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):

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 = 0.164 ± 0.029
η = 0.340 ± 0.017
(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 = 0.171 ± 0.041
η = ± 0.387 ± 0.031



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 = 0.768 ± 0.039 (from UT sides)
sin 2β = 0.759 ± 0.039 (from UT sides + εK)
sin 2β = 0.697 ± 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 = (83 ± 19)o
(up to π ambiguity)

prediction on γ
(EPS) [JPG]

ALL OTHER INFOS:
γ = (63.1 ± 4.6)o


determination of γ
(EPS) [JPG]

FULL FIT:
γ = (64.1 ± 4.6)o


direct determination of α
(EPS) [JPG]

DIRECT DETERMINATION:
α = (92 ± 7)o (SM solution only)

prediction on α
(EPS) [JPG]

ALL OTHER INFOS:
α = (93.1 ± 5.8)o

determination of α
(EPS) [JPG]

FULL FIT:
α = (93.5 ± 4.6)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 = (108 ± 5)o

determination of 2β+γ
(EPS) [JPG]

FULL FIT:
2β+γ = (108 ± 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 = (18.6 ± 2.3) 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| = (3.67 ± 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| = (4.17 ± 0.06)10-2


prediction on Vtd
(EPS) [JPG]
FULL FIT:
|Vtd| = (8.49 ± 0.28)10-3

prediction on Vtd/Vts
(EPS) [JPG]
FULL FIT:
|Vtd/Vts| = 0.207 ± 0.007

prediction on Rb
(EPS) [JPG]
FULL FIT:
Rb = 0.379 ± 0.015


prediction on Rt
(EPS) [JPG]
FULL FIT:
Rt = 0.901 ± 0.031

prediction on Imλt
(EPS) [JPG]
FULL FIT:
Imλt = (13.7 ± 0.7)10-5


prediction on Reλt
(EPS) [JPG]
FULL FIT:
Reλt = (-0.320 ± 0.013)10-3



Prediction On Other Bs Quantities


prediction on sin2β_s
(EPS) [JPG]

FULL FIT:
sin2βs = 0.036 ± 0.002


Summary of the Results


Results from the Full Fit
Parameter
Value ± Error
95% probability
99% probability
ρ
0.164 ± 0.029 [0.107,0.222] [0.089,0.240]
η
0.340 ± 0.017 [0.307,0.373] [0.297,0.384]
α(o)
93.5 ± 4.6 [84.7,102.6] [82.0,105.5]
β(o)
22.2 ± 0.9 [20.4,24.0] [19.9,24.5]
γ(o)
64.1 ± 4.6 [55.1,73.0] [52.4,75.8]
2β+γ(o)
108 ± 5 [98,117] [95,120]
sin 2α
-0.126 ± 0.16 [-0.429,0.185] [-0.511,0.264]
sin 2β
0.697 ± 0.023 [0.651, 0.742] [0.635, 0.756]
sin (2β+γ)
0.952 ± 0.026 [0.894,0.991] [0.872,0.995]
sin2βs
0.0363 ± 0.0018 [0.0328,0.0398] [0.0317,0.0410]
Im λt [10-5]
13.7 ± 0.7 [12.4, 15.0] [12.2, 15.4]
Re λt [10-3]
-0.320 ± 0.013 [-0.346, -0.295] [-0.354, -0.288]
Δms (ps-1)
17.7 ± 0.1 [17.5, 17.9] [17.4, 18.0]
|Vub|[10-3]
3.66 ± 0.15 [3.38, 3.95] [3.27, 4.04]
|Vcb|[10-2]
4.17 ± 0.06 [4.05, 4.28] [4.01, 4.32]
|Vtd|[10-3]
8.49 ± 0.28 [7.93,9.04] [7.76,9.21]
Rb
0.379 ± 0.015 [0.35, 0.41] [0.34, 0.42]
Rt
0.906 ± 0.031 [0.84,0.96] [0.82,0.98]
|Vtd/Vts|
0.207 ± 0.007 [0.193, 0.221] [0.188, 0.225]

Prediction from ALL OTHER INFOS
Parameter
Value ± Error
95% probability
99% probability
sin 2β
0.760 ± 0.036 [0.688, 0.830] [0.664, 0.850]
γ(o)
63.1 ± 4.6 [53.7,72.0] [51.3,75.1]
α(o)
93.1 ± 5.8 [81.7,104.3] [78.2,107.8]
2β+γ(o)
108 ± 5 [98, 117] [95, 120]
Δms (ps-1)
18.6 ± 2.3 [14.4, 23.5] [13.3, 25.3]
|Vub|[10-3]
3.44 ± 0.16 [3.12, 3.77] [3.03, 3.89]



Table of Inputs

Input values for parameters and constraints entering in the UT fit. Most of the experimental averages are taken from HFAG . For the CKM angles we use the pdf's obtained combining the available experimental information (see here for details). All the other inputs are listed below.


Constraints, Parameters Value Gauss Error Flat Error Comments
λ 0.2258 0.0014 -
|Vcb| (10-3) 41.3 1.0 1.8 Average of exclusive
|Vcb| (10-3) 41.6 0.7 - Average of inclusive
|Vub| 10-4 (excl.) 35.0 4.0 - HFAG BR + Lattice QCD
|Vub| 10-4(incl. HFAG) 44.9 3.3 - HFAG average
mb (GeV/c2) 4.21 0.08 -
mc (GeV/c2) 1.3 0.1 -
Δ(md) (ps-1) 0.507 0.005 - WA (CDF/CLEO/LEP/Babar/Belle)
Δ(ms) (ps-1) 17.77 0.12 - CDF Likelihood is used.
mt (GeV/c2) 161.2 1.7 - (CDF/D0)
fBs √BBs (MeV) 262 35 - Lattice QCD
ξ 1.23 0.06 - Lattice QCD
|εK |10-3 2.280 0.013 -
BK 0.79 0.04 0.08 Lattice QCD
fK (GeV) 0.160 - -
Δ(mK) (10-2 ps-1) 0.5301 - -
αs(MZ) 0.119 0.003 -
GF (10-5 GeV-2) 1.16639 - -
mW (GeV/c2) 80.425 - -
mBd (GeV/c2) 5.279 - -
mBs (GeV/c2) 5.375 - -
mK0 (GeV/c2) 0.497648 - -

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