Results and Predictions

Results on:
ρ - η   plane    sin2β    Δ ms   γ   sin2α   NP QCD parameters  
Summary of Results
Table of Inputs

Results in the ρ - η   plane


(ρ-η) allowed region

 
Allowed regions for (ρ - η). The closed contours at 68% and 95% probability are shown. The full lines correspond to 95% probability regions for the constraints, given by the measurements of | Vub|/| Vcb|, εK, Δmd, Δms and sin2β. The dotted curve corresponds to the 95% upper limit obtained from the experimental study of B0s oscillations.
 

η = 0.348 ± 0.028
ρ = 0.172 ± 0.047

(ρ-η) allowed region (no ε_K)

 
Allowed regions for (ρ - η) (contours at 68%, 95%) as selected by the measurements of | Vub|/| Vcb|, Δmd and by the limit on Δms are compared with the bands (at 68% and 95% C.L.) from the measurements of CP violating quantities in the kaon εK) and in the B (sin2β) sectors.
 

η = 0.344 ± 0.041
ρ = 0.154 ± 0.061



ρ p.d.f. (all constraints)

p.d.f. of ρ (all constraints)


η p.d.f. (all constraints)

p.d.f. of η (all constraints)



sin 2β (results/predictions)



prediction on sin2β from UT sides

prediction on sin2β from UT sides only
prediction on sin2β from all measurements

prediction on sin2β from all measurements


PREDICTIONS:

sin 2β = 0.724 +0.043 -0.050 (from UT sides)
sin 2β = 0.707 +0.043 -0.053 (from UT sides + εk)
sin 2β = 0.725 ± 0.033 (all constraints)


MEASUREMENT:
sin 2β = 0.739 ± 0.048 (from J/Ψ,K0)



Δms (results/predictions)



Δms distribution (Δms not used)          Δms distribution from all measurements

PREDICTIONS:
Δms = 21.1 ± 3.1
     
Δms = 18.3 ± 1.6
(Δms not used)
     
(with all constraints)

DIRECT MEASUREMENT:
Δms > 14.5 @ 95 % C.L.


γ (results/predictions)



prediction on γ

PREDICTIONS:
γ = (61.5 ± 7.0)°
(with all constraints)


sin 2α (results/predictions)



prediction on sin2α

PREDICTIONS:
sin 2α = -0.16 ± 0.26
(with all constraints)



sin(2β+γ) (results/predictions)



prediction on sin(2β+γ)

PREDICTIONS:
sin(2β+γ) > 0.94 @ 68% CL
(sin(2β+γ) > 0.88 @ 95% CL)
(with all constraints)



Non Perturbative (NP) QCD parameters


One can use the overconstraining of the fit to get a posteriori pdfs for the NP QCD parameters entering the analysis. In particular, using a flat pdf in a large range rather than that one from theory turns the experimental information in a constraint on the parameter, since ρ and η   are determined by all the other bounds.


B_K p.d.f. (all constraints)
p.d.f. of BK from the other bounds
BK = 0.64 ± 0.10

f_Bs sqrt(B_Bs) p.d.f. (all constraints)
p.d.f. of fBs√ BBs(MeV) from the other bounds
fBs√ BBs = 0.262 ± 14

xi p.d.f. (all constraints)
p.d.f. of ξ from the other bounds
ξ = 1.13 ± 0.11

(f_Bs sqrt(B_Bs)-B_K) allowed region
The 68% and 95% contours in the fBs√BBs(MeV)- BK plane

(xi-B_K) allowed region
The 68% and 95% contours in the BK-ξ plane

(xi-f_Bs sqrt(B_Bs)) allowed region
The 68% and 95% contours in the fBs√BBs(MeV)-ξ plane



Summary of the Results


Results from the Standard Fit
Parameter
Value ± Error
95% probability
99% probability
η
0.348 ± 0.028 [0.293, 0.403] [0.275, 0.418]
ρ
0.172 ± 0.047 [0.082, 0.270] [0.051, 0.302]
sin 2β
0.725 ± 0.033 [0.645, 0.772] [0.627, 0.793]
sin 2α
-0.16 ± 0.26 [-0.62, 0.35] [-0.75, 0.48]
γ(°)
61.5 ± 7.0 [47.5, 76.6] [42.3, 81.6]
sin(2β+γ)
> 0.944 > 0.883 > 0.841
Im λt [10-5]
13.5 ± 1.0 [11.5, 15.3] [10.8, 15.9]
Δ(ms) (ps-1)
18.3 ± 1.6 [15.4,23.1] [15.1,27.0]
fBs √BBs (MeV)
264 ± 13 [239, 289] [233, 311]
ξ
1.22 ± 0.05 [1.13, 1.32] [1.10, 1.35]
BK
0.74 ± 0.08 [0.62,0.93] [0.60,0.99]

Prediction on parameters using all other constraints
Parameter
Value ± Error
95% probability
99% probability
sin 2β
0.707 +0.043 -0.053 [0.602,0.788] [0.570,0.810]
Δ(ms) (ps-1)
21.1 ± 3.1 [15.3, 27.7] [13.6, 29.8]
fBs √BBs (MeV)
263 ± 14 [236, 290] [231, 320]
ξ
1.13 +0.12 -0.09 [0.95, 1.41] [0.92, 1.57]
BK
0.65 ± 0.10 [0.49, 0.87] [0.45, 0.99]
BK vs ξ
BK
0.54 +0.18 -0.09 [0.41,0.99] [0.39,1.18]
ξ
1.33 ± 0.20 [0.96,1.67] [0.89,1.20]
BK vs Bs √BBs (MeV)
BK
0.63 ± 0.10 [0.48,0.87] [0.44,1.02]
fBs √BBs (MeV)
252 ± 13 [228,283] [219,325]
Bs √BBs (MeV) vs ξ
fBs √BBs (MeV)
>0.23 >0.22
ξ
>0.98 >0.92



Table of Inputs

Input values for parameters and constraints entering in the CKM-Fit. Most of these values have been agreed at the CKM Workshops and HFAG


Constraints, Parameters Value Gauss Error Flat Error Comments
sin 2β 0.739 0.048 -
λ 0.2265 0.0020 -
|Vcb| (10-3) 42.1 2.1 - Average of exclusive
|Vcb| (10-3) 41.4 0.7 0.6 Average of inclusive
|Vub| 10-4 (excl.) 33.0 2.4 4.6
|Vub| 10-4(incl. LEP) 40.9 6.2 4.7 LEP average
|Vub| 10-4(incl. HFAG) 45.7 6.1 - HFAG average (no LEP)
mb (GeV/c2) 4.21 0.08 -
mc (GeV/c2)   1.3 0.1 -
Δ(md) (ps-1) 0.503 0.006 - WA (CDF/CLEO/LEP/Babar/Belle)
Δ(ms) (ps-1) > 14.5 @ 95 % C.L. - - Sensitivity at 18.3 (CDF/LEP/SLD)
The Likelihood Ratio is used.
mt (GeV/c2) 167 5 - (CDF/D0)
fBs √BBs (MeV) 276 38 - Lattice QCD
ξ 1.24 0.04 0.06 Lattice QCD
ηb 0.55 0.01 -
|εK |10-3 2.280 0.013 -
BK 0.86 0.06 0.14 Lattice QCD
η1 1.38 0.53 -
η2 0.574 0.004 -
η3 0.47 0.04 -
fK (GeV) 0.161 - -
Δ(mK) (10-2 ps-1) 0.493677 - -
αs 0.119 0.003 -
GF (10-5 GeV-2) 1.16639 - -  
mW (GeV/c2) 80.22 - -
mBd (GeV/c2) 5.279 - -
mBs (GeV/c2) 5.375 - -
mK (GeV/c2) 0.4977 - -

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