Comparison of UTfit with or without angles determinations


The new constraints on UT angles from the CP violating quantities measured at the B-factories can be used now-days to constraint ρ and η and to further constraint the Standard Model. Because of this bundance of results, one can determine CKM parameters using only the determinations of the angles of the Unitarity Triangle, shown below.
sin2β
sin2β
angle α
2alpha from pipi and rhorho
angle γ
gamma using all
cos 2β
cos 2beta
sin(2β+γ)
(2beta+gamma) with r flat

On the other side, an independent determination of the same quantities can be obtained by the determination of sides of the triangle (through the study of semileptonic B decays and B mixing processes) and the measurement of εK in the Kaon sector. This was indeed the strategy used to predict sin2β before the precise direct measurement from BaBar and Belle.

|Vub/Vcb|
|Vub/Vcb| from semileptonic B decays
εK
eps_K
Δmd
Dmd
Δmd/Δms
Dmd/Dms

Thanks to the available precision, the comparison of the two regions provides now a meaningful test of the consistency of the Standard Model in the falvour sector. In the case of the angles fit, the bound from Vcb is also used, to determine the missing parameter A of the CKM matrix and to obtain predictions on all the UT related quantities.


Results in ρ- η plane with or without UT angles measurements


(ρ-η) region from angles
(EPS) [JPG]

Allowed regions for (ρ - η), given by the measurements of sin2β, cos2β, β from D0π0, α, γ, and 2β+γ. The closed contours at 68% and 95% probability are shown. The full lines correspond to 95% probability regions for each constraint.

ρ = 0.120 ± 0.034
η = 0.335 ± 0.020


(ρ-η) allowed region without using angles
(EPS) [JPG]

Allowed regions for (ρ - η). given by the measurements of | Vub|/| Vcb|, εK, Δmd, and Δmd/Δms. The closed contours at 68% and 95% probability are shown. The full lines correspond to 95% probability regions for each constraint.

ρ = 0.175 ± 0.027
η = 0.360 ± 0.023


Summary of the Results


Results from Angles Only
Parameter
Value ± Error
95.45% probability
99.73% probability
A
0.808 ± 0.013 [0.783,0.835] [0.775,0.843]
λ
0.2259 ± 0.0016 [0.2228,0.2287] [0.2220,0.2296]
ρ
0.120 ± 0.034 [0.053,0.194] [0.024,0.241]
η
0.334 ± 0.020 [0.296,0.375] [0.278,0.397]
α(o)
88.6 ± 5.5 [77.9,100.7] [73.2,107.8]
β(o)
20.8 ± 1.1 [18.7,23.0] [17.6,24.2]
γ(o)
70.2 ± 5.6 [58.1,81.1] [51.0,85.9]
2β+γ(o)
111.5 ± 5.5 [99,123] [92,127]
sin 2α
-0.040 ± 0.19 [-0.37,0.41] [-0.59,0.54]
sin 2β
0.663 ± 0.028 [0.606,0.719] [0.578,0.747]
sin(2β+γ)
0.921 ± 0.037 [0.84,0.98] [0.79,1.00]
Im λt [10-5]
13.1 ± 0.8 [11.5,15.4] [10.8,15.8]
Δ(ms) (ps-1)
18.6 ± 4.1 [11.3,27.5] [8.1,32.8]
|Vub|[10-3]
3.41 ± 0.18 [3.06, 3.77] [2.90, 3.97]
|Vcb|[10-2]
4.12 ± 0.05 [4.03, 4.21] [3.99, 4.26]
|Vtd|[10-3]
8.75 ± 0.34 [8.01,9.43] [7.55,9.74]
Rb
0.357 ± 0.018 [0.322, 0.394] [0.305, 0.413]
Rt
0.940 ± 0.035 [0.863, 1.01] [0.815, 1.04]
|Vtd/Vts|
0.217 ± 0.009 [0.198,0.233] [0.186,0.241]


Results from sides+εK (no angles)
Parameter
Value ± Error
95% probability
99% probability
A
0.809 ± 0.013 [0.783,0.834] [0.776,0.843]
λ
0.2258 ± 0.0016 [0.2228,0.2287] [0.2220,0.2296]
ρ
0.175 ± 0.027 [0.119,0.228] [0.093,0.254]
η
0.360 ± 0.023 [0.316,0.406] [0.299,0.431]
α(o)
92.3 ± 4.0 [84.3,100.4] [80.8,104.4]
β(o)
23.5 ± 1.5 [20.9,27.24] [19.9,28.43]
γ(o)
63.9 ± 3.8 [56.4,72.9] [52.9,75.2]
2β+γ(o)
110.5 ± 4.5 [101,120] [96, 124]
sin 2α
-0.08 ± 0.14 [-0.36,0.19] [-0.49,0.31]
sin 2β
0.731 ± 0.036 [0.666,0.801] [0.640,0.830]
Im λt [10-5]
14.1 ± 0.8 [12.6,15.8] [11.8,16.7]
Δ(ms) (ps-1)
17.75 ± 0.15 [17.40,18.00] [17.30,18.10]
|Vub|[10-3]
3.83 ± 0.22 [3.44, 4.27] [3.31, 4.45]
|Vcb|[10-2]
4.12 ± 0.05 [4.03, 4.20] [4.00, 4.26]
|Vtd|[10-3]
8.36 ± 0.33 [7.73,9.02] [7.54,9.24]
Rb
0.401 ± 0.024 [0.359,0.449] [0.344,0.472]
Rt
0.898 ± 0.027 [0.847,0.955] [0.819,0.978]
|Vtd/Vts|
0.206 ± 0.006 [0.194,0.219] [0.187,0.225]

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