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 = 0.163 ± 0.028
η = 0.344 ± 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 = 0.171 ± 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 = 0.764 ± 0.039 (from UT sides)
sin 2β = 0.755 ± 0.040 (from UT sides + εK)
sin 2β = 0.701 ± 0.022 (all constraints)


MEASUREMENT:
sin 2β = 0.675 ± 0.026 (from b → ccs)



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



direct determination of γ
(EPS) [JPG]

DIRECT DETERMINATION:
γ = (82 ± 20)o
(up to π ambiguity)

prediction on γ
(EPS) [JPG]

ALL OTHER INFOS:
γ = (64.2 ± 4.3)o


determination of γ
(EPS) [JPG]

FULL FIT:
γ = (64.6 ± 4.2)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 ± 6)o

determination of α
(EPS) [JPG]

FULL FIT:
α = (92.7 ± 4.2)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 = (110 ± 5)o

determination of 2β+γ
(EPS) [JPG]

FULL FIT:
2β+γ = (109 ± 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 = (18.4 ± 2.2) ps-1

result on DeltaMs
(EPS) [JPG]
FULL FIT:
Δ ms = (17.77 ± 0.12) 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| = (3.47 ± 0.16)10-3


determination of Vub
(EPS) [JPG]
FULL FIT:
|Vub| = (3.68 ± 0.14)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| = (4.16 ± 0.06)10-2


prediction on Vtd
(EPS) [JPG]
FULL FIT:
|Vtd| = (8.50 ± 0.27)10-3

prediction on Vtd/Vts
(EPS) [JPG]
FULL FIT:
|Vtd/Vts| = 0.208 ± 0.007

prediction on Rb
(EPS) [JPG]
FULL FIT:
Rb = 0.381 ± 0.014


prediction on Rt
(EPS) [JPG]
FULL FIT:
Rt = 0.904 ± 0.028

prediction on Imλt
(EPS) [JPG]
FULL FIT:
Imλt = (13.8 ± 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 = 0.037 ± 0.002


Summary of the Results


Results from the Full Fit
Parameter
Value ± Error
95% probability
99% probability
ρ
0.163 ± 0.028 [0.106,0.217] [0.088,0.234]
η
0.344 ± 0.016 [0.312,0.375] [0.303,0.386]
α(o)
92.7 ± 4.2 [84.3,101.2] [81.5,104.2]
β(o)
22.2 ± 0.9 [20.5, 24.0] [20.0, 24.6]
γ(o)
64.6 ± 4.2 [56.2,73.3] [53.5,76.2]
2β+γ(o)
108.5 ± 4.5 [100,118] [97,120]
sin 2α
-0.101 ± 0.15 [-0.387,0.193] [-0.48,0.286]
sin 2β
0.701 ± 0.022 [0.657, 0.744] [0.645, 0.757]
sin (2β+γ)
0.939 ± 0.026 [0.879,0.982] [0.856,0.988]
sin2βs
0.0366 ± 0.0017 [0.0333,0.0401] [0.0322,0.0412]
Im λt [10-5]
13.8 ± 0.7 [12.5, 15.0] [12.1, 15.4]
Re λt [10-3]
-0.320 ± 0.013 [-0.345, -0.295] [-0.353, -0.288]
Δms (ps-1)
17.77 ± 0.12 [17.54, 18.01] [17.47, 18.08]
|Vub|[10-3]
3.68 ± 0.14 [3.39, 3.95] [3.33, 4.04]
|Vcb|[10-2]
4.16 ± 0.06 [4.04, 4.27] [4.0, 4.31]
|Vtd|[10-3]
8.5 ± 0.27 [7.97,9.04] [7.8,9.21]
Rb
0.381 ± 0.014 [0.353, 0.409] [0.345, 0.418]
Rt
0.904 ± 0.028 [0.847,0.961] [0.828,0.98]
|Vtd/Vts|
0.208 ± 0.007 [0.194, 0.221] [0.189, 0.226]

Prediction from ALL OTHER INFOS
Parameter
Value ± Error
95% probability
99% probability
sin 2β
0.759 ± 0.037 [0.686, 0.828] [0.662, 0.848]
γ(o)
64.3 ± 4.4 [55.8, 73.1] [53.8, 76.1]
α(o)
92.9 ± 5.7 [81.5,104] [77.8,107.2]
2β+γ(o)
108.5 ± 4.5 [100, 118] [97, 120]
Δms (ps-1)
18.4 ± 2.2 [14.3, 23.1] [13.2, 24.9]
|Vub|[10-3]
3.47 ± 0.16 [3.17, 3.79] [3.08, 3.89]



Table of Inputs

Input values for parameters and constraints entering in the UT fit. Most of these values have been agreed at CKM Workshops CKM05 Workshops and HFAG . The novelities come from the new values of Vub, sin2β and mt from Lepton Photon 2005 conference.


Constraints, Parameters Value Gauss Error Flat Error Comments
sin 2β 0.675 0.026 -
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 -
|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) 163.8 3.2 - (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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