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Parameter | Value | Ref. / Comments |
---|---|---|
τ(Bd) | (1.536 ± 0.014) ps | HFAG - Oscillations/Lifetime (Winter 2004) |
Δmd | (0.502 ± 0.007) ps1 | HFAG - Oscillations/Lifetime (Winter 2004) |
|A⊥|2 (CP-odd fraction in B0→ J/ψK* CP sample) |
0.245 ± 0.015 ± 0.004 (note: acceptance-corrected central value; the uncorrected value is: 0.230) |
BaBar: PRD 71 (2005) 032005 |
0.181 ± 0.012 ± 0.008 | Belle-CONF-0438, hep-ex/0408104 | |
0.211 ± 0.011 | Average (CL = 0.0025 → 3.0σ) |
Parameter: sin(2β)/sin(2φ1) (if β/φ1 dominant weak phase) | ||||
---|---|---|---|---|
Mode | BABAR | Belle | Average | Ref. / Comments |
Charmonium: | N(BB)=227m | N(BB)=152m | - |
BABAR-CONF-04/38, hep-ex/0408127 (submitted to PRL) Belle, PR D71 (2005) 072003 |
J/ψKS, ψ(2S)KS, χc1KS, ηCKS | 0.75 ± 0.04stat | 0.73 ± 0.06stat | ||
J/ψKL (ηCP=+1) | 0.57 ± 0.09stat | 0.77 ± 0.13stat | ||
J/ψK*0 (K*0 → KSπ0) | 0.96 ± 0.32stat | 0.10 ± 0.45stat | ||
All charmonium | 0.722 ± 0.040 ± 0.023 | 0.728 ± 0.056 ± 0.023 |
0.725 ± 0.037 (0.033stat-only) |
CL = 0.91 |
s-penguin: | N(BB)=209-227m | N(BB)=275m | ||
φK0 | 0.50 ± 0.25 +0.070.04 | 0.06 ± 0.33 ± 0.09 | 0.34 ± 0.20 CL=0.30 |
BaBar: hep-ex/0502019 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
η'KS | 0.30 ± 0.14 ± 0.02 | 0.65 ± 0.18 ± 0.04 | 0.43 ± 0.11 CL=0.13 (1.5σ) |
BaBar: hep-ex/0502017 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
f0KS | 0.95 +0.230.32 ± 0.10 | 0.47 ± 0.41 ± 0.08 | 0.39 ± 0.26 CL=0.008 (2.7σ) |
BABAR-CONF-04/019, hep-ex/0408095 Belle-CONF-0435, hep-ex/0409049 |
π0KS | 0.35 +0.300.33 ± 0.04 | 0.30 ± 0.59 ± 0.11 | 0.34 +0.270.29 CL=0.94 |
BABAR: hep-ex/0503011 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
ωKS | 0.50 +0.340.38 ± 0.02 | 0.75 ± 0.64 +0.130.16 | 0.55 +0.300.32 CL=0.74 |
BABAR-CONF-05/001, hep-ex/0503018
Belle-CONF-0435, hep-ex/0409049 |
K+KKS (excluding φKS) |
0.55 ± 0.22 ± 0.04 ± 0.11CP-even (fCP-even= 0.89 ± 0.08 ± 0.06 [moments]) |
0.49 ± 0.18 ± 0.04 +0.170.00CP-even (fCP-even= 1.03 ± 0.15 ± 0.05 [SU(2)]) |
0.53 ± 0.17 CL=0.72 (rescaled to average fCP-even= 0.93 ± 0.09) |
BaBar: hep-ex/0502019 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
KSKSKS | 0.71 +0.320.38 ± 0.04 | 1.26 ± 0.68 ± 0.20 | 0.26 ± 0.34 CL=0.014 (2.5σ) |
BaBar: hep-ex/0502013 (submitted to PRL) Belle: hep-ex/0503023 (submitted to PRL) |
All b → s-penguin | 0.43 ± 0.07 | CL=0.17 (1.4σ) | ||
All modes | 0.665 ± 0.0033 | CL=0.006 (2.7σ) | ||
Direct comparison of charmonium and s-penguin averages (see comments below): CL=2.1×104 (3.7 σ) |
Parameter: sin(2β)/sin(2φ1) | ||||
---|---|---|---|---|
Experiment | Value | Ref. / Comments | ||
ALEPH | 0.84 +0.821.04 ± 0.16 | PL B492 (2000) 259-274 | ||
OPAL | 3.2 +1.82.0 ± 0.5 | EPJ C5 (1998) 379-388 | ||
CDF (full Run I) | 0.79 +0.410.44(stat+syst) | PRD 61 (2000) 072005 |
Parameter: sin(2β)/sin(2φ1) | ||||
---|---|---|---|---|
All charmonium | 0.726 ± 0.037 |
Parameter: C=A (if not stated otherwise) | ||||
---|---|---|---|---|
Mode | BABAR | Belle | Average | Ref. / Comments |
Charmonium | |λ| = 0.950 ± 0.031 ± 0.013 |
|λ| = 1.007 ± 0.041 ± 0.033 |
0.969 ± 0.028 (0.025stat-only) CL=0.30 |
BABAR-CONF-04/38, hep-ex/0408127 (submitted to PRL) Belle, PR D71 (2005) 072003 |
C = 0.051 ± 0.033 ± 0.014 | C = 0.007 ± 0.041 ± 0.033 |
C = 0.031 ± 0.029
(0.025stat-only)
CL=0.30 |
||
φK0 | 0.00 ± 0.23 ± 0.05 | 0.08 ± 0.22 ± 0.09 | 0.04 ± 0.17 CL=0.81 |
BaBar: hep-ex/0502019 (submitted to PRD-RC) Belle-CONF-0435, hep-ex/0409049 |
η'KS | 0.21 ± 0.10 ± 0.02 | 0.19 ± 0.11 ± 0.05 | 0.04 ± 0.08 CL=0.011 (2.5σ) |
BaBar: hep-ex/0502017 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
f0KS | 0.24 ± 0.31 ± 0.15 | 0.39 ± 0.27 ± 0.08 | 0.14 ± 0.22 CL=0.16 (1.4σ) |
BABAR-CONF-04/019, hep-ex/0408095 Belle-CONF-0435, hep-ex/0409049 |
π0KS | 0.06 ± 0.18 ± 0.03 | 0.12 ± 0.20 ± 0.07 | 0.09 ± 0.14 CL=0.83 |
BABAR: hep-ex/0503011 (submitted to PRL) Belle-CONF-0435, hep-ex/0409049 |
ωKS | 0.56 +0.290.27 ± 0.03 | 0.26 ± 0.48 ± 0.15 | 0.48 ± 0.25 CL=0.61 |
BABAR-CONF-05/001, hep-ex/0503018
Belle-CONF-0435, hep-ex/0409049 |
K+KKS (excluding φKS) |
0.10 ± 0.14 ± 0.06 | 0.08 ± 0.12 ± 0.07 | 0.09 ± 0.10 CL=0.92 |
BaBar: hep-ex/0502019 (submitted to PRD-RC) Belle-CONF-0435, hep-ex/0409049 |
KSKSKS | 0.34 +0.280.25 ± 0.05 | 0.54 ± 0.34 ± 0.09 | 0.41 ± 0.21 |
BaBar: hep-ex/0502013 (submitted to PRL) Belle: hep-ex/0503023 (submitted to PRL) |
All b → s-penguin | 0.021 ± 0.049 | CL=0.15 ⇒ 1.4σ | ||
All modes | 0.018 ± 0.025 | CL=0.17 ⇒ 1.4σ | ||
Direct comparison of charmonium average and s-penguin average (see comments above): CL=0.36 ⇒ 0.9σ |
Constraining CJ/ψ Ks
from ACP(B+ → J/ψ K+)
and ASL: as suggested by
Y. Nir,
one can obtain a powerful SM constraint on
|λ| = |q/p||A-bar/A| via the relations
ASL = (1|q/p|4)/(1+|q/p|4)
and
ACP(B+ → J/ψ K+)
= (|A-bar/A|21)/(|A-bar/A|2+1),
where ASL denotes the CP asymmetry in semileptonic
B decays,
and ACP(B+ → J/ψ K+)
is the CP-violating charge asymmetry measured in
B+ → J/ψ K+ decays.
Averaging the ASL results from
BABAR,
Belle,
CLEO,
ALEPH and
OPAL
(using also the BABAR
measurement of |q/p| from fully reconstructed B decays),
as well as the ACP(B+ → J/ψ K+)
results from
BABAR,
Belle and
CLEO,
we find respectively
ASL = 0.0026 ± 0.0067
(see
HFAG oscillation group
for more details) and
ACP(B+ → J/ψ K+)
= 0.007 ± 0.019. This
gives
|q/p| = 1.0013 ± 0.0034 and
|A-bar/A| = 0.993 ± 0.018,
and hence
|λ|indirect = 0.994 ± 0.018, which
is C = 0.006 ± 0.018
(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, the identification of |λ|, measured through the C coefficient in B0 → J/ψ K0, with |q/p||A-bar/A| assumes ΔΓBd=0. The systematic error on C from a width difference ΔΓBd/ΓBd~0.02 has been estimated by BABAR to be 0.0009. |
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) |
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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) |
Constraining the Unitarity Triangle (ρ, η):
the measurement of sin(2β)/sin(2φ1) 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 and UTfit sites for results on global CKM fits using different fit techniques and input quantities. |
Experiment | sin(2β/2φ1)J/ψK* | cos(2β/2φ1)J/ψK* | Correlation | Ref. / Comments |
---|---|---|---|---|
BABAR'04 N(BB)=88m |
0.10 ± 0.57 ± 0.14 | 3.32 +0.760.96 ± 0.27 | -0.37 | PRD 71 (2005) 032005 |
Belle'04 N(BB)=275m |
0.30 ± 0.32 ± 0.02 | 0.31 ± 0.91 ± 0.11
[using Solution II] |
? | Belle-CONF-0438, hep-ex/0408104 |
Average | 0.21 ± 0.28 (CL = 0.55 → 0.6σ) |
1.69 ± 0.67 (CL = 0.026 → 2.2σ) |
? | See remark below table |
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) | |
![]() eps gif gif (high res) |
![]() eps gif gif (high res) |
Experiment | SD*+D* | CD*+D* | Correlation | Ref. / Comments |
---|---|---|---|---|
BABAR'05 N(BB)=227m |
0.65 ± 0.26 ± 0.04 +0.090.07[RT] | 0.04 ± 0.14 ± 0.02 | - | BABAR temporary reference
RT = 0.124 ± 0.044 ± 0.007 |
Belle'04 N(BB)=152m |
0.75 ± 0.56 ± 0.10 ± 0.06[RT] | 0.26 ± 0.26 ± 0.05 ± 0.01[RT] | - |
hep-ex/0501037 (submitted to PLB) RT = 0.19 ± 0.08 ± 0.01 |
Average(*) | 0.67 ± 0.25 | 0.09 ± 0.12 | - | χ2
= 0.02 (CL=0.89) [S] χ2 = 0.53 (CL=0.47) [C] |
Experiment | S+(D*+D) | C+(D*+D) | S+(D*D+) | C+(D*D+) | A(D*+D+) | Ref. / Comments |
---|---|---|---|---|---|---|
BABAR'03 N(BB)=88m |
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'04 N(BB)=152m (combined fully and partially rec. B decays) |
0.55 ± 0.39 ± 0.12 | 0.37 ± 0.22 ± 0.06 | 0.96 ± 0.43 ± 0.12 | 0.23 ± 0.25 ± 0.06 | 0.07 ± 0.08 ± 0.04 | PRL 93 (2004) 201802 |
Average | 0.61 ± 0.36 | 0.39 ± 0.20 | 0.75 ± 0.38 | 0.09 ± 0.21 | 0.03 ± 0.07 |
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. |
![]() eps gif gif(high res) |
![]() eps gif gif(high res) |
Mode | Experiment | SKsπ0γ | CKsπ0γ = AKsπ0γ | Correlation | Ref. / Comments |
---|---|---|---|---|---|
K*(892)γ | BABAR'05 N(BB)=232m |
0.21 ± 0.40 ± 0.05 | 0.40 ± 0.23 ± 0.04 | 0.064 | BABAR temporary reference |
Belle'05 N(BB)=275m |
0.79 +0.630.50 ± 0.10 | 0.00 +0.370.38 ± 0.11 | 0.037 |
hep-ex/0503008 (submitted to PRL) |
|
Average | 0.38 ± 0.34 | 0.30 ± 0.20 | +0.056 | χ2 = 1.4 (CL=0.50) | |
KSπ0γ (incl. K*γ) |
BABAR'05 N(BB)=232m |
0.06 ± 0.37 | 0.48 ± 0.22 | 0.066 | BABAR temporary reference |
Belle'05 N(BB)=275m |
0.58 +0.460.38 ± 0.11 | 0.03 ± 0.34 ± 0.11 | 0.02 |
hep-ex/0503008 (submitted to PRL) |
|
Average | 0.26 ± 0.29 | 0.36 ± 0.19 | 0.043 | χ2 = 1.9 (CL=0.38) |
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) | |
![]() 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. |
![]() eps gif gif (high res) |
The Penguin-to-tree ratio:
using as input the measured
Cππ and Sππ 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 Bd→ π+π
decays within the Standard Model. Note that the definition of P/T is
convention-dependent (see, e.g.,
GroRos02).
One can choose to eliminate the charm quark in
the penguin loop using CKM unitarity, so that the amplitudes are
parameterized as follows:
|
Experiment | ACP(ρπ) | Sρπ | Cρπ | ΔSρπ | ΔCρπ | Correlations | Ref. / Comments | |
---|---|---|---|---|---|---|---|---|
BABAR'04 N(BB)=213m |
0.088 ± 0.049 ± 0.013 | 0.10 ± 0.14 ± 0.04 | 0.34 ± 0.11 ± 0.05 | 0.22 ± 0.15 ± 0.03 | 0.15 ± 0.11 ± 0.03 | Table | BABAR-CONF-04/038, hep-ex/0408099 | |
Belle'04 N(BB)=152m |
0.16 ± 0.10 ± 0.02 | 0.28 ± 0.23 +0.100.08 | 0.25 ± 0.17 +0.020.06 | 0.30 ± 0.24 ± 0.09 | 0.38 ± 0.18 +0.020.04 | Table | PRL 94 (2005) 121801 | |
Average | 0.102 ± 0.045 | 0.13 ± 0.13 | 0.31 ± 0.10 | 0.09 ± 0.13 | 0.22 ± 0.10 | Table | ||
Significance of CPV in the decay: Δχ2 = χ2(Acp=C=0) χ2 = 14.5 (CL = 0.00070, that is: 3.4σ) |
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+|21)/(|κ+|2+1) = (ACP(ρπ)+Cρπ+ACP(ρπ)ΔCρπ)/(1+ΔCρπ + ACP(ρπ)Cρπ), A+(ρπ) = (|κ+|21)/(|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 +0.130.14. 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. |
![]() eps gif gif (high res) |
||||||||||||||||||||
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)×106.
|
Experiment | α/φ2 (deg) | δ+ (deg) | Ref. / Comments | ||||
---|---|---|---|---|---|---|---|
BABAR'04 N(BB)=213m |
113 +2717 ± 6 | 67 +2831 ± 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) |
Experiment | Sρρ,long | Cρρ,long | Correlation | Ref. / Comments |
---|---|---|---|---|
BABAR'05 N(BB)=232m |
0.33 ± 0.24 +0.080.14 | 0.03 ± 0.18 ± 0.09 | 0.042 |
BABAR hep-ex/0503049 (submitted ro PRL) |
Belle | not yet available |
Constraining α: using as input the measured Cρρ,long and Sρρ,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. |
The Penguin-to-tree ratio: using as input the measured Cρρ,long and Sρρ,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. |
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] +2918[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. |
![]() eps gif gif (high res) |
The decays Bd → D+π+, Bd → D*+π+ and Bd → D+ρ+ provide sensitivity to γ/φ3 because of the interference between the Cabibbo-favoured amplitude (e.g. B0 → Dπ+) 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 BdBd-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., rDπ = |A(B0 → D+π)/A(B0 → Dπ+)|. Each of the ratios rDπ, rD*π and rDρ 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 → Ds+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:
Here we convert the Belle results to express them in terms of a and c. Explicitly, the conversion reads:
Belle D*π (partial reconstruction): | aπ* = (S+ + S)/2 |
cπ* = (S+ S)/2 | |
Belle D*π (full reconstruction): | aπ* = + ( 2 RD*π sin( 2φ1+φ3 + δD*π ) + 2 RD*π sin( 2φ1+φ3 δD*π ) )/2 |
cπ* = + ( 2 RD*π sin( 2φ1+φ3 + δD*π ) 2 RD*π sin( 2φ1+φ3 δD*π ) )/2 | |
Belle Dπ (full reconstruction): | aπ = ( 2 RDπ sin( 2φ1+φ3 + δDπ ) + 2 RDπ sin( 2φ1+φ3 δDπ ) )/2 |
cπ = ( 2 RDπ sin( 2φ1+φ3 + δDπ ) 2 RDπ sin( 2φ1+φ3 δDπ ) )/2 |
At present we do not rescale the results to a
common set of input parameters. Also, common systematic errors
are not considered.
Observable | BABAR | Belle | Average(*) | Ref. / Comments | ||
---|---|---|---|---|---|---|
partially reconstructed N(BB)=227m |
fully reconstructed N(BB)=110m |
partially reconstructed N(BB)=152m |
fully reconstructed N(BB)=152m |
|||
aπ* | 0.034 ± 0.014 ± 0.009 | 0.049 ± 0.031 ± 0.020 | 0.030 ± 0.028 ± 0.018 | 0.060 ± 0.040 ± 0.019 | 0.027 ± 0.013
(CL=0.22) |
BABAR: hep-ex/0504035 (submitted to PRD) (partially reco.) BABAR-CONF-04/029, hep-ex/0408059 (fully reco.) Belle: hep-ex/0408106 (submitted to PLB) (partially reco.) Belle: PRL 93 (2004) 031802; Erratum-ibid. 93 (2004) 059901 |
cπ* | 0.019 ± 0.022 ± 0.013
(lepton tags only) |
0.044 ± 0.054 ± 0.033
(lepton tags only) |
0.005 ± 0.028 ± 0.018 | 0.049 ± 0.040 ± 0.019 | 0.001 ± 0.018
(CL=0.52) |
|
aπ | - | 0.032 ± 0.031 ± 0.020 | - | 0.062 ± 0.037 ± 0.018 | 0.045 ± 0.027
(CL=0.59) |
|
cπ | - | 0.059 ± 0.055 ± 0.033
(lepton tags only) |
- | 0.025 ± 0.037 ± 0.018 | 0.035 ± 0.035
(CL=0.66) |
|
aρ | - | 0.005 ± 0.044 ± 0.021 | - | - | 0.005 ± 0.049 | |
cρ | - | 0.147 ± 0.074 ± 0.035
(lepton tags only) |
- | - | 0.147 ± 0.082 |
Compilation of the above results. |
![]() eps gif gif(high res) |
ACP+ = [Γ(B → D(*)CP+K(*)) Γ(B+ → D(*)CP+K(*)+)] / Sum , |
RCP+ = [Γ(B → D(*)CP+K(*)) + Γ(B+ → D(*)CP+K(*)+)] / [Γ(B → D(*)0 K(*)) + Γ(B+ → D(*)0-bar K(*)+)]. |
Mode | Experiment | ACP+ | ACP | RCP+ | RCP | Ref. / Comments |
---|---|---|---|---|---|---|
DCPK | BABAR'04 N(BB)=214m |
0.40 ± 0.15 ± 0.08 | 0.21 ± 0.17 ± 0.07 | 0.87 ± 0.14 ± 0.06 | 0.80 ± 0.14 ± 0.08 | BABAR-CONF-04/039, hep-ex/0408082 |
Belle'04 N(BB)=275m |
0.07 ± 0.14 ± 0.06 | 0.11 ± 0.14 ± 0.05 | 0.98 ± 0.18 ± 0.10 | 1.29 ± 0.16 ± 0.08 | Belle-CONF-0443 | |
Average |
0.22 ± 0.11 | 0.02 ± 0.12 | 0.91 ± 0.12 | 1.02 ± 0.12 | ||
D*CPK | BABAR'04 N(BB)=123m |
0.10 ± 0.23 +0.030.04 | - | 1.06 ± 0.26 +0.100.09 | - | PRD 71, 031102 (2005) |
Belle'04 N(BB)=275m |
0.27 ± 0.25 ± 0.04 | 0.26 ± 0.26 ± 0.03 | 1.43 ± 0.28 ± 0.06 | 0.94 ± 0.28 ± 0.06 | Belle-CONF-0443 | |
Average |
0.18 ± 0.17 | 0.26 ± 0.26 | 1.24 ± 0.20 | 0.94 ± 0.29 | ||
DCPK* | BABAR'04 N(BB)=227m |
0.09 ± 0.20 ± 0.06 | 0.33 ± 0.34 ± 0.10 0.06(*) | 1.77 ± 0.37 ± 0.12 | 0.76 ± 0.29 ± 0.06 +0.040.14(*) | BABAR-CONF-04/012, hep-ex/0408069 |
Belle'03 N(BB)=96m |
0.02 ± 0.33 ± 0.07 | 0.19 ± 0.50 ± 0.04 | - | - | Belle-CONF-0316, hep-ex/0307074 | |
Average |
0.07 ± 0.18 | 0.16 ± 0.29 | 1.77 ± 0.39 | 0.76 ± +0.300.33 |
Constraining γ/φ3:
The rate ratios and asymmetries of the GLW method can be
expressed in terms of amplitude ratios and strong phase differences,
as well as the weak phase difference γ/φ3.
For the GLW observables, one has:
|
AKπ = [Γ(B → [K+π]D(*)K(*)) Γ(B+ → [Kπ+]D(*)K(*)+)] / [Γ(B → [K+π]D(*)K(*)) + Γ(B+ → [Kπ+]D(*)K(*)+)] , |
RKπ = [Γ(B → [K+π]D(*)K(*)) + Γ(B+ → [Kπ+]D(*)K(*)+)] / [Γ(B → [Kπ+]D(*)K(*)) + Γ(B+ → [K+π]D(*)K(*)+)] . |
Mode | Experiment | AKπ | RKπ | Ref. / Comments |
---|---|---|---|---|
DK
D→Kπ |
BABAR'04 N(BB)=227m |
- | 0.013 +0.0110.009 | BABAR-CONF-04/13, hep-ex/0408028 |
Belle'04 N(BB)=275m |
0.88 +0.770.62 ± 0.06 | 0.023 +0.0160.014 ± 0.001 | PRL 94, 091601 (2005) | |
Average |
0.88 +0.770.62 | 0.017 ± 0.009 | ||
D*K
D* → Dπ0 D→Kπ |
BABAR'04 N(BB)=227m |
- | -0.001+0.0100.006 | BABAR-CONF-04/13, hep-ex/0408028 |
Average |
- | -0.001+0.0100.006 | ||
D*K
D* → Dγ D→Kπ |
BABAR'04 N(BB)=227m |
- | 0.011+0.0190.013 | BABAR-CONF-04/13, hep-ex/0408028 |
Average |
- | 0.011+0.0190.013 |
Constraining γ/φ3:
As for the GLW method,
the rate ratios and asymmetries of the ADS method can be
expressed in terms of amplitude ratios and strong phase differences,
as well as the weak phase difference γ/φ3.
For the ADS observables, one has:
|
Mode | Experiment | AKπ | RKπ | Ref. / Comments |
---|---|---|---|---|
Dπ
D→Kπ |
Belle'04 N(BB)=275m |
0.30 +0.290.25 ± 0.06 | 0.0035 +0.00100.0009 ± 0.0002 | PRL 94, 091601 (2005) |
Average |
0.30 +0.300.26 | 0.0035 +0.00100.0009 |
Experiment | Mode | γ/φ3 (°) | δB (°) | rB | Ref. / Comments |
---|---|---|---|---|---|
Belle'04
N(BB)=275m |
DK
D→KSπ+π |
64 ± 19 ± 13 ± 11 | 157 ± 19 ± 11 ± 21 | 0.21 ± 0.08 ± 0.03 ± 0.04 | Belle-CONF-0476, hep-ex/0411049 |
D*K
D*→Dπ0 D→KSπ+π |
75 ± 57 ± 11 ± 11 | 321 ± 57 ± 11 ± 21 | 0.12 +0.160.11 ± 0.02 ± 0.04 | ||
Combined | 68 +1415 ± 13 ± 11 | - | - | ||
BABAR'05
N(BB)=227m |
DK
D→KSπ+π |
- | 104 ± 45 +1721 +1624 | 0.12 ± 0.08 ± 0.03 ± 0.04 | hep-ex/0504039 (submitted to PRL), |
D*K
D*→Dπ0 & D*→Dγ D→KSπ+π |
- | 296 ± 41 +1412 ± 15 | 0.17 ± 0.10 ± 0.03 ± 0.03 | ||
Combined | 70 ± 31 +1210 +1411 | - | - | ||
Average | UNDER CONSTRUCTION |
Experiment | Mode | γ/φ3 (°) | δB (°) | rB | Ref. / Comments |
---|---|---|---|---|---|
Belle'05
N(BB)=275m |
DK*
K* → KSπ D→KSπ+π |
112 ± 35 ± 9 ± 11 ± 8 | 353 ± 35 ± 8 ± 21 ± 49 | 0.25 ± 0.18 ± 0.09 ± 0.04 ± 0.08 | BELLE-CONF-0502, hep-ex/0504013 |
Average | UNDER CONSTRUCTION |