Subatomic Physics

9.9. References 271
• There are three possible causes of CP Violation in kaon decays: The first one
is in the K1 and K2 mixing (mass mixing):
KL = K2 + ɛK1
�
1+ | ɛ | 2 , KS = K1 − ɛK2
� ,, (9.91)
1+ | ɛ | 2
where ɛ is a measure of the CP-violation. It is the KL and KS which have definite
lifetimes. Experimentally, it is found that
ɛ =(2.284 ± 0.014) × 10 −3 . (9.92)
The second possibile cause of CP Violation is in the decay matrix element itself.
A third one is an interference beween these two causes. The CP violation in the
decay matrix element, measured by a parameter called ɛ ′ , occurs due to an admixture
of isospin 2 to isospin 0 (or change of isospin by 3/2 vs. 1/2 in the decay), see
Problem 9.46. The ratio of ɛ ′ to ɛ is of the order of 10 −3 . •
9.9 References
General references concerning invariance properties are given in Section 7.7.
Discontinuous transformations and unitary and antiunitary operators are treated
in detail in Messiah, Vol. II, Chapter XV. Some of the theoretical aspects of parity
and time reversal are discussed in E. M. Henley, “Parity and Time Reversal Invariance
in Nuclear Physics,” Annu. Rev. Nucl. Sci. 19, 367 (1969), and in Symetries
and Fundamental Interactions in Nuclei, ed. W.C. Haxton and E.M. Henley, World
Sci., Singapore, 1995. A detailed treatise is Robert G. Sachs, The Physics of Time
Reversal Invariance, University of Chicago Press, Chicago, 1987. The theory and
status of these symmetries are discussed in a number of reviews: E.N. Fortson and
L.L. Lewis, “Atomic Parity Nonconservation Experiments,” Phys. Rep. 113, 289
(1984); E.G. Adelberger and W. Haxton, “Parity Violation in the Nucleon–Nucleon
Interaction,” Annu. Rev. Nucl. Part. Sci. 35, 501 (1985); E.M. Henley, “Status of
Some Symmetries”, Prog. Part. Nucl. Phys., (A. Faessler, ed.) 20, 387 (1987); and
Tests of Time Reversal Invariance, (N.R. Roberson, C.R. Gould, and J.D. Bowman,
eds.) World Scientific, Teaneck, NJ, 1988.
A popular account of CP and T violation is given by N. Fortson, P. Sandars,
and S. Barr, Phys. Tod. 56, 33 (June 2003); see also R. G. Sachs, Science 176, 587
(1972). CP violation in the K and B meson systems can be found on R. Kleinknecht,
Experimental Clarification in the Neutral K Meson and B Meson Systems, Springer,
NY, 2003; and in P. Bloch and L. Tauscher, Annu. Rev. Nucl. Part. Sci. 53, 123
(2003); see also CP Violation in Particle, Nuclear and Astrophysics, ed.M.Beyer,
Springer, New York, 2002; and I.I. Bigi and A.I. Sanda, CP Violation in Nature—A
Status Report, Comm. Nucl. Part. Phys. 14, 149 (1985); I.B. Khriplovich, S.K.
Lamoreaux, CP violation without strangeness: electric dipole moments of particles,
atoms, and molecules, Berlin ; New York : Springer-Verlag, 1997.