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 2006 updates (ICHEP06): 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 = 0.147 ± 0.029
η = 0.342 ± 0.016
(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 = 0.167 ± 0.041
η = ± 0.373 ± 0.033



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 = 0.739 ± 0.044 (from UT sides)
sin 2β = 0.736 ± 0.042 (from UT sides + εK)
sin 2β = 0.690 ± 0.023 (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 = (88 ± 16)o
(up to π ambiguity)

prediction on γ
(EPS) [JPG]

ALL OTHER INFOS:
γ = (65.1 ± 6.5)o


determination of γ
(EPS) [JPG]

FULL FIT:
γ = (66.7 ± 6.4)o


direct determination of α
(EPS) [JPG]

DIRECT DETERMINATION:
α = (91 ± 8)o (SM solution only)

prediction on α
(EPS) [JPG]

ALL OTHER INFOS:
α = (91.0 ± 6.1)o

determination of α
(EPS) [JPG]

FULL FIT:
α = (91.2 ± 5.4)o

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

DIRECT DETERMINATION:
2β+γ = (± 90 ± 46)o

prediction on sin(2β+γ)
(EPS) [JPG]

ALL OTHER INFOS:
2β+γ = (111 ± 13)o

determination of 2β+γ
(EPS) [JPG]

FULL FIT:
2β+γ = (111 ± 13)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| = (4.09 ± 0.26)10-3


prediction on Vub
(EPS) [JPG]
ALL OTHER INFOS:
|Vub| = (3.44 ± 0.16)10-3


determination of Vub
(EPS) [JPG]
FULL FIT:
|Vub| = (3.55 ± 0.15)10-3


direct determination of Vcb
(EPS) [JPG]
DIRECT DETERMINATION:
|Vcb| = (4.15 ± 0.07)10-2
ALL OTHER INFOS: n.a.

prediction on Vcb
(EPS) [JPG]
FULL FIT:
|Vcb| = (4.09 ± 0.05)10-2


prediction on Vtd
(EPS) [JPG]
FULL FIT:
|Vtd| = (8.49 ± 0.27)10-3

prediction on Vtd/Vts
(EPS) [JPG]
FULL FIT:
|Vtd/Vts| = 0.211 ± 0.007

prediction on Rb
(EPS) [JPG]
FULL FIT:
Rb = 0.373 ± 0.015


prediction on Rt
(EPS) [JPG]
FULL FIT:
Rt = 0.918 ± 0.030

prediction on Imλt
(EPS) [JPG]
FULL FIT:
Imλt = (13.3 ± 0.6)10-5


prediction on Reλt
(EPS) [JPG]
FULL FIT:
Reλt = (-0.315 ± 0.012)10-3



Prediction On Other Bs Quantities


prediction on sin2β_s
(EPS) [JPG]

FULL FIT:
sin2βs = 0.037 ± 0.002


Summary of the Results


Results from the Full Fit
Parameter
Value ± Error
95% probability
99% probability
ρ
0.147 ± 0.029 [0.092,0.204] [0.076,0.222]
η
0.342 ± 0.012 [0.311,0.374] [0.301,0.384]
α(o)
91.2 ± 6.1 [81.3,101.4] [79.1,103.8]
β(o)
21.9 ± 1.0 [20.1,23.7] [19.5,24.3]
γ(o)
66.7 ± 6.4 [60.3,73.1] [54.8,78.7]
2β+γ(o)
111 ± 13 [12.1,14.5] [11.7,14.9]
sin 2α
-0.047 ± 0.152 [-0.3507,0.2406] [-0.4384,0.3172]
sin 2β
0.690 ± 0.023 [0.645,0.736] [0.630,0.750]
sin (2β+γ)
0.932 ± 0.029 [0.872,0.980] [0.851,0.988]
sin2βs
0.0365 ± 0.0017 [0.0332,0.0399] [0.0321,0.0411]
Im λt [10-5]
13.3 ± 0.6 [12.1,14.5] [11.7,14.9]
Re λt [10-3]
-0.315 ± 0.012 [-0.338,-0.292] [-0.345,-0.285]
Δms (ps-1)
17.7 ± 0.1 [17.5,17.9] [17.4,18.0]
|Vub|[10-3]
3.55 ± 0.15 [3.27,3.83] [3.20,3.91]
|Vcb|[10-2]
4.1 ± 0.05 [4.00,4.18] [3.97,4.21]
|Vtd|[10-3]
8.49 ± 0.27 [7.95,9.01] [7.79,9.17]
Rb
0.373 ± 0.015 [0.344,0.404] [0.336,0.413]
Rt
0.918 ± 0.030 [0.858,0.973] [0.840,0.989]
|Vtd/Vts|
0.211 ± 0.007 [0.197,0.224] [0.192,0.228]

Prediction from ALL OTHER INFOS
Parameter
Value ± Error
95% probability
99% probability
sin 2β
0.744 ± 0.039 [0.666,0.817] [0.641,0.837]
γ(o)
65.1 ± 6.5 [53.1,77.2] [50.3,80.0]
α(o)
91 ± 6 [79.6,102.3] [76.9,105.0]
2β+γ(o)
111 ± 13 [88,134] [82,140]
Δms (ps-1)
17.5 ± 2.1 [13.7,21.8] [12.7,23.5]
|Vub|[10-3]
3.44 ± 0.16 [3.13,3.76] [3.04,3.86]