536
K. Kleinknecht and U. Uwer
The moduli for the decay of N 0 to f and the decay of N 0 to its CP conjugate state
f are equal if CP is conserved, and vice versa:
|A f | = |A f | ,
|A f | = |A f | .
(9.54)
(If f is a CP eigenstate, this is simplified to |A f | = |A f |).
Now CP violation may occur in three different ways:
1. CP violation in the mixing, if |q/p| = 1, called “indirect CP violation”.
2. CP violation in the decay amplitudes, when (9.54) is not valid, called “direct CP
violation”.
3. CP violation in the interference, when the phase of the expression
A f A ∗
f A f A ∗
f
p
2 /q
2
(9.55)
is not zero.
These three types of CP violation are characterized by the following details:
1. CPviolation in the mixing. This type of CP violation will show up if the mass
eigenstates of a neutral meson system are different from the CP eigenstates, i.e.
if |q/p| = 1 (or ε = 0) and if there is a relative phase between M 12 and Γ 12 . For
the neutral kaon system, this is evident from the existence of the decay K L →
π + π − , where |ε| ∼ 2 × 10 −3 , and from the charge asymmetry in semileptonic
decays δ L which is proportional to 2 e ε. For the neutral B system, this effect
could be seen also in the charge asymmetry of semileptonic decays
a SL =
Γ (B 0 (t) → l + νX) − Γ (B 0 (t) → l − ¯
νX)
Γ (B 0 (t) → l + νX) + Γ (B 0 (t) → l − ¯
νX)
.
(9.56)
This asymmetry is expected to be small in the Standard Model of order Γ //m
or O(10 −3 ).
2. CPviolation in the decay amplitude. This effect appears if the decay amplitude
A f of the neutral meson N 0 to a final state f is different from the amplitude A f
of the antiparticle N 0 to the charge-conjugate state f , i.e. |A f /A f | = 1. In the
neutral-kaon decay to two π mesons, this is realized by the interference of two
decay amplitudes, one with = 1/2 to an isospin I = 0 state, and another
with = 3/2 to an isospin I = 2 state. The amplitude of direct CP violation
is denoted by ε and proceeds through penguin diagram processes. The observed
magnitude of this amplitude is |ε | ∼ 4×10 −6 . In the neutral B meson system, the
required two decay amplitudes with different weak phases and different strong
phases could be a penguin diagram and a tree diagram, e.g. for the decay to
the final state K − π + or K + π − . The b → s penguin diagram has a dominant
K. Kleinknecht and U. Uwer
The moduli for the decay of N 0 to f and the decay of N 0 to its CP conjugate state
f are equal if CP is conserved, and vice versa:
|A f | = |A f | ,
|A f | = |A f | .
(9.54)
(If f is a CP eigenstate, this is simplified to |A f | = |A f |).
Now CP violation may occur in three different ways:
1. CP violation in the mixing, if |q/p| = 1, called “indirect CP violation”.
2. CP violation in the decay amplitudes, when (9.54) is not valid, called “direct CP
violation”.
3. CP violation in the interference, when the phase of the expression
A f A ∗
f A f A ∗
f
p
2 /q
2
(9.55)
is not zero.
These three types of CP violation are characterized by the following details:
1. CPviolation in the mixing. This type of CP violation will show up if the mass
eigenstates of a neutral meson system are different from the CP eigenstates, i.e.
if |q/p| = 1 (or ε = 0) and if there is a relative phase between M 12 and Γ 12 . For
the neutral kaon system, this is evident from the existence of the decay K L →
π + π − , where |ε| ∼ 2 × 10 −3 , and from the charge asymmetry in semileptonic
decays δ L which is proportional to 2 e ε. For the neutral B system, this effect
could be seen also in the charge asymmetry of semileptonic decays
a SL =
Γ (B 0 (t) → l + νX) − Γ (B 0 (t) → l − ¯
νX)
Γ (B 0 (t) → l + νX) + Γ (B 0 (t) → l − ¯
νX)
.
(9.56)
This asymmetry is expected to be small in the Standard Model of order Γ //m
or O(10 −3 ).
2. CPviolation in the decay amplitude. This effect appears if the decay amplitude
A f of the neutral meson N 0 to a final state f is different from the amplitude A f
of the antiparticle N 0 to the charge-conjugate state f , i.e. |A f /A f | = 1. In the
neutral-kaon decay to two π mesons, this is realized by the interference of two
decay amplitudes, one with = 1/2 to an isospin I = 0 state, and another
with = 3/2 to an isospin I = 2 state. The amplitude of direct CP violation
is denoted by ε and proceeds through penguin diagram processes. The observed
magnitude of this amplitude is |ε | ∼ 4×10 −6 . In the neutral B meson system, the
required two decay amplitudes with different weak phases and different strong
phases could be a penguin diagram and a tree diagram, e.g. for the decay to
the final state K − π + or K + π − . The b → s penguin diagram has a dominant