that experiment as well as from general theorems requiring CPT
invariance it is believed that time-reversal (T) invariance is also violated. The correct theoretical
model to explain this result has remained uncertain until this day.
The articles collected here are mainly concerned with the phenomenological description of
the observed CP violation in the K° system and with theoretical models designed to explain
this. Chapter 1 provides the history leading to the 1964 discovery. Chapter 2 contains reprints
of some more recent definitive experiments, together with the phenomenological analysis that
was developed to interpret CP violation in the K° system. Chapter 3 describes the variety of
models that were developed to explain this CP violation, all of which go beyond the standard
electroweak theory in some respect. Chapter 4 is devoted to the explanation based on the
standard electroweak theory with three generations of quarks.
Outside the K° system only two types of experiments are covered here:
(a) CP violation in the B° system is included in chapter 4, because this is the one place
where large effects are predicted in the standard model;
(b) the electric dipole moment of the neutron is covered in chapter 5, because this provides
what appears to be the most sensitive direct test for T invariance violation.
A number of important subjects could not be covered. These include
(1) general formalism for T and CP in quantum mechanics;
(2) CP or T violation tests in hyperon decay, nuclear beta decay, very rare K meson decays,
and high-energy collisions;
(3) the cosmological origin of the baryon asymmetry.
There exist a large number of reviews and books concerning CP and T violation. Among
these are L. Wolfenstein, Present Status of CP Violation, Ann. Rev. Nucl. Sci. 36 (1986) 137;
R.G. Sachs, Physics of Time Reversal, University of Chicago Press (1987); C. Jarlskog, CP
Violation, World Scientific (1989).
Acknowledgements
The following articles have been reprinted by kind permission of the publisher, The
American Institute of Physics:
From Physical Review:
T.D. Lee, R. Oehme and C.N. Yang, Remarks on possible noninvariance under time reversal
and charge conjugation, Phys. Rev. 106 (1957) 340-345; P.K. Kabir, What is not invariant
under time reversal, Phys. Rev. D 2 (1970) 540-542; G.C. Branco, Spontaneous CP noncon-
servation and natural flavor conservation: A minimal model, Phys. Rev. D 22 (1980) 2901-2905;
H.-Y. Cheng, Weinberg CP-violation model revisited, Phys. Rev. D 34 (1986) 1397-1403; R.N.
Mohapatra and J.C. Pati, Left-right gauge symmetry and an "isoconjugate" model of CP
violation, Phys. Rev. D 11 (1975) 566-571; J.H. Smith, E.M. Purcell and N.F. Ramsey,
Experimental limit to the electric dipole moment of the neutron, Phys. Rev. 108 (1957)
120-122.
From Physical Review Letters:
J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Evidence for the 2TT decay of the K°
2
meson, Phys. Rev. Lett. 13 (1964) 138-140; T.T. Wu and_C.N. Yang, Phenomenological
analysis of violation of CP invariance in decay of K° and K°, Phys. Rev. Lett. 13 (1964)
380-385; L. Wolfenstein, Violation of CP invariance and the possibility of very weak
interactions, Phys. Rev. Lett. 13 (1964) 562-564; S. Weinberg, Gauge Theory of CP noncon-
servation, Phys. Rev. Lett. 37 (1976) 657-661; R.D. Peccei and H.R. Quinn, CP conservation in
the presence of pseudoparticles, Phys. Rev. Lett. 38 (1977) 1440-1443.
From Reviews of Modern Physics:
V.L. Fitch, The discovery of charge-conjugation parity asymmetry, Rev. Mod. Phys. 53 (1981)
367-371; J.W. Cronin, C.P. Symmetry violation - the search for its origin, Rev. Mod. Phys. 53
(1981) 373-383.
From JETP Letters:
I.S. Altarev, Yu.V. Borisov, N.V. Borovikova, A.B. Brandin, A.I. Egorov, S.N. Ivanov, E.A.
Kolomensku, M.S. Lasakov, V.M. Lobashev, A.N. Pirozhkov, A.P. Serebrov, Yu.V. Sobolev,
R.R. Tal'daev, and B.V. Shul'gina, Search for an electric dipole moment of the neutron, JETP
Lett. 44 (1987) 460-465.
From Soviet Journal of Nuclear Physics:
L.B. Okun', Note concerning CP parity, Sov. J. Nucl. Phys. 1 (1965) 670.
The following article has been reprinted from Helvetica Physica Acta by kind permission of
the publisher, Birkhauser Verlag:
C.P. Enz and R.R. Lewis, On the phenomenological description of CP violation for K-mesons
and its consequences, Helv. Phys. Acta 38 (1965) 860-876.
The following article has been reprinted from Progress of Theoretical Physics by kind
permission of the publication office of Progress of Theoretical Physics:
M. Kobayashi and T. Maskawa, CP-violation in the renormalizable theory of weak interaction,
Prog. Theor. Phys. 49 (1973) 652-657.
vii
viii
The following article has been reprinted from Proceedings of the Oxford International
Conference on Elementary Particle Physics by kind permission of the publication office of the
Rutherford Appleton Laboratory:
J.S. Bell and J. Steinberger, Weak interaction of kaons, Proc. Oxford International Conference
on Elementary Particle Physics (1965) 195-208 and 221.
1. History
Introduction
Symmetry principles have played an important role in the development of our ideas about
fundamental processes. We are interested here in three discrete symmetries which relate a given
state or process to one other state or process; these are
P: Parity, or the inversion of all spatial coordinates,
T: Time-reversal, the replacement of t by -1,
C: Particle-antipartide conjugation, the replacement of all particles by their antiparticles.
In first instance, these symmetries were discovered as symmetries of established physical
laws. Thus Wigner [1] discovered that P and T are symmetries of the Schrodinger equation
applied to atomic and molecular systems. Similarly, C was discovered as a symmetry of
quantum electrodynamics [2].
Nuclear physics required the introduction of two new interactions: the weak interaction to
describe beta-decay, and the strong interaction for nuclear forces. Because these interactions
had no classical analogue, they had to be invented ab initio. Then, it became natural to assume
that the same symmetries held for the new interactions. However, the consequences of making
this assumption were not analyzed in any systematic fashion for a long time. An important
point made by Luders in 1954 [3] was that if P symmetry is assumed, then the consequences of
C invariance are identical to those of T invariance. A way of stating this result is that, although
it is easy to construct theories that violate C, P or T symmetry, every relativistic local quantum
field theory is invariant under the combined symmetry operation CPT.
It was pointed out by Lee and Yang in 1956 [4] that no experiments involving weak
interactions tested the parity symmetry P. This led to the discovery in 1957 [5] that parity
symmetry was violated as much as possible in nuclear beta-decay as well as in pion and muon
decay. The resulting V-A theory that became established after these discoveries involved a
maximal violation of both C and P but retained invariance under the CP and the T
transformations. This possibility was first emphasized by Landau and others [6] after the
Lee-Yang paper but before the experiments.
Even before P violation was discovered, Lee et al. [7] looked at possible ways of testing the C
and T symmetries subject to the overall CPT invariance. They found that K° decay was of
particular interest. Their analysis is in terms of C violation, but the quantities they discuss (a
and the charge asymmetry r) are equally measures of CP violation. (To say this in another way,
the C-violating observables discussed do not involve any P violation so they are also CP-violat-
ing.) Once it was realized that C was violated in the weak interactions, it was the CP symmetry
that was important to test with the K° system.
If CP invariance is assumed, the K° states with definite masses and lifetimes are K and K
a 2
which are even and odd under CP. It then follows that only K can decay into two pions while
:
K would decay into three pions. This prediction, originally made by Gell-Mann and Pais [8],
2
was verified with the observation of two types of decay, a short-lived Ks going to TT+TT~ or
TT0TT0 and a long lived KL going to three pions. In 1964, Christenson et al. [9] discovered that
KL had a small branching ratio into TT+TT~. This decay was indicated at the same time in an
experiment by Abashian et al. [10]. This suggested strongly that CP invariance was not an exact
1
2 L. Wolfenstein
symmetry. The history of this discovery and its consequences are presented in the Nobel
lectures of Fitch [11] and Cronin [12]. The possibilities of alternative explanations not involving
CP violation are discussed by Cronin. The observation [13] of interference between the K and
L
Ks decays into TT+TT~ provides definite evidence for CP violation. Note that the paper of Lee et
al. [7] already discusses the CP-violating interference effect.
References
[1] E.P. Wigner, Z. Phys. 43 (1927) 624; Gott. Nadir. (1932) 546.
The latter classic paper on time reversal is reproduced as chapter 26 of E.P. Wigner, Group Theory (Academic
Press, 1959).
[2] H.A. Kramers, Proc. Acad. Sci. Amsterdam 40 (1937) 814.
[3] G. Luders, Danske Videns Selskab Mat-Fys Medd. 28, No. 5 (1954); see also Annals of Physics 2 (1957) 1.
[4] T.D. Lee and C.N. Yang, Phys. Rev. 104 (1956) 254.
[5] C.S. Wu, E. Ambler, R.W. Hayward, D.D. Hoppes and R.P. Hudson, Phys. Rev. 105 (1957) 1413.
[6] L. Landau, Nucl. Phys. 3 (1957) 127. Paper 1, this volume.
See also T.D. Lee and C.N. Yang, Phys. Rev. 105 (1957) 1671;
A. Salam, Nuovo Cimento 5 (1957) 249;
R. Gatto, Phys. Rev. 106 (1957) 168.
[7] T.D. Lee, R. Oehme and C.N. Yang, Phys. Rev. 106 (1957) 340. Paper 2, this volume.
[8] M. Gell-Mann and A. Pais, Phys. Rev. 97 (1955) 1387.
[9] J.H. Christenson, J.W. Cronin, V.L. Fitch and R. Turlay, Phys. Rev. Lett. 13 (1964) 138. Paper 3, this volume.
[10] A. Abashian, R.J. Abrams, D.W. Carpenter, G.P. Fischer, B.M.K. Nefkens and J.H. Smith, Phys. Rev. Lett. 13
(1964) 243.
[11] V.L. Fitch, Rev. Mod. Phys. 53 (1981) 367. Paper 4, this volume.
[12] J.W. Cronin, Rev. Mod. Phys. 53 (1981) 373. Paper 5, this volume.
[13] V.L. Fitch, R.F. Roth, J.S. Russ and W. Vernon, Phys. Rev. Lett. 15 (1965) 73.
1
Nuclear Physics 3 (1957) 127—131; North-Holland Publishing Co., Amsterdam
ON THE CONSERVATION LAWS FOR WEAK INTERACTIONS
L. LANDAU
Institute for Physical Problems, USSR Academy of Sciences, Moscow
Received 9 January 1957
Abstract: A variant of the theory is proposed in which non-conservation of parity can be
introduced without assuming asymmetry of space with respect to inversion.
Various possible consequences of non-conservation of parity are considered which
pertain to the properties of the neutrino and in this connection some processes involv-
ing neutrinos are examined on the assumption that the neutrino mass is exactly zero.
1. Combined Parity
As is well known, the unusual properties of K-mesons have created a
perplexing situation in modern physics. The correlation between rc-mesons
in r-decay (K+ -> 27i+-\-7t~) leads to the necessity of assigning a 0~ state
to K+-mesons. This kind of system, however, cannot decay into two n-
mesons (K+ -> 7I++TZ°). We are thus faced with the dilemma of either
assuming that two different K-mesons exist or that the conservation laws
are violated in K-meson decay. In the first case one must then explain the
identity of masses (which are equal to within two electron masses)and the
near coincidence in lifetime of the 0 and r-decays. One may attempt to
explain the equality of K-meson masses by postulating, as Lee and Yang x)
have done, the existence of some hitherto unknown symmetry property
of nuclear forces which transforms the r-meson into a 0-meson. If, however,
decay involving a neutrino (K+->//++i>, K+-^/z+ +*>+JZ°, K+ -> e++7i°+v)
is considered to be essentially the same for particles of various parity a
difference in lifetime related to the different rate of r and 0-decay (& 8 %
and ^ 25 %) should be anticipated. This discrepancy should be not less
than 30—40 %, a result which seems to be inconsistent with experiment2).
Thus we come to the conclusion that the hypothesis of the existence of
two different K+-mesons is contrary to the experimental facts and the only
alternative is to assume that the generally accepted conservation laws are
violated in K-decay. Since there is no reason to think that the law of con-
servation of angular momentum is untenable, we are apparently dealing
here with a direct violation of the law of conservation of parity.
It might seem at first glance that non-conservation of parity implies
asymmetry of space with respect to inversion. If however, complete isotropy
of space (conservation of angular momentum) is taken into account this
127
CPSC 5 - paper 1 3
128 L. LANDAU
type of asymmetry would seem to be extremely strange and in my opinion
a simple rejection of parity conservation would create a difficult situation
in theoretical physics. I would like to point out a solution of this problem
which consists in the following. As is well known, both the law of conser-
vation of parity and charge conjugation invariance undoubtedly hold in
strong interactions. Let us now assume that each of these conservation laws
does not hold separately in weak interactions. However, invariance with
respect to the set of both operations (which we shall call combined in-
version) will be assumed to exist. In combined inversion, space inversion
and transformation of a particle into an antiparticle occur simultaneously.
It is easy to see that invariance of the interactions with respect to com-
bined inversion leaves space completely symmetrical, and only the electrical
charges will be asymmetrical. The effect of this asymmetry on the symmetry
of space is no greater than that due to chemical stereo-isomerism.
On the other hand the law of conservation of parity of charged particles
will not hold as the operator of combined inversion does not transform
charged particles into themselves.
Furthermore, it is easy to see that the constants characterizing the
particles and antiparticles (masses, lifetimes) should be identical since, as a
result of invariance with respect to combined inversion, all processes
involving particles and antiparticles should differ from each other only
in regard to space inversion. Graphically speaking, a K~-meson is a mirror
reflected K+-meson.
Truly neutral particles, that is, particles which are identical to their
antiparticles, transform into themselves in combined inversion. Conse-
quently, with respect to these particles combined inversion leads to a law
of conservation of combined parity. It should be emphasized that con-
servable parity is the product of ordinary parity and charge parity of the
particles. Evidently, in this sense the 7r°-meson is an odd particle; the
K °(6>°)-meson which decays into 2 rc-mesons is an even particle and the
1
K °-meson predicted by Gell-Mann and Pais 3) and recently discovered
2
experimentally 4) is an odd particle. Combined inversion changes the sign
of the magnetic field of a photon but does not change that of the electric
field. The ordinary parities of electric and magnetic multipoles are reversed
for combined inversion.
It is easy to show from the foregoing that despite the absence of ordinary
parity the particles cannot possess dipole moments. Indeed, the only vector
which can be constructed from ^-operators for a particle at rest is its spin
vector which is even with respect to inversion and odd with respect to
charge. It is consequently odd with respect to combined inversion and, in
accord with the foregoing regarding the electromagnetic field, it defines
only a magnetic but not an electric moment.
CPSC 5 - paper 1
ON THE CONSERVATION LAWS FOR WEAK INTERACTIONS 129
Lee and Yang 5) t have shown that non-conservation of parity leads to
correlations in a number of hyperon production and decay processes. It
can be shown that a consequence of invariance with respect to combined
inversion is that the weak interaction operators in the Lagrangian contain
real coefficients. This circumstance, however, does not appreciably modify the
qualitative picture which is obtained in the general case of non-conservation
of parity. Therefore asymmetry of hyperon decay with respect to the plane
of their creation, which has been predicted by Lee and Yang 5), will also
hold in this case.
I would like to express my deep appreciation to L. Okun, B. Ioffe and
A. Rudik for discussions from which the idea of this part of the present
paper emerged.
2. Properties of the Neutrino
Rejection of the law of conservation of parity entails the possibility of
existence of new properties of the neutrino. The Dirac equation for the case
of zero mass splits into two independent pairs of equations. It will be
recalled that in the usual theory one cannot confine oneself to a single
pair of equations since both pairs transform into each other as a result of
space inversion. If, however, we restrict our attention to combined inversion
we arrive at the possibility of describing the neutrino by a single pair of
equations. In the sense of the usual scheme this would signify that the
neutrino is always polarized in the direction of its motion (or in the op-
posite direction). The polarization of the antineutrino is correspondingly
reversed. According to this model the neutrino is not a truly neutral particle
and this agrees with the fact that double /?-decay has not been observed
experimentally and especially with the results of experiments on induced
j8-decay. We shall call this kind of neutrino a longitudinally polarized
neutrino or briefly a longitudinal neutrino.
In the usual theory the neutrino mass is zero, so to say, accidentally.
Thus, account of neutrino interactions automatically leads to the appearance
of a definite, albeit vanishingly small, rest mass. The mass of the lon-
gitudinal neutrino, on the other hand, vanishes automatically and this
situation cannot be altered by the existence of any type of interaction.
The longitudinal neutrino concept appreciably reduces the possible
number of types of weak interaction operators. Consider, for example, the
decay of a //-meson into an electron and two neutrinos. In the usual manner
we represent the interaction operator as the product of operators consisting
of //-meson and electron ^-operators on the one hand and ^-operators of
the two neutrinos on the other. For the longitudinal neutrino only one
combination can be made from the two neutrino operators—a scalar (a
t I would like to sincerely thank the authors for sending me a preprint of their paper.
CPSC 5 - paper 1
