21
CP Violation and Oscillation Phenomena
In this chapter we shall continue with the phenomenology of weak interactions,
introducing two topics which have been the focus of intense experimental effort
in the recent decade: CP violation in B meson decays, and oscillations in both
neutral meson and neutrino systems. In the following chapter we take up again
the gauge theory theme, with the Glasow-Salam-Weinberg electroweak theory.
CP violation was first discovered in the decays of neutral K mesons (Christenson et al. 1964), but we shall not follow a historical approach to this subject. Instead we shall concentrate on B-meson decays, where the effects are
far larger, and much clearer to interpret theoretically than in the K-meson
case. CP violation is reviewed in Branco et al. (1999), Bigi and Sanda (2000)
and Harrison and Quinn (1998). We aim simply to illustrate the principles
with some particular examples. In particular, we shall generally not discuss
theoretical predictions; our main emphasis will be on describing selected experiments which have allowed determinations of the angles α, β and γ of the
unitarity triangle, figure 20.10.
We saw in section 20.7.3 that, in the Standard Model, CP violation is
attributable solely to one irreducible phase degree of freedom, δ, in the CKM
matrix V. Clearly, to measure this phase, it is necessary (as usual in quantum
mechanics) to create situations where it enters into the interference between
two complex amplitudes. Two situations may be distinguished (Carter and
Sanda 1980):
(i) interference between two decay amplitudes B
0
→ X and B ¯ 0 → X,
¯
where the B
0 and B
0 have been produced in a coherent state by mixing,
and decay to a common hadronic final state X;
(ii) interference between two different amplitudes for a single B-meson to
decay to a final state X.
Method (ii) (‘direct CP violation’) can be applied to charged as well as neutral
mesons.
The mixing in method (i) is formally similar to that involved in neutrino
oscillations, which we treat after the meson case. We shall therefore start in
section 21.1 with an example illustrating method (ii). We set up the mixing
formalism and apply it to CP violation in B decays in section 21.2; we discuss
K decays in section 21.3. Neutrino oscillations are treated in section 21.4.
329
CP Violation and Oscillation Phenomena
In this chapter we shall continue with the phenomenology of weak interactions,
introducing two topics which have been the focus of intense experimental effort
in the recent decade: CP violation in B meson decays, and oscillations in both
neutral meson and neutrino systems. In the following chapter we take up again
the gauge theory theme, with the Glasow-Salam-Weinberg electroweak theory.
CP violation was first discovered in the decays of neutral K mesons (Christenson et al. 1964), but we shall not follow a historical approach to this subject. Instead we shall concentrate on B-meson decays, where the effects are
far larger, and much clearer to interpret theoretically than in the K-meson
case. CP violation is reviewed in Branco et al. (1999), Bigi and Sanda (2000)
and Harrison and Quinn (1998). We aim simply to illustrate the principles
with some particular examples. In particular, we shall generally not discuss
theoretical predictions; our main emphasis will be on describing selected experiments which have allowed determinations of the angles α, β and γ of the
unitarity triangle, figure 20.10.
We saw in section 20.7.3 that, in the Standard Model, CP violation is
attributable solely to one irreducible phase degree of freedom, δ, in the CKM
matrix V. Clearly, to measure this phase, it is necessary (as usual in quantum
mechanics) to create situations where it enters into the interference between
two complex amplitudes. Two situations may be distinguished (Carter and
Sanda 1980):
(i) interference between two decay amplitudes B
0
→ X and B ¯ 0 → X,
¯
where the B
0 and B
0 have been produced in a coherent state by mixing,
and decay to a common hadronic final state X;
(ii) interference between two different amplitudes for a single B-meson to
decay to a final state X.
Method (ii) (‘direct CP violation’) can be applied to charged as well as neutral
mesons.
The mixing in method (i) is formally similar to that involved in neutrino
oscillations, which we treat after the meson case. We shall therefore start in
section 21.1 with an example illustrating method (ii). We set up the mixing
formalism and apply it to CP violation in B decays in section 21.2; we discuss
K decays in section 21.3. Neutrino oscillations are treated in section 21.4.
329