9 Symmetry Violations and Quark Flavour Physics
611
Often a different naming convention, also shown in Fig. 9.38, is used to label the
three angles. The UT angles are constraint by the CP observables discussed in
Sect. 9.6:
β = (21.9 ± 0.7)
◦
(9.226)
γ = (73.5
+4.2
−5.1 )
◦
(9.227)
The measurement of the angle α has not been discussed in Sect. 9.6. It is measured
using the observation of time-dependent CP violation in the decays B 0 → ππ,
ρρ, and πρ by BABAR and Belle. The average of this measurements result into
[133, 134],
α = (84.5
+5.9
−5.2 )
◦ .
(9.228)
The sum of three angles, α + β + γ = (180 ± 7)
◦ , is consistent with the
expectation and represents a first test of the unitarity of the CKM matrix. An
additional constraint of the CKM phases and thus of the UT angles comes from the
measurement of time-dependent CP violation in B 0
s decays and the measurement of
the phase β s (with φ s = −2β s , see Sect. 9.6),
β s = arg
−
V ts V ∗
tb
V cs V ∗
cb
= (0.60 ± 0.89)
◦ .
(9.229)
In addition to the measurements of CP violation in the B meson systems also the
measurements of CP violation in the K 0 ¯
K 0 mixing, | K | = (2.233 ± 0.015) × 10 −3
(see Sect. 9.5) provides information about the CKM matrix. The measurement of
| K | can be translated into an approximate hyperbolic constraint on the apex ( ¯
ρ, ¯
η)
of the UT [135].
The sides of the unitarity triangle are accessible by measuring decay rates and
mixing frequencies. In the following the experimental determination of the CKM
elements as well as a test of the unitarity of the CKM matrix is discussed.
9.7.2 Determination of the CKM Matrix Elements
1. |V ud |. Precise determinations of |V ud | are available from nuclear beta decays,
from the decay of the free neutron and from semileptonic pion decays (π + →
π 0 e + ν). The most precise value results from an analysis of superallowed 0 + →
0 + nuclear beta decays which are pure vector transitions. The measurements of
the transition energies, the partial branching fractions, and the half-lives of the
parent nuclei together with radiative and isospin-symmetry-breaking corrections
allow the determination of the corrected F t-value, from which, by using the
muon life-time, |V ud | can be determined. The average of the fourteen most
611
Often a different naming convention, also shown in Fig. 9.38, is used to label the
three angles. The UT angles are constraint by the CP observables discussed in
Sect. 9.6:
β = (21.9 ± 0.7)
◦
(9.226)
γ = (73.5
+4.2
−5.1 )
◦
(9.227)
The measurement of the angle α has not been discussed in Sect. 9.6. It is measured
using the observation of time-dependent CP violation in the decays B 0 → ππ,
ρρ, and πρ by BABAR and Belle. The average of this measurements result into
[133, 134],
α = (84.5
+5.9
−5.2 )
◦ .
(9.228)
The sum of three angles, α + β + γ = (180 ± 7)
◦ , is consistent with the
expectation and represents a first test of the unitarity of the CKM matrix. An
additional constraint of the CKM phases and thus of the UT angles comes from the
measurement of time-dependent CP violation in B 0
s decays and the measurement of
the phase β s (with φ s = −2β s , see Sect. 9.6),
β s = arg
−
V ts V ∗
tb
V cs V ∗
cb
= (0.60 ± 0.89)
◦ .
(9.229)
In addition to the measurements of CP violation in the B meson systems also the
measurements of CP violation in the K 0 ¯
K 0 mixing, | K | = (2.233 ± 0.015) × 10 −3
(see Sect. 9.5) provides information about the CKM matrix. The measurement of
| K | can be translated into an approximate hyperbolic constraint on the apex ( ¯
ρ, ¯
η)
of the UT [135].
The sides of the unitarity triangle are accessible by measuring decay rates and
mixing frequencies. In the following the experimental determination of the CKM
elements as well as a test of the unitarity of the CKM matrix is discussed.
9.7.2 Determination of the CKM Matrix Elements
1. |V ud |. Precise determinations of |V ud | are available from nuclear beta decays,
from the decay of the free neutron and from semileptonic pion decays (π + →
π 0 e + ν). The most precise value results from an analysis of superallowed 0 + →
0 + nuclear beta decays which are pure vector transitions. The measurements of
the transition energies, the partial branching fractions, and the half-lives of the
parent nuclei together with radiative and isospin-symmetry-breaking corrections
allow the determination of the corrected F t-value, from which, by using the
muon life-time, |V ud | can be determined. The average of the fourteen most