HFAG CPV & Unitarity Triangle - Results Winter 2004

Results on Time-Dependent CP Measurements: Winter 2004 (Moriond 2004)

Averages are performed for

Time-dependent CP asymmetries in b → cc-bar s and b → s penguin (sin2β/φ₁)
Time-dependent CP asymmetries in b → cc-bar d (D⁽*⁾⁺D⁽*⁾^–, J/ψ π⁰) (sin2β_eff)
Time-dependent CP asymmetries in B_d→ π⁺π^– (sin2α_eff/φ_2,eff)
Time-dependent CP asymmetries in B_d→ ρ^+–π^–+ (sin2α_eff)
Time-dependent CP asymmetries in B_d→ ρ⁺ρ^– (sin2α_eff/φ_2,eff)
Time-dependent CP Asymmetries in B_d→ D⁽*^)+–π^–+ (sin(2β+γ/phi₃))
Dalitz Plot Analysis of B→ D⁰(→ K_Sπ⁺π^–, ...)K (γ)

Legend: if not stated otherwise,

if two errors are given, the first is statistical and the second systematic
if one error is given it represents the total error, where statistical and systematic uncertainties have been added in quadrature.

We use Combos v3.20 (homepage, manual) for the rescaling of the experimental results to a common set of input parameters.

021003

Time-dependent CP Asymmetries in b → cc-bar s and b → qq-bar s (penguin)

The experimental results have been rescaled to a common set of input parameters (see table below).

Parameter	Value	Ref. / Comments
τ(B_d)	(1.536 ± 0.014) ps	HFAG - Oscillations/Lifetime (Winter 2004)
Δm_d	(0.502 ± 0.007) ps^–1	HFAG - Oscillations/Lifetime (Winter 2004)
\|A_^\|²	0.160 ± 0.032 ± 0.014	BABAR, PRL 87 (2001) 241801
	0.192 ± 0.023 ± 0.026	Belle, PL B538 (2002) 11-20
	0.176 ± 0.025	Average used for rescaling

We obtain for sin(2β/φ₁) in the different decay modes:
(Both BABAR and Belle assigned the (correlated) systematic error of 0.008 to sin(2β/φ₁) for the uncertainty on tag side CP asymmetries due to Doubly-Cabibbo-suppressed B decays. See Ref. PRL 91 (2003) 161801.)

Parameter: sin(2β/φ₁) (if β/φ₁ dominant weak phase)
Mode	BABAR	Belle	Average	Ref. / Comments
J/ψK_S, ψ(2S)K_S, χ_c1K_S, η_CK_S	0.76 ± 0.07_stat	0.73 ± 0.06_stat	-	BABAR PRL 89 (2002) 201802 Belle-CONF-0353, LP'03 (preliminary)
J/ψK_L (η_CP=+1)	0.72 ± 0.16_stat	0.80 ± 0.13_stat
J/ψK⁰ (K⁰ → K_Sπ⁰	0.22 ± 0.52_stat	0.10 ± 0.45_stat
All charmonium	0.741 ± 0.067 ± 0.034	0.733 ± 0.057 ± 0.028	0.736 ± 0.049 (0.043_stat-only)	CL = 0.93
ΦK⁰	0.47 ± 0.34 ^+0.08_–0.06	–0.96 ± 0.50 ^+0.09_–0.11	0.02 ± 0.29 (0.28_stat-only) CL=0.021	BABAR hep-ex/0403026 (submitted to PRL) BABAR PRL 91 (2003) 161801 PRL 91, 261602 (2003) BABAR Moriond-EW (2004) (preliminary)
η'K_S	0.02 ± 0.34 ± 0.03	0.43 ± 0.27 ± 0.05	0.27 ± 0.21 (0.21_stat-only) CL=0.35
f₀K_S	1.62 ^+0.51_–0.56 ± 0.10	not yet available	1.62 ^+0.51_–0.56 ± 0.10
π⁰K_S	0.48 ^+0.38_–0.47 ± 0.11	not yet available	0.48 ^+0.38_–0.47 ± 0.11
K⁺K^–K_S	0.56 ± 0.25 ± 0.04 ^+0.17_–0.00	0.51 ± 0.26 ± 0.05 ^+0.18_–0.00	0.54 ± 0.18 ^+0.17_–0.00 (0.18_stat-only) CL=0.89
All b → s penguin	0.42 ± 0.12 (0.12_stat-only)			CL = 0.03
All modes	0.690 ± 0.045 (0.41_stat-only)			CL = 0.0088

Note that

Assuming a single and vanishing weak phase dominates the decay amplitudes of the penguin modes, one has S_η = –ηsin(2β/φ₁), where η is the CP eigenvalue of the final state. Namely, η=+1 for f₀K_S, K⁺K^–K_S and η=–1 for ΦK_S, η'K_S, π⁰K_S and CP(K_S)=–CP(K_L).
The mode K⁺K^–K_S may have both CP-even and CP-odd contributions. From an isospin analysis Belle concludes that K⁺K^–K_S is primarily CP-even (η=+1), with a fraction of 1.03 ± 0.15 ± 0.05. This result is confirmed by BABAR, who find a CP-even fraction of 0.98 ± 0.15 ± 0.04.
Averaging over all s penguin modes assumes that contributions with non-zero weak phases to the decay amplitudes can be neglected.

Including the earlier sin(2β/φ₁) measurements using B_d → J/ψK_S decays:

Parameter: sin(2β/φ₁)
Experiment	Value	Ref. / Comments
ALEPH	0.84 ^+0.82_–1.04 ± 0.16	PL B492 (2000) 259-274
OPAL	3.2 ^+1.8_–2.0 ± 0.5	EPJ C5 (1998) 379-388
CDF (full Run I)	0.79 ^+0.41_–0.44(stat+syst)	PRD 61 (2000) 072005

we find the only slightly modified averages:

Parameter: sin(2β/φ₁)
All charmonium	0.739 ± 0.048
All modes	0.692 ± 0.045

The cosine coefficient: the experiments determine |λ| for the charmonium modes and C = –A = (1–|λ|²)/(1+|λ|²) for the penguin modes. We recompute C from |λ| for the following averages.

Parameter: C=–A (if not stated otherwise)
Mode	BABAR	Belle	Average	Ref. / Comments
Charmonium	\|λ\| = 0.948 ± 0.051 ± 0.030	0.950 ± 0.049 ± 0.034 (added DCSD systematics)	0.949 ± 0.045 (0.035_stat-only) CL = 0.98	BABAR PRL 89 (2002) 201802 Belle PRD 66 (2002) 071102
Charmonium	C = 0.053 ^+0.055_–0.052 ^+0.032_–0.031	0.051 ^+0.053_–0.050 ^+0.035_–0.036 (added DCSD systematics)	0.052 ^+0.048_–0.046 (0.037_stat-only) CL = 0.98	BABAR PRL 89 (2002) 201802 Belle PRD 66 (2002) 071102
ΦK_S	0.01 ± 0.33 ± 0.10	0.15 ± 0.29 ± 0.08 (added DCSD systematics)	0.09 ± 0.23 CL=0.76	BABAR hep-ex/0403026 (submitted to PRL) BABAR PRL 91 (2003) 161801 PRL 91, 261602 (2003) BABAR Moriond-EW (2004) (preliminary)
η'K_S	0.10 ± 0.22 ± 0.04 (added DCSD systematics)	0.01 ± 0.16 ± 0.05 (added DCSD systematics)	0.04 ± 0.13 CL=0.75
f₀K_S	0.27 ± 0.36 ± 0.12	not yet available	0.27 ± 0.36 ± 0.12
π⁰K_S	0.40 ^+0.27_–0.28 ± 0.10	not yet available	0.40 ^+0.27_–0.28 ± 0.10
K⁺K^–K_S	–0.10 ± 0.19 ± 0.09	0.17 ± 0.16 ± 0.05 (added DCSD systematics)	0.07 ± 0.13 CL=0.31
All b → s penguin	0.09 ± 0.08 (0.08_stat-only)			CL = 0.92
All modes	0.059 ± 0.039 (0.033_stat-only)			CL = 0.97

Digression and plots:

Constraining C_{J/ψ Ks} from A_CP(B⁺ → J/ψ K⁺) and A_SL: as suggested by Y. Nir, one can obtain a powerful SM constraint on |λ| = |q/p||A-bar/A| via the relations A_SL = (1–|q/p|⁴)/(1+|q/p|⁴) and A_CP(B⁺ → J/ψ K⁺) = (|A-bar/A|²–1)/(|A-bar/A|²+1), where A_SL denotes the CP asymmetry in semileptonic B decays, and A_CP(B⁺ → J/ψ K⁺) is the CP-violating charge asymmetry measured in B⁺ → J/ψ K⁺ decays. Averaging the A_SL results from BABAR, CLEO, ALEPH and OPAL, as well as the A_CP(B⁺ → J/ψ K⁺) results from BABAR, Belle and CLEO, we find A_SL = 0.001 ± 0.014 and A_CP(B⁺ → J/ψ K⁺) = –0.007 ± 019. This gives |q/p| = 0.9996 ^+0.0068_–0.0067, |A-bar/A| = 0.993 ± 0.018, and hence |λ|_indirect = 0.992 ± 0.019 (see right hand plot below).
Discussion: the amplitude relation between neutral and charged B → J/ψ K decays has been found by Fleischer-Mannel to hold up to negligible corrections of the order O(λ³). However, it was pointed out by D. Kirkby that the identification of |λ|, measured through the C coefficient in B⁰ → J/ψ K⁰, with |q/p||A-bar/A| assumes ΔΓ_Bd=0. The ratio ΔΓ_Bd/Δm_Bd it is expected to be small in the SM.

Compilation of results for –ηS ≈ sin(2β/φ₁) and C
(the two right hand plots show averages)

eps gif gif(high res)

Constraining the Unitarity Triangle (ρ, η): the measurement of sin(2β) from charmonium modes can be compared in the ρ-bar-η-bar plane (ρ-bar, η-bar being the parameters in the exact (unitary) Wolfenstein parameterization of the CKM matrix) with the constraints from other experimental inputs.

Visit the CKMfitter homepage and the UTfit homepage for results on global CKM fits using different fit techniques and input quantities.

Time-dependent CP Asymmetries in b → cc-bar d (D⁽⁾⁺D⁽⁾^–, J/ψ π⁰)

Due to possible significant penguin pollution both, the cosine and the sine coefficients of the Cabibbo-suppressed b → cc-bar d decays are free parameters of the theory. Absence of penguin pollution would signify S_{cc-bar d}=–sin(2β/φ₁) and C_{cc-bar d}=0.

At present we do not apply a rescaling of the results to a common, updated set of input parameters. Both, BABAR and Belle use the PDG 2002 values for the neutral B lifetime and oscillation frequency in their time-dependent likelihood fits.

Experiment	S_J/ψπ0	C_J/ψπ0 = –A_J/ψπ0	Correlation	Ref. / Comments
BABAR'02 N(BB)=88m	0.05 ± 0.49 ± 0.16	0.38 ± 0.41 ± 0.09	–0.12	PRL 91 (2003) 061802
Belle'03 N(BB)=151m	–0.72 ± 0.42 ± 0.08	0.01 ± 0.29 ± 0.07	–0.12	Belle CONF-0342 (LP'03)
Average (preliminary)	–0.40 ± 0.33	0.13 ± 0.24	–0.12	χ² = 2.1 (CL = 0.36 → 0.9σ)
Figures:	eps gif gif (high res)	eps gif gif (high res)	nothing

We convert Im(λ) = S/(1 + C) and |λ|² = (1 – C)/(1 + C), taking into account correlations:

Experiment	S_D+D–	C_D+D–	Correlation	Ref. / Comments
BABAR'03 N(BB)=88m	Im(λ) = 0.05 ± 0.29 ± 0.10	\|λ\| = 0.75 ± 0.19 ± 0.02	0.18	PRL 91 (2003) 131801 f(CP-odd) = 0.063 ± 0.055 ± 0.009
BABAR'03 N(BB)=88m	S = 0.06 ± 0.37 ± 0.13	C = 0.28 ± 0.23 ± 0.02	–0.15	PRL 91 (2003) 131801 f(CP-odd) = 0.063 ± 0.055 ± 0.009
Belle	not yet available

Experiment	S_+–(D*⁺D^–)	C_+–(D*⁺D^–)	S_–+(D*^–D⁺)	C_–+(D*^–D⁺)	A_+–	Ref. / Comments
BABAR'03 N(BB)=89m	–0.82 ± 0.75 ± 0.14	–0.47 ± 0.40 ± 0.12	–0.24 ± 0.69 ± 0.12	–0.22 ± 0.37 ± 0.10	–0.03 ± 0.11 ± 0.05	PRL 90 (2003) 221801
Belle	not yet available

Compilation of results for sin(2β_eff/φ_1,eff)=–S (left figure) and C (right figure) from time-dependent b → cc-bar d analyses. The results are compared to the values from the corresponding charmonium averages.

eps gif gif(high res)

021003

Time-dependent CP Asymmetries in B_d→ π⁺π^–

At present we do not apply a rescaling of the results to a common, updated set of input parameters. Correlation due to common systematics are neglected in the following averages.

Experiment	S_ππ	C_ππ = –A_ππ	Correlation	Ref. / Comments
BABAR'03 N(BB)=123m	–0.40 ± 0.22 ± 0.03	–0.19 ± 0.19 ± 0.05	–0.02	BABAR-Plot-0053 (preliminary)
updated Winter'04: Belle'04 N(BB)=152m	–1.00 ± 0.21 ± 0.07	–0.58 ± 0.15 ± 0.07	–0.286	hep-ex/0401029
Average	–0.74 ± 0.16	–0.46 ± 0.13	–0.17	χ² = 6.9 (CL = 0.031 → 2.2σ)
Figures:	eps gif gif (high res)	eps gif gif (high res)	nothing

Digression and plots:

(The following numerical exercises involve the SU(2) and SU(3) partners of the B_d→ π⁺π^– decay. The relevant branching ratios and direct CP-violating asymmetries are taken from HFAG - Rare Decays (Winter 2004) averages.)

The Penguin-to-tree ratio: using as input the measured C_ππ and S_ππ coefficients together with the Wolfenstein parameters ρ and η from the Global CKM fit using standard constraints, one can infer module and phase of the complex penguin to tree (P/T) ratio in B_d→ π⁺π^– decays within the Standard Model. Note that the definition of P/T is convention-dependent (see, e.g., GroRo02). We choose to eliminate the charm quark in the penguin loop using CKM unitarity, so that the amplitudes can be parameterized as follows:

A(B_d→ π⁺π^–)	=	R_u e^{i γ} T + R_t e^{i –β}P ,
A(B_d-bar→ π⁺π^–)	=	R_u e^{–i γ} T + R_t e^{i β} P .

Plots for confidence level representations of the P/T phase versus its module can be found on the corresponding CKMfitter and UTfit pages.

Time-dependent CP Asymmetries in B_d→ ρ^+–π^–+

The CP(t) analysis of B_d→ ρ^+–π^–+ decays involves 5 different parameters, one of which – the charge asymmetry A_CP(ρπ) – is time-independent. The decay rate is given by
f^{ρ^+–π^–+}(Q_tag,Δt) = (1 +– A_CP(ρπ)) e^–|Δt|/τ/4τ × [1 + Q_tag(S_ρπ+–ΔS_ρπ)sin(ΔtΔm) – Q_tag(C_ρπ+–ΔC_ρπ)cos(ΔtΔm)] ,
where Q_tag=+1(–1) when the tagging meson is a B⁰ (B⁰-bar). CP symmetry is violated if either one of the following conditions is true: A_CP(ρπ)≠0, C_ρπ≠0 or S_ρπ≠0. The first two correspond to "direct" CP violation, while the last condition is CP violation in the interference of decay amplitudes with and without B_d mixing.

At present we do not apply a rescaling of the results due to the fit dependence on the B_d lifetime and oscillation frequency.

Experiment	A_CP(ρπ)	S_ρπ	C_ρπ	ΔS_ρπ	ΔC_ρπ	Correlations	Ref. / Comments
BABAR'03 N(BB)=123m	–0.114 ± 0.062 ± 0.027	–0.13 ± 0.18 ± 0.04	0.35 ± 0.13 ± 0.05	0.33 ± 0.18 ± 0.03	0.20 ± 0.13 ± 0.05	Table	LP'03 update: BABAR-Plot-0055 (preliminary)
Belle	not yet available

Digression and plots:

Direct CP violation: as shown by Charles it is convenient to transform the experimentally motivated direct CP parameters A_CP(ρπ) and C_ρπ into the physically motivated
A^+–(ρπ) = (|κ^+–|²–1)/(|κ^+–|²+1) = –(A_CP(ρπ)+C_ρπ+A_CP(ρπ)ΔC_ρπ)/(1+ΔC_ρπ + A_CP(ρπ)C_ρπ),
A^–+(ρπ) = (|κ^–+|²–1)/(|κ^–+|²+1) = (–A_CP(ρπ)+C_ρπ+A_CP(ρπ)ΔC_ρπ)/(–1+ΔC_ρπ + A_CP(ρπ)C_ρπ),
where κ^+–=(q/p)Abar^–+/A^+– and κ^–+=(q/p)Abar^+–/A^–+. With this definition A^–+(ρπ) (A^+–(ρπ)) describes direct CP violation in B_d decays where the ρ is emitted (not emitted) by the spectator interaction.

Taking into account experimental correlations, one finds
A^+–(ρπ) = –0.18 ± 0.13 ± 0.05,
A^–+(ρπ) = –0.52 ^+0.17_–0.19 ± 0.07,
where the first errors are statistical and the second systematic. The two quantities are experimentally correlated to +51%. The probability to observe these numbers in the absence of direct CP violation is 1.5%. See right hand plot for a confidence level representation in the A^+–(ρπ) versus A^–+(ρπ) plane.

eps gif gif (high res)

Flavor-charge specific branching fractions: the charge and flavor asymmetry parameters A_CP(ρπ), C_ρπ and ΔC_ρπ can be used to derive flavor-charge specific rates from the HFAG branching fraction BR(B_d→ ρ^+–π^–+)=(24.0 ± 2.5) 10^–6.

For individual B flavors and ρ charges:
BR_{B_f→ρ^Qπ^–Q}(f,Q)=0.5(1+Q A_CP(ρπ))(1+f(C_ρπ +Q ΔC_ρπ))BR(B_d→ ρ^+–π^–+),
where Q is the ρ charge, f(B_d)=1 and f(B_d-bar)=–1. One finds

BR_{B→ ρ⁺π^–}	=	(16.5 ^+3.1 _–2.8) 10^–6
BR_{B→ ρ^–π⁺}	=	(15.4 ^+3.2 _–2.9) 10^–6
BR_{B-bar→ ρ⁺π^–}	=	(4.8 ^+2.6 _–2.3) 10^–6
BR_{B-bar→ ρ^–π⁺}	=	(11.4 ^+2.8 _–2.6) 10^–6

For flavor-averaged inclusive branching fractions:
BR_{B→ ρπ}(+–) = 0.5(BR_{B→ρ⁺π^–} + BR_{B-bar→ ρ^–π⁺}),
BR_{B→ ρπ}(–+) = 0.5(BR_{B→ρ^–π⁺} + BR_{B-bar→ ρ⁺π^–}),
where the individual charge-flavor branching fractions are defined on the left. The total (flavor-averaged) ρπ branching fraction is then the sum BR_{B→ ρπ}(+–) + BR_{B→ ρπ}(–+). One finds

BR_{B→ ρπ}(+–)	=	(13.9 ^+2.2 _–2.1) 10^–6
BR_{B→ ρπ}(–+)	=	(10.1 ^+2.1 _–1.9) 10^–6

with an anti-correlation of –28% among the two branching fractions.

Time-dependent CP Asymmetries in B_d→ ρ⁺ρ^–

The vector particles in the pseudoscalar to vector-vector decay B_d→ ρ⁺ρ^– can have longitudinal and transverse relative polarization with different CP properties. The BABAR Collaboration determines the fraction of longitudinally polarized events with an angular analysis to be f_long=0.99±0.03^+0.04_–0.03, so that a per-event transversity analysis can be avoided and only the longitudinal CP parameters are determined. At present we do not apply a rescaling of the results to a common, updated set of input parameters.

Experiment	S_long	C_long	Correlation	Ref. / Comments
BABAR'04 N(BB)=123m	–0.19 ± 0.33 ± 0.11	–0.23 ± 0.24 ± 0.14	0.04	BABAR Moriond-EW (2004) (preliminary)
Belle	not yet available

Digression and plots:

(The following numerical exercises involve the SU(2) and SU(3) partners of the B_d→ ρ⁺ρ^– decay. The relevant branching ratios and direct CP-violating asymmetries are taken from HFAG - Rare Decays (Winter 2004) averages.)

The Penguin-to-tree ratio: using as input the measured C_long and S_long coefficients together with the Wolfenstein parameters ρ and η using standard constraints, one can infer module and phase of the complex penguin to tree (P/T) ratio as done in the ππ case. Plots for confidence level representations of the P/T phase versus its module can be found on the corresponding CKMfitter and UTfit pages.

Constraining α: using as input the measured C_long and S_long coefficients together with the present (HFAG) ρρ branching fractions and longitudinal polarization fractions (including the limit on ρ⁰ρ⁰, for which the polarization is unknown), one can perform the Gronau-London isospin analysis (electroweak penguins can be taken into account, while other SU(2)-breaking effects are usually neglected). Plots for confidence level representations of the P/T phase versus its module can be found on the corresponding CKMfitter and UTfit pages.

021003

Time-dependent CP Asymmetries in B_d→ D⁽*^)+–π^–+

Albeit not CP eigenstates, partially and fully reconstructed B_d→ D⁽*^)+–π^–+ decays provide sensitivity to γ because of the interference between the Cabibbo-favoured amplitude of the decay B_d→ D⁽*^)–π⁺ with the doubly Cabibbo-suppressed amplitude of B_d→ D⁽*⁾⁺π^–. The relative weak phase between these two amplitudes is –γ and, when combined with the B_dB_d-bar mixing phase, the total phase difference is –(2β+γ) [–(2φ₁+φ₃)]. The interpretation of the observables in terms of UT angles requires external input on the ratio r⁽*⁾=|A(B⁰-bar→ D⁽*^)–+π^+–)/A(B⁰→ D⁽*^)–+π^+–)|. This can be obtained experimentally from the corresponding flavor-tagged branching fractions, or from similar modes that are easier to measure, like ratios of branching fractions of the charged B⁺→ D⁽*⁾⁺π⁰ to the neutral Cabibbo-favored mode, or involving self-tagging decays with strangeness like B_d→ D_s⁽*^)–π⁺. Corrections, e.g., for SU(3) breaking in the latter case, have to be applied, the theoretical uncertainties of which are hard to quantify.

BABAR and Belle use two sets of observables:
S⁽*^)± = 2r⁽*⁾sin(2β+γ±δ⁽*⁾)
and
a⁽*⁾ = (S⁽*⁾⁺+S⁽*^)–)/2 = 2r⁽*⁾sin(2β+γ)cos(δ⁽*⁾)
c⁽*⁾ = (S⁽*⁾⁺–S⁽*^)–)/2 = 2r⁽*⁾cos(2β+γ)sin(δ⁽*⁾)
so that S⁽*⁾⁺=a⁽*⁾+c⁽*⁾ and S⁽*^)–=a⁽*⁾–c⁽*⁾. (Note that Belle multiplies the S coefficient by the CP parity (-1)^L; the two experiments chose the convention so that S*^±[BABAR]=S*^±[Belle] and S^±[BABAR]=–S^±[Belle], and hence a*,c*[BABAR]=a*,c*[Belle] and a,c[BABAR]=–a,c[Belle]). These definitions are valid in the limit of small r⁽*⁾≈0.02 only. Due to the disparate strength of the two interfering amplitudes, CP asymmetry is expected to be small, so that the possible occurence of CP violation on the tag side becomes an important obstacle. Tag side CPV is absent for semileptonic B decays (mostly lepton tags). The parameter a⁽*⁾ is independent of tag side CPV.

At present we do not rescale the results to a common set of input parameters. Also, common systematic errors are not subtracted.

Observable	BABAR		Belle	Average*	Ref. / Comments
Observable	partially reconstructed	fully reconstructed	fully reconstructed	Average*	Ref. / Comments
a*	–0.063 ± 0.024 ± 0.014	–0.068 ± 0.038 ± 0.020	0.060 ± 0.040 ± 0.017	–0.037 ± 0.021 CL=0.04	BABAR hep-ex/0310037 (partial. rec., preliminary) (submitted to PRL) BABAR hep-ex/0309017 (fully rec., preliminary) (submitted to PRL) Belle hep-ex/0308048 (submitted to PRL)
c*	–0.004 ± 0.037 ± 0.020 (lepton tags only)	0.031 ± 0.070 ± 0.033 (lepton tags only)	0.049 ± 0.040 ± 0.019	0.022 ± 0.028 CL=0.68
a	-	–0.022 ± 0.038 ± 0.020	–0.062 ± 0.037 ± 0.016	–0.043 ± 0.029 CL=0.50
c	-	0.025 ± 0.068 ± 0.033 (lepton tags only)	–0.025 ± 0.037 ± 0.018	–0.014 ± 0.036 CL=0.56

⁽*⁾If one wants to constrain |sin(2β+γ)| from these measurements, one is in general advised to use toy Monte Carlo methods (e.g., à la Feldman-Cousin) to take into account the modification of the confidence level due to the presence of the triginometric boundaries. While CL modifications are significant for the BABAR result using partially reconstructed D*π decays, a straightforward Prob(Δχ²,1) interpretation of the CL is a good approximation of the complete toy-evaluated CL for the HFAG averages.

Dalitz Plot Analysis of B→ D⁰(→K_Sπ⁺π^–, ...)K

The decay B⁺→ D⁰(D⁰-bar)K⁺ occurs through a Cabbibo-favored (doubly Cabibbo-suppressed) branch. The corresponding amplitudes interfere if the D⁰ and D⁰-bar decay to a common final state, such as K_Sπ⁺π^– or K_SK⁺K^–, etc. Since the Cabibbo-suppressed amplitude invokes the CKM element V_ub, the phase difference between these two processes measures the UT angle γ/φ₃. A Dalitz plots analysis allows to simultaneously determine γ/φ₃ and an unknown strong phase δ.

Experiment	γ/φ₃	Ref. / Comments
Belle'04 N(BB)=152m	81° ± 19°(1σ*) ± 13° ± 11°_model	Belle Lake Luise (2004) and Belle Moriond (2004) (preliminary)
BABAR	not yet available

⁽*⁾ Note that Dalitz plot phases are not Gaussian quantities in general. The 2σ error on γ has been evaluated by Belle to be 46°.

This page is maintained by Andreas Höcker and was last updated on April 9, 2004

Results on Time-Dependent CP Measurements: Winter 2004 (Moriond 2004)

Time-dependent CP Asymmetries in b → cc-bar s and b → qq-bar s (penguin)

Time-dependent CP Asymmetries in b → cc-bar d (D(*)+D(*)–, J/ψ π0)

Time-dependent CP Asymmetries in Bd→ π+π–

Time-dependent CP Asymmetries in Bd→ ρ+–π–+

Time-dependent CP Asymmetries in Bd→ ρ+ρ–

Time-dependent CP Asymmetries in Bd→ D(*)+–π–+

Dalitz Plot Analysis of B→ D0(→KSπ+π–, ...)K

Time-dependent CP Asymmetries in b → cc-bar d (D⁽⁾⁺D⁽⁾^–, J/ψ π⁰)

Time-dependent CP Asymmetries in B_d→ π⁺π^–

Time-dependent CP Asymmetries in B_d→ ρ^+–π^–+

Time-dependent CP Asymmetries in B_d→ ρ⁺ρ^–

Time-dependent CP Asymmetries in B_d→ D⁽*^)+–π^–+

Dalitz Plot Analysis of B→ D⁰(→K_Sπ⁺π^–, ...)K