Results and Predictions

Latest analysis within the Standard Model to be found in the following two papers.

for the detailed constraint description:
M. Bona et al. [UTfit Collaboration], "The 2004 UTfit Collaboration Report on the Status of the Unitarity Triangle in the Standard Model", JHEP 0507 (2005) 028. hep-ph/0501199
for the latest numerical results:
M. Bona et al. [UTfit Collaboration], "The Unitarity Triangle Fit in the Standard Model and Hadronic Parameters from Lattice QCD: A Reappraisal after the Measurements of Δms and BR(B → τν)" hep-ph/0606167

Results including Summer 2008 updates (ICHEP08): Previous results: see the Archive

Results in the ρ - η plane


(ρ-η) allowed region
(EPS) [JPG]

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,Δmd/Δms, α, β, γ, ΔΓd/Γd, ΔΓs/Γs, ASLd, and the dimuon asymmetry from D0.

ρ = 0.155 ± 0.022
η = 0.342 ± 0.014
(ρ-η) allowed region (sides only)
(EPS) [JPG]

Allowed regions for (ρ - η) (contours at 68%, 95%) as selected by the measurements of | Vub|/| Vcb|, Δmd and Δms are compared to the bounds (at 95% probability) from the measurements of CP violating quantities in the kaon (εK) and in the B (α, β and γ) sectors.

ρ = 0.176 ± 0.028
η = ± 0.359 ± 0.026



ρ p.d.f. (all constraints)
(EPS) [JPG]

p.d.f. of ρ (all constraints)


η p.d.f. (all constraints)
(EPS) [JPG]

p.d.f. of η (all constraints)



sin 2β (results/predictions)



prediction on sin2β from UT sides
(EPS) [JPG]

prediction on sin2β from UT sides only
prediction on sin2β from all measurements
(EPS) [JPG]

sin2β from all measurements


PREDICTIONS:

sin 2β = 0.731 ± 0.038 (from UT sides)
sin 2β = 0.731 ± 0.036 (from UT sides + εK)
sin 2β = 0.695 ± 0.020 (all constraints)


MEASUREMENT:
sin 2β = 0.668 ± 0.028 (from b → ccs)



γ,α and sin(2β+γ) (results/predictions)



direct determination of γ
(EPS) [JPG]

DIRECT DETERMINATION:
γ = (78 ± 12)o
(up to π ambiguity)

prediction on γ
(EPS) [JPG]

ALL OTHER INFOS:
γ = (64.2 ± 3.1)o


determination of γ
(EPS) [JPG]

FULL FIT:
γ = (65.6 ± 3.3)o


direct determination of α
(EPS) [JPG]

DIRECT DETERMINATION:
α = (90 ± 8) o (SM solution only)

prediction on α
(EPS) [JPG]

ALL OTHER INFOS:
α = (92.4 ± 4.1)o

determination of α
(EPS) [JPG]

FULL FIT:
α = (92.0 ± 3.4)o

direct determination of sin(2β+γ)
(EPS) [JPG]

DIRECT DETERMINATION:
2β+γ = (± 90 ± 32)o

prediction on sin(2β+γ)
(EPS) [JPG]

ALL OTHER INFOS:
2β+γ = (109.5 ± 3.5)o

determination of 2β+γ
(EPS) [JPG]

FULL FIT:
2β+γ = (109.5 ± 3.5)o



sides and mixing (results/predictions)



direct determination of Δms
(EPS) [JPG]
DIRECT DETERMINATION:
Δ ms = (17.77 ± 0.12) ps-1

prediction on Δm<sub>s</sub>
(EPS) [JPG]
ALL OTHER INFOS:
Δ ms = (17.5 ± 2.1) ps-1

result on DeltaMs
(EPS) [JPG]
FULL FIT:
Δ ms = (17.7 ± 0.1) ps-1

direct determination of Vub
(EPS) [JPG]
DIRECT DETERMINATION:
|Vub| = (3.80 ± 0.22)10-3


prediction on Vub
(EPS) [JPG]
ALL OTHER INFOS:
|Vub| = (3.48 ± 0.16)10-3


determination of Vub
(EPS) [JPG]
FULL FIT:
|Vub| = (3.60 ± 0.12)10-3


direct determination of Vcb
(EPS) [JPG]
DIRECT DETERMINATION:
|Vcb| = (4.12 ± 0.04)10-2
ALL OTHER INFOS: n.a.

prediction on Vcb
(EPS) [JPG]
FULL FIT:
|Vcb| = (4.13 ± 0.05)10-2


prediction on Vtd
(EPS) [JPG]
FULL FIT:
|Vtd| = (8.51 ± 0.22)10-3

prediction on Vtd/Vts
(EPS) [JPG]
FULL FIT:
|Vtd/Vts| = 0.209 ± 0.005

prediction on Rb
(EPS) [JPG]
FULL FIT:
Rb = 0.376 ± 0.013


prediction on Rt
(EPS) [JPG]
FULL FIT:
Rt = 0.911 ± 0.022

prediction on Imλt
(EPS) [JPG]
FULL FIT:
Imλt = (13.6 ± 0.6)10-5


prediction on Reλt
(EPS) [JPG]
FULL FIT:
Reλt = (-0.318 ± 0.010)10-3



Prediction On Other Bs Quantities


prediction on sin2β_s
(EPS) [JPG]

FULL FIT:
sin2βs = 0.0366 ± 0.0015


Summary of the Results


Results from the Full Fit
Parameter
Value ± Error
95.45% probability
99.73% probability
A
0.810 ± 0.013 [0.785,0.836] [0.777,0.845]
λ
0.2259 ± 0.0016 [0.2229,0.2287] [0.2220,0.2296]
ρ
0.154 ± 0.022 [0.110,0.198] [0.089,0.220]
η
0.342 ± 0.014 [0.315,0.371] [0.302,0.386]
α(o)
92.0 ± 3.4 [85.1,99.2] [81.9,102.7]
β(o)
22.0 ± 0.8 [20.5,23.7] [19.7,24.6]
γ(o)
65.6 ± 3.3 [58.7,72.5] [55.3,75.9]
2β+γ(o)
109.5 ± 3.5 [102,117] [98,120]
sin 2α
-0.08 ± 0.12 [-0.32,0.16] [-0.44,0.27]
sin 2β
0.695 ± 0.020 [0.656,0.736] [0.636,0.757]
sin (2β+γ)
0.937 ± 0.022 [0.887,0.977] [0.863,0.989]
sin2βs
0.0366 ± 0.0015 [0.0336,0.0397] [0.0322,0.0413]
Im λt [10-5]
13.6 ± 0.6 [12.4,14.6] [11.9,15.2]
Re λt [10-3]
-0.318 ± 0.010 [-0.338,-0.298] [-0.348,-0.288]
Δms (ps-1)
17.7 ± 0.1 [17.4,18.0] [17.3,18.1]
|Vub|[10-3]
3.60 ± 0.12 [3.37,3.86] [3.26,4.00]
|Vcb|[10-2]
4.13 ± 0.05 [4.04,4.22] [4.01,4.26]
|Vtd|[10-3]
8.51 ± 0.22 [8.06,8.94] [7.84,9.17]
Rb
0.376 ± 0.013 [0.352,0.403] [0.340,0.418]
Rt
0.911 ± 0.022 [0.865,0.956] [0.841,0.978]
|Vtd/Vts|
0.209 ± 0.0075 [0.198,0.220] [0.193,0.225]
JCP
2.98 ± 0.12 [2.75,3.22] [2.68,3.31]

Prediction from ALL OTHER INFOS
Parameter
Value ± Error
95.45% probability
99.73% probability
sin 2β
0.736 ± 0.034 [0.672,0.802] [0.645,0.830]
γ(o)
64.2 ± 3.1 [56.7,71.1] [53.3,73.9]
α(o)
92.4 ± 4.1 [84.1,100.5] [80.3,104.8]
2β+γ(o)
109.5 ± 3.5 [102,117] [98,120]
Δms (ps-1)
16.8 ± 1.6 [13.8,20.4] [12.5,22.5]
|Vub|[10-3]
3.48 ± 0.16 [3.19,3.80] [3.02,3.96]

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