598
K. Kleinknecht and U. Uwer
is obtained [87] which corresponds to a value of the phase β of,
β = (21.9 ± 0.7)
◦ or β = (68.1 ± 0.7)
◦ ,
where the ambiguity is not resolved.
9.6.5.2 B 0
s Meson
Analogue to the measurement of the CKM phase β in the B 0 system, the measurement of a corresponding CP violating phase β s , defined in Sect. 9.7, can be
performed in the B 0
s system, assuming that the B 0
s oscillation can be resolved. The
golden channel used is the decay B 0
s → J/ψφ. Due to its higher mass the B 0
s system
cannot be produced at the ϒ(4S) resonance and β s was therefore not accessible at
the B-factories.
The two Tevatron experiments CDF and D0 have performed explorative studies
of the decay B 0
s → J/ψφ [102, 103] and also first measurements [104, 105] but
the results have been limited by the number of recorded signal events. The first
significant measurement of the phase 6 φ s = −2β s has been presented by the LHCb
experiment in 2011 [106].
In the decay B 0
s → J/ψφ the final-state is composed of two vector particles
and angular momentum conservation allows for the relative angular momentum
values L = 0, 1 or 2. The final-state J/ψφ is thus not a pure CP-state but a
linear combination of CP-even and CP-odd eigenstates depending on the relative
angular momentum L of the two vector mesons: η CP = η CP (J /ψ)η CP (φ)(−1) L =
(−1) L . The measurement of the time dependent CP asymmetry requires a separate
treatment of the CP-odd and CP-even states which can be achieved statistically by
analyzing the angular distribution of the final-state particles J/ψ → μ + μ − and
φ → K + K − . To measure the angular distribution of the final state particles it is
common to use the helicity basis. The three decay angles necessary to describe the
decay are denoted by (θ K , θ μ , ϕ h ) and are defined in Fig. 9.31. The polar angle θ K
(θ μ ) is the angle between the K + (μ + ) momentum and the direction opposite to the
B 0
s momentum in the K + K − (μ + μ − ) centre-of-mass system. The azimuthal angle
between the K + K − and μ + μ − planes is ϕ h .
The analysis of the B 0
s → J/ψφ events is further complicated by a small
fraction of non-resonant B 0
s → J/ψK + K − decays (CP-odd) which interfere with
the φ meson decaying to two charged kaons. These non-resonant events need to be
considered. Effectively one therefore studies B 0
s decays to J/ψK + K − .
6 In the Standard Model the phase φ s determined by the measurement of the time-dependent CP
asymmetry in the decay B 0
s → J/ψφ equals in leading order to −2β s with β s being defined in
Sect. 9.7. However, in case of new physics effects the two phases could differ. In the context of this
textbook these differences are ignored.
K. Kleinknecht and U. Uwer
is obtained [87] which corresponds to a value of the phase β of,
β = (21.9 ± 0.7)
◦ or β = (68.1 ± 0.7)
◦ ,
where the ambiguity is not resolved.
9.6.5.2 B 0
s Meson
Analogue to the measurement of the CKM phase β in the B 0 system, the measurement of a corresponding CP violating phase β s , defined in Sect. 9.7, can be
performed in the B 0
s system, assuming that the B 0
s oscillation can be resolved. The
golden channel used is the decay B 0
s → J/ψφ. Due to its higher mass the B 0
s system
cannot be produced at the ϒ(4S) resonance and β s was therefore not accessible at
the B-factories.
The two Tevatron experiments CDF and D0 have performed explorative studies
of the decay B 0
s → J/ψφ [102, 103] and also first measurements [104, 105] but
the results have been limited by the number of recorded signal events. The first
significant measurement of the phase 6 φ s = −2β s has been presented by the LHCb
experiment in 2011 [106].
In the decay B 0
s → J/ψφ the final-state is composed of two vector particles
and angular momentum conservation allows for the relative angular momentum
values L = 0, 1 or 2. The final-state J/ψφ is thus not a pure CP-state but a
linear combination of CP-even and CP-odd eigenstates depending on the relative
angular momentum L of the two vector mesons: η CP = η CP (J /ψ)η CP (φ)(−1) L =
(−1) L . The measurement of the time dependent CP asymmetry requires a separate
treatment of the CP-odd and CP-even states which can be achieved statistically by
analyzing the angular distribution of the final-state particles J/ψ → μ + μ − and
φ → K + K − . To measure the angular distribution of the final state particles it is
common to use the helicity basis. The three decay angles necessary to describe the
decay are denoted by (θ K , θ μ , ϕ h ) and are defined in Fig. 9.31. The polar angle θ K
(θ μ ) is the angle between the K + (μ + ) momentum and the direction opposite to the
B 0
s momentum in the K + K − (μ + μ − ) centre-of-mass system. The azimuthal angle
between the K + K − and μ + μ − planes is ϕ h .
The analysis of the B 0
s → J/ψφ events is further complicated by a small
fraction of non-resonant B 0
s → J/ψK + K − decays (CP-odd) which interfere with
the φ meson decaying to two charged kaons. These non-resonant events need to be
considered. Effectively one therefore studies B 0
s decays to J/ψK + K − .
6 In the Standard Model the phase φ s determined by the measurement of the time-dependent CP
asymmetry in the decay B 0
s → J/ψφ equals in leading order to −2β s with β s being defined in
Sect. 9.7. However, in case of new physics effects the two phases could differ. In the context of this
textbook these differences are ignored.