HFAG Unitarity Triangle - Results Summer 2003

Results on Time-Dependent CP Measurements: Summer 2003 (Lepton-Photon 2003 [LP'03], FNAL)

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 → dd-bar s (K_Sπ⁰) (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→ 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)	(1.534 ± 0.013) ps	HFAG - Oscillations/Lifetime (Summer 2003)
Δm_d	(0.502 ± 0.006) ps^–1	HFAG - Oscillations/Lifetime (Summer 2003)
\|A_^\|²	no update for LP'03: 0.160 ± 0.032 ± 0.014	BABAR, PRL 87 (2001) 241801
	no update for LP'03: 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	no update for LP'03: 0.741 ± 0.067 ± 0.034	0.733 ± 0.057 ± 0.028	0.736 ± 0.049 (0.043_stat-only)	CL = 0.93
ΦK_S	0.45 ± 0.43 ± 0.07	–0.96 ± 0.50 ^+0.09_–0.11	–0.14 ± 0.33 (0.33_stat-only) CL=0.036	BABAR LP'03 (preliminary) BABAR PRL 91 (2003) 161801 Belle hep-ex/0308035 (submitted to PRL)
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
K⁺K^–K_S	not yet available	0.51 ± 0.26 ± 0.05 ^+0.18_–0.00	0.51 ± 0.26 ± 0.05 ^+0.18_–0.00
All b → s penguin	0.24 ± 0.15 (0.15_stat-only)			CL = 0.11
All modes	0.692 ± 0.047 (0.42_stat-only)			CL = 0.0097

Note that

The sine coefficient, S_ξ, of the s penguins modes with CP eigenvalue ξ gives S = –ξsin(2β/φ₁) (minus sign due to the occurrence of a V_ts in the penguin decay amplitude). The modes ΦK_S and η'K_S are CP-odd (ξ=–1), while K⁺K^–K_S may have both CP-even and CP-odd contributions. From an angular analysis Belle concludes that K⁺K^–K_S is primarily CP-even (ξ=+1), with a fraction of 1.03 ± 0.15 ± 0.05.
Averaging over all s penguin modes assumes that the flavor singlet contribution in η'K_S, providing an additional phase γ, is negligible.

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

Parameter: sin(2β/φ₁) (no updates for LP'03)
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	0.695 ± 0.047

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	no update for LP'03: \|λ\| = 0.948 ± 0.051 ± 0.030	no update for LP'03: 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	no update for LP'03: C = 0.053 ^+0.055_–0.052 ^+0.032_–0.031	no updated for LP'03: 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	–0.38 ± 0.37 ± 0.12	0.15 ± 0.29 ± 0.08 (added DCSD systematics)	–0.04 ± 0.24 CL=0.28	BABAR LP'03 (preliminary) BABAR PRL 91 (2003) 161801 Belle-CONF-0344, LP'03 (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
K⁺K^–K_S	not yet available	0.17 ± 0.16 ± 0.05 (added DCSD systematics)	0.17 ± 0.16 ± 0.05
All b → s penguin	0.07 ± 0.09 (0.09_stat-only)			CL = 0.76
All modes	0.056 ± 0.040 (0.034_stat-only)			CL = 0.93

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 sin(2β/φ₁)
(the two right hand plots show averaged values; note that π⁰K_S is not a pure s-penguin but may have tree contributions)

eps gif gif(high res)

Constraining 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 improved Wolfenstein parameterization of the CKM matrix) with the constraints from other experimental input. The right hand figures show these constraints with and without using the HFAG average of sin(2β) in the global fit.	α, β, γ convention:		φ₁, φ₂, φ₃ convention:
	eps gif gif (high res)	eps gif gif (high res)	eps gif gif (high res)	eps gif gif (high res)

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
no update for LP'03: 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
no update for LP'03: 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)

Time-dependent CP Asymmetries in b → dd-bar s (K_Sπ⁰)

The measurement of the time-dependent CP asymmetry in the decay B_d→K_Sπ⁰ is complicated by the lifetime of the K_S. Thus, in spite of the decent branching fraction of this mode, the errors on the CP parameters are large. If the penguin amplitude is dominant (the tree amplitude is Cabibbo and color-suppressed), this mode approximately measures S_{K_Sπ⁰}=sin(2β/φ₁) and C_{K_Sπ⁰}=0. Tree contributions could modify these relations.

Experiment	S_{K_Sπ⁰}	C_{K_Sπ⁰}	Ref. / Comments
BABAR	0.48 ^+0.38_–0.47 ± 0.11	0.40 ^+0.27_–0.28 ± 0.10	PLOT-0053 preliminary (LP'03)
Belle	not yet available

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)
no update for LP'03: Belle'02 N(BB)=85m	–1.23 ± 0.41 ^+0.08_–0.07	–0.77 ± 0.27 ± 0.08	–0.02	Phys.Rev. D68 (2003) 012001
Average	–0.58 ± 0.20	–0.38 ± 0.16	–0.02	χ² = 6.1 (CL = 0.047 → 2.0σ)
Figures:	eps gif gif (high res)	eps gif gif (high res)	nothing

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 .

See the right hand plot for a confidence level representation of the P/T phase versus its module.

eps gif gif (high res)

Constraining α: using as input the measured C_ππ and S_ππ coefficients together with the present (HFAG) ππ branching fractions of all charges and B_dflavors (including the newly discovered π⁰π⁰), one can perform various numerical analyses aiming at a constraint on α.

The Gronau-London SU(2) analysis (electroweak penguins and other SU(2)-breaking sources are neglected here).
Assuming SU(3) symmetry, one can identify the module of the penguin occurring in the π⁺π^– amplitude with the Cabibbo-enhanced penguin in B_d decays to K⁺π^–. No SU(3)-breaking corrections are applied here.
Assuming SU(3) symmetry, one can identify the module of the penguin occurring in the π⁺π^– amplitude with the penguin decay of a B⁺ to K⁰π⁺. First order SU(3)-breaking corrections have been applied here.
In contrast to the phenomenological methods above, once can apply QCD Factorization (BBNS) predicting the complex penguin-to-tree ratio, to constrain α from the time-dependent CP measurement.

The confidence levels obtained with these methods are shown in the right hand figure. It is compared to the constraint obtained from the global CKM fit using the standard constraints (including the HFAG average of sin(2β).

eps gif gif (high res)

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'02 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	BABAR hep-ex/0306030 (submitted to PRL) LP'03 update: BABAR-Plot-0055 (preliminary)
Belle	not yet available

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.

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	0.063 ± 0.041 ± 0.016 ± 0.013_D*lν	–0.038 ± 0.021 CL=0.05 (2.0σ)	BABAR hep-ex/0310037 (partial. rec., preliminary) (submitted to PRL) BABAR hep-ex/0309017 (fully rec., preliminary) (submitted to PRL) Belle hep-ex/0308048 (preliminary)
c*	–0.004 ± 0.037 ± 0.020 (lepton tags only)	0.031 ± 0.070 ± 0.033 (lepton tags only)	0.030 ± 0.041 ± 0.016 ± 0.030_D*lν	0.012 ± 0.030 CL=0.85 (0.2σ)
a	-	–0.022 ± 0.038 ± 0.020	–0.058 ± 0.038 ± 0.013	–0.041 ± 0.029 CL=0.54 (0.6σ)
c	-	0.025 ± 0.068 ± 0.033 (lepton tags only)	–0.036 ± 0.038 ± 0.013 ± 0.036_DCSD	–0.015 ± 0.044 CL=0.51 (0.7σ)

⁽*⁾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	δ	Correlations	Ref. / Comments
Belle'03 N(BB)=151m	95° ^+25°_–20° ± 13° ± 10°_model	162° ^+20°_–25° ± 12° ± 24°_model	?	Belle-CONF-0343, hep-ex/0308043 (preliminary)
BABAR	not yet available

This page is maintained by Andreas Höcker and was last updated on September 8, 2003

Results on Time-Dependent CP Measurements: Summer 2003 (Lepton-Photon 2003 [LP'03], FNAL)

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 b → dd-bar s (KSπ0)

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

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

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 → dd-bar s (K_Sπ⁰)

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→ D⁽*^)+–π^–+

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