9 Symmetry Violations and Quark Flavour Physics
605
• The Grossman-Ligeti-Soffer (GLS) method [125] is similar to the ADS method
but uses singly Cabibbo-suppressed decays such as D → K S K + π − decays.
• The Giri-Grossman-Soffer-Zupan (GGSZ) method [126] uses self-conjugate
multibody D meson decay modes like K S π + π − or K S K + K − and requires an
analysis of the Dalitz plot to account for the varying D decay parameters. A
model-dependent analysis assumes specific D decay amplitudes while a modelindependent approach uses external input for the strong-phase difference δ D and
the D amplitude ratio r D in bins of the Dalitz space.
Simultaneous fits to several observables, CP asymmetries or ratios of suppressed
to favored modes, allow the determination of the decay parameters including the
CKM phase γ . The main issue with all methods is the small overall branching
fraction of the observable decays which range from 5 × 10 −5 to 5 × 10 −9 [127].
The precise determination of the CKM phase γ therefore requires a very large datasample. The B factories have pioneered different methods to determine γ , however
the achieved overall statistical precision on γ was limited. Combining the different
methods and quoting a single result for γ , BABAR and Belle report the following
values [127]:
γ = (69 ± 17)
◦ (BABAR) ,
γ = (68 ± 14)
◦ (Belle) .
The breakthrough towards a precision determination of the phase γ came
when the LHCb experiment was able to measure even very rare doubly Cabibbosuppressed decays such as B − →
π − K +
D
K − and its charge-conjugated
counter-parts with sufficiently high statistics to observe CP asymmetries. Figure 9.37 shows as an example the decay B − →
π − K +
D
K − as well as the
decay B − →
π − K +
D
π − which also provides sensitivity to γ together with the
corresponding charge conjugated decays [128]. The observed yields clearly signal
direct CP violation for both channels. LHCb has analysed B + → DK + decays
with a multitude of different decay modes of the neutral D, B + → D ∗ K + and
B + → DK ∗+ decays and B 0 → DK ∗ decays. In addition time-dependent analyses
of B 0
s → D ∓
s K ± and B 0 → D ∓ π ± are performed and measure combinations of
the CKM phases γ and β s or β, respectively. The combination of the different LHCb
measurements [129] finally result into a value of
γ = (74.0
+5.0
−5.8 )
◦ (LHCb) ,
(9.212)
in perfect agreement with the early measurements by BABAR and Belle. For the
average of all γ measurements one finds [87],
γ = (73.5
+4.2
−5.1 )
◦ .
(9.213)
605
• The Grossman-Ligeti-Soffer (GLS) method [125] is similar to the ADS method
but uses singly Cabibbo-suppressed decays such as D → K S K + π − decays.
• The Giri-Grossman-Soffer-Zupan (GGSZ) method [126] uses self-conjugate
multibody D meson decay modes like K S π + π − or K S K + K − and requires an
analysis of the Dalitz plot to account for the varying D decay parameters. A
model-dependent analysis assumes specific D decay amplitudes while a modelindependent approach uses external input for the strong-phase difference δ D and
the D amplitude ratio r D in bins of the Dalitz space.
Simultaneous fits to several observables, CP asymmetries or ratios of suppressed
to favored modes, allow the determination of the decay parameters including the
CKM phase γ . The main issue with all methods is the small overall branching
fraction of the observable decays which range from 5 × 10 −5 to 5 × 10 −9 [127].
The precise determination of the CKM phase γ therefore requires a very large datasample. The B factories have pioneered different methods to determine γ , however
the achieved overall statistical precision on γ was limited. Combining the different
methods and quoting a single result for γ , BABAR and Belle report the following
values [127]:
γ = (69 ± 17)
◦ (BABAR) ,
γ = (68 ± 14)
◦ (Belle) .
The breakthrough towards a precision determination of the phase γ came
when the LHCb experiment was able to measure even very rare doubly Cabibbosuppressed decays such as B − →
π − K +
D
K − and its charge-conjugated
counter-parts with sufficiently high statistics to observe CP asymmetries. Figure 9.37 shows as an example the decay B − →
π − K +
D
K − as well as the
decay B − →
π − K +
D
π − which also provides sensitivity to γ together with the
corresponding charge conjugated decays [128]. The observed yields clearly signal
direct CP violation for both channels. LHCb has analysed B + → DK + decays
with a multitude of different decay modes of the neutral D, B + → D ∗ K + and
B + → DK ∗+ decays and B 0 → DK ∗ decays. In addition time-dependent analyses
of B 0
s → D ∓
s K ± and B 0 → D ∓ π ± are performed and measure combinations of
the CKM phases γ and β s or β, respectively. The combination of the different LHCb
measurements [129] finally result into a value of
γ = (74.0
+5.0
−5.8 )
◦ (LHCb) ,
(9.212)
in perfect agreement with the early measurements by BABAR and Belle. For the
average of all γ measurements one finds [87],
γ = (73.5
+4.2
−5.1 )
◦ .
(9.213)