602
K. Kleinknecht and U. Uwer
To observe large asymmetries the interfering amplitudes should have different
weak and strong phases. While the weak phases, and in particular the weak phase
difference, are determined by the CKM parameters, the theoretical determination
of the strong phases is difficult. The B meson are subject to both, short and longdistance QCD effects which cannot be treated perturbatively.
In the following, two classes of B decays exhibiting large direct CP violation
will be discussed: B decays to charmless final-states, i.e. to final-states without D
mesons, and decays to charmed final-states of the type B → DK.
9.6.6.1 Direct CP Violation in Charmless B Decays
As sketched in Fig. 9.34 charmless two-body B decays such as B 0 → K + π − can
proceed via two topologically very different classes of decay amplitudes, tree and
penguin processes, which carry different weak and in generally also different strong
phases. Large direct CP violation is therefore expected for these decays.
First experimental evidence for direct CP violation in B meson decays was
reported by the Belle collaboration in 2004 for the decay B 0 → π + π − [114].
As the neutral B meson decays here to a CP eigenstate the formalism of (9.194)
and (9.207) has to be applied, i.e. the observable time dependent asymmetry can be
parametrized by the coefficient A dir
ππ describing the effect of direct CP asymmetry
and the coefficient A mix
ππ to describe the effect of indirect CP violation through
interference of diagrams with and without mixing. Belle observed a deviation of the
coefficient A dir
ππ from zero, i.e. direct CP violation, at the level of 3.2σ . The result
suggested large interference effects between the relevant tree and penguin diagrams
and was confirmed by subsequent measurements. Today, the most recent value of
this coefficient is A dir
ππ = 0.32 ± 0.04 [87] and confirms the early hints for direct
CP violation in B 0 → π + π − .
The two B-factory experiments, BABAR and Belle, also studied B 0 → K + π −
decays where large penguin contributions were expected. Both collaborations
performed time-independent analyses and reported the observation of large direct
CP violations for B 0 → K + π − decays ( Babar: A CP = −0.133 ± 0.030 ± 0.009
[115]; Belle: A CP = −0.101 ± 0.025 ± 0.005 [116]). Both measurements represent
the first doubtless observation of large direct CP violation in the B 0 system. It is
Fig. 9.34 Tree-level (left) and penguin (right) contribution to the charmless two-body decay
B 0 → K + π −
K. Kleinknecht and U. Uwer
To observe large asymmetries the interfering amplitudes should have different
weak and strong phases. While the weak phases, and in particular the weak phase
difference, are determined by the CKM parameters, the theoretical determination
of the strong phases is difficult. The B meson are subject to both, short and longdistance QCD effects which cannot be treated perturbatively.
In the following, two classes of B decays exhibiting large direct CP violation
will be discussed: B decays to charmless final-states, i.e. to final-states without D
mesons, and decays to charmed final-states of the type B → DK.
9.6.6.1 Direct CP Violation in Charmless B Decays
As sketched in Fig. 9.34 charmless two-body B decays such as B 0 → K + π − can
proceed via two topologically very different classes of decay amplitudes, tree and
penguin processes, which carry different weak and in generally also different strong
phases. Large direct CP violation is therefore expected for these decays.
First experimental evidence for direct CP violation in B meson decays was
reported by the Belle collaboration in 2004 for the decay B 0 → π + π − [114].
As the neutral B meson decays here to a CP eigenstate the formalism of (9.194)
and (9.207) has to be applied, i.e. the observable time dependent asymmetry can be
parametrized by the coefficient A dir
ππ describing the effect of direct CP asymmetry
and the coefficient A mix
ππ to describe the effect of indirect CP violation through
interference of diagrams with and without mixing. Belle observed a deviation of the
coefficient A dir
ππ from zero, i.e. direct CP violation, at the level of 3.2σ . The result
suggested large interference effects between the relevant tree and penguin diagrams
and was confirmed by subsequent measurements. Today, the most recent value of
this coefficient is A dir
ππ = 0.32 ± 0.04 [87] and confirms the early hints for direct
CP violation in B 0 → π + π − .
The two B-factory experiments, BABAR and Belle, also studied B 0 → K + π −
decays where large penguin contributions were expected. Both collaborations
performed time-independent analyses and reported the observation of large direct
CP violations for B 0 → K + π − decays ( Babar: A CP = −0.133 ± 0.030 ± 0.009
[115]; Belle: A CP = −0.101 ± 0.025 ± 0.005 [116]). Both measurements represent
the first doubtless observation of large direct CP violation in the B 0 system. It is
Fig. 9.34 Tree-level (left) and penguin (right) contribution to the charmless two-body decay
B 0 → K + π −