Results on Time-Dependent CP Measurements:
Winter (Moriond) 2005.

• 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.
• in general: we do not rescale (inflate) the error of an average if inconsistencies between measurements occur.

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

• Assuming that a single and vanishing weak phase dominates the decay amplitudes of the s-penguin modes, one has S_η = –η×sin(2β), where η is the CP eigenvalue of the final state. Namely, η=+1 for f₀K_S, K_SK_SK_S, and η=–1 for φK_S, η'K_S, π⁰K_S, ωK_S, and CP(K_S)=–CP(K_L).
• The mode K⁺K^–K_S may have both CP-even and CP-odd contributions. The CP-even fraction is experimentally derived from an isospin analysis (Belle) or a moments analysis (BABAR).
• Averaging over all s-penguin modes assumes that contributions with non-zero weak phases to the decay amplitudes can be neglected. Note that this assumption may be significantly violated due to doubly CKM-suppressed V_ub penguin amplitudes, and, in some cases, doubly CKM-suppressed and color-suppressed V_ub tree amplitudes that contribute to the decay amplitude. While one can reasonably expect that the golden mode φK⁰ has theoretical uncertainties of the order of 0.05 or smaller, these can be significantly larger for the others (in particular for the non-ss-bar-resonance modes: π⁰K_S, ωK_S and K⁺K^–K_S).
• The presence of a small O(λ²) weak phase in the decay of the s-penguin modes introduces a phase shift that corresponds to the weak phase 2β_s, measured in a time-dependent CP analysis of the decay B_s→ J/ψΦ. Using the Wolfenstein parameterization, and neglecting higher order terms in ρ, η and λ, we can estimate this shift to be:
  S(s-penguin) = –η×sin(2β)[cc-bar s]·(1 + Δ). Numerically, using the global CKM fit results for the Wolfenstein parameters, one finds: Δ = 3.3%, which corresponds to a shift of 2β of +2.1 degrees.

Compilation of results for –η×S ≈ sin(2β)/sin(2φ1) from charmonium and s-penguin decays: BABAR (left) and Belle (right) separately.	eps gif gif(high res)	eps gif gif(high res)
Compilation of results for –η×S ≈ sin(2β)/sin(2φ1) from charmonium and s-penguin decays: BABAR and Belle are shown on one plot.	eps gif gif(high res)
Compilation of results for –η×S ≈ sin(2β)/sin(2φ1) and C: averages of experiments.	eps gif gif(high res)	eps gif gif(high res)
Compilation of results for –η×S ≈ sin(2β)/sin(2φ1) from charmonium and s-penguin decays: world averages.	eps gif gif(high res)

Time-dependent transversity analysis of B⁰→ J/ψK* (cos(2β)/cos(2φ₁))

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

Experiment	SJ/ψπ0	CJ/ψπ0 = –AJ/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'04 N(BB)=152m	–0.72 ± 0.42 ± 0.09	0.01 ± 0.29 ± 0.03	–0.12	PRL 93 (2004) 261801
Average	–0.40 ± 0.33	0.12 ± 0.24	–0.12	χ2 = 2.1 (CL=0.36 → 0.9σ)
Figures:	eps gif gif (high res)	eps gif gif (high res)

Compilation of results for sin(2βeff/φ1,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.

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Time-dependent Analysis of B⁰→ K_Sπ⁰γ

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

Experiment	Sππ	Cππ = –Aππ	Correlation	Ref. / Comments
BABAR'04 N(BB)=227m	–0.30 ± 0.17 ± 0.03	–0.09 ± 0.15 ± 0.04	–0.016	hep-ex/0501071 (submitted to PRL)
Belle'05 N(BB)=275m	–0.67 ± 0.16 ± 0.06	–0.56 ± 0.12 ± 0.06	–0.09	hep-ex/0502035 (submitted to PRL)
Average	–0.50 ± 0.12	–0.37 ± 0.10	–0.056	χ2 =7.9 (CL=0.019 ⇒ 2.3σ)
Figures:	eps gif gif (high res)	eps gif gif (high res)

Constraining α: using as input the measured Cππ and Sππ coefficients together with the present (HFAG) ππ branching fractions and CP asymmetries (including the direct CP-asymmetry measurement for B0→ π0π0), one can perform the Gronau-London isospin analysis. The plot on the right hand side uses the statistical interpretation of the CKMfitter analysis (Rfit) (see the UTfit pages for a Bayesian interpretation). Here, it does not include the Fiertz treatment of electroweak penguins for ππ. Including it would lead to a shift in α of approximately –2 deg. All other SU(2)-breaking effects are also neglected.

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

CP violation in the decay: as shown by Charles it is convenient to transform the experimentally motivated CP parameters ACP(ρπ) and Cρπ into the physically motivated ones A+–(ρπ) = (|κ+–|2–1)/(|κ+–|2+1) = –(ACP(ρπ)+Cρπ+ACP(ρπ)ΔCρπ)/(1+ΔCρπ + ACP(ρπ)Cρπ), A–+(ρπ) = (|κ–+|2–1)/(|κ–+|2+1) = (–ACP(ρπ)+Cρπ+ACP(ρπ)ΔCρπ)/(–1+ΔCρπ + ACP(ρπ)Cρπ), where κ+–=(q/p)Abar–+/A+– and κ–+=(q/p)Abar+–/A–+. With this definition A–+(ρπ) (A+–(ρπ)) describes CP violation in Bd decays where the ρ is emitted (not emitted) by the spectator interaction. Taking into account experimental correlations, one finds A+–(ρπ) = –0.15 ± 0.09, A–+(ρπ) = –0.47 +0.13–0.14. The two quantities have a linear correlation coefficient of +59%. See right hand plot for a confidence level representation in the A+–(ρπ) versus A–+(ρπ) plane.

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Flavor-charge specific branching fractions: the charge and flavor asymmetry parameters ACP(ρπ), Cρπ and ΔCρπ can be used to derive flavor-charge specific rates from the HFAG branching fraction BR(Bd→ ρ+–π–+)=(24.0 ± 2.5)×10–6. For individual B flavors and ρ charges, we define: BRBf→ρQπ–Q(f,Q)=0.5(1+Q ACP(ρπ))(1+f(Cρπ +Q ΔCρπ))BR(Bd→ ρ+–π–+), where Q is the ρ charge, f(Bd)=1 and f(Bd-bar)=–1. One finds BRB→ ρ+π– = (16.5 +2.7 –2.5 )×10–6, BRB→ ρ–π+ = (14.4 +2.4 –2.2 )×10–6, BRB-bar→ ρ+π– = (5.1 +1.9 –1.7 )×10–6, BRB-bar→ ρ–π+ = (12.0 +2.2 –2.0 )×10–6. For flavor-averaged inclusive branching fractions: BRB→ ρπ(+–) = 0.5(BRB→ρ+π– + BRB-bar→ ρ–π+), BRB→ ρπ(–+) = 0.5(BRB→ρ–π+ + BRB-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 BRB→ ρπ(+–) + BRB→ ρπ(–+). One finds BRB→ ρπ(+–) = (13.9 +2.2 –2.1 )×10–6, BRB→ ρπ(–+) = (10.1 +2.1 –1.9 )×10–6, with an anti-correlation of –28% among the two branching fractions.

Experiment	α/φ2 (deg)	δ+– (deg)	Ref. / Comments
BABAR'04 N(BB)=213m	113 +27–17 ± 6	–67 +28–31 ± 7	BABAR-CONF-04/038, hep-ex/0408099
Belle	not yet available
Confidence levels for α (left hand plot) and δ+– (right hand plot) as found by BABAR	eps gif gif (high res)	eps gif gif (high res)

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

Combined α constraint from b → uu-bar d transitions: averaging the confidence level curves from the ππ and ρρ isospin analyses as well as the ρπ Dalitz plot analysis, leads to a the combined constraint: α = (101 +16 –9[1σ] +29–18[2σ]) deg, where the first errors given are at one and the second at two standard deviations, respectively. The isospin analyses are performed following the statistical interpretation of the CKMfitter analysis (Rfit) (see the UTfit pages for a Bayesian interpretation). Here, it does not include the Fiertz treatment of electroweak penguins for ππ and ρρ, leading to a shift in α of approximately –2 deg. All other SU(2)-breaking effects are also neglected.

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Time-dependent CP Asymmetries in B_d → D^+–π^–+, B_d → D*^+–π^–+ and B_d → D^+–ρ^–+

The decays B_d → D^+–π^–+, B_d → D*^+–π^–+ and B_d → D^+–ρ^–+ provide sensitivity to γ/φ₃ because of the interference between the Cabibbo-favoured amplitude (e.g. B⁰ → D^–π⁺) with the doubly Cabibbo-suppressed amplitude (e.g. B⁰ → D⁺π^–). The relative weak phase between these two amplitudes is –γ/–φ₃ and, when combined with the B_dB_d-bar mixing phase, the total phase difference is –(2β+γ)/–(2φ₁+φ₃).

The size of the CP violating effect in each mode depends on the ratio of magnitudes of the suppressed and favoured amplitudes, e.g., r_Dπ = |A(B⁰ → D⁺π^–)/A(B⁰ → D^–π⁺)|. Each of the ratios r_Dπ, r_D*π and r_Dρ is expected to be about 0.02, and can be obtained experimentally from the corresponding suppressed charged B decays, (e.g., B⁺ → D⁺π⁰) using isospin, or from self-tagging decays with strangeness (e.g., B⁰ → D_s⁺π^–), using SU(3). In the latter case, the theoretical uncertainties are hard to quantify. The smallness of the r values makes direct extractions from, e.g., the D^+–π^–+ system very difficult.

Both BABAR and Belle exploit partial reconstructions of D*^+–π^–+ to increase the available statistics. Both experiments also reconstruct D^+–π^–+ and D*^+–π^–+ fully, and BABAR includes the mode D^+–ρ^–+. Additional states with similar quark content are also possible, but for vector-vector final states an angular analysis is required, while states containing higher resonances may suffer from uncertainties due to nonresonant or other contributions.

BABAR and Belle use different observables:

• BABAR defines the time-dependent PDF by
  f^+–(η, Δt) = e^–|Δt|/τ/4τ × [ 1 –+ S_ζ sin(ΔmΔt) –+ η C_ζ cos(ΔmΔt) ]
  where the first (second) sign is used when the tagging meson is a B⁰ (B⁰-bar). [Note here that a tagging B⁰ (B⁰-bar) corresponds to –S_ζ (+S_ζ).] The parameters η and ζ take the values +1 and + (–1 and –) if the final state is, e.g., D^–π⁺ (D⁺π^–). The parameters actually measured by BaBar, are denoted a and c. In the fit, the substitutions C_ζ = 1 and S_ζ = a –+ η b_i – η c_i are made. [Note that S₊ = a – c and S_– = a + c, so a = (S₊ + S_–)/2, c = (S_– – S₊)/2.] The subscript i denotes the tagging category. These are motivated by the possibility of CP violation on the tag side, which is absent for semileptonic B decays (mostly lepton tags). The parameter a is independent of tag side CPV. These parameters are the same for the partially and fully reconstructed B decay analyses from BABAR.
• The parameters used by Belle in the analysis using partially reconstructed B decays, are similar to the S parameters defined above. However, in the Belle definition, a tagging B⁰ corresponds to a + sign in front of the sine coefficient; furthermore the correspondance between the super/subscript and the final state is opposite, so that S_+– (BABAR) = – S^–+ (Belle). In this analysis, only lepton tags are used, so there is no effect from tag-side CPV. In the Belle analysis using fully reconstructed B decays, this effect is measured and taken into account using D*^+–l^–+ν decays; in neither Belle analysis are the a, b and c parameters used. In the latter case, the measured parameters are 2R_D⁽*⁾π sin( 2φ₁+φ₃ +– δ_D⁽*⁾π ); the definition is such that S^+– (Belle) = –2R_D*πsin( 2φ₁+φ₃ +– δ_D*π ). However, the definition includes an angular momentum factor (–1)^L, and so for the results in the Dπ system, there is an additional factor of –1 in the conversion.

Here we convert the Belle results to express them in terms of a and c. Explicitly, the conversion reads:

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

Compilation of the above results.

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GLW Analyses of B^– → D⁽*⁾K⁽*^)–

ADS Analyses of B^– → D⁽*⁾K⁽*^)– and B^– → D⁽*⁾π^–

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