A Mathematica based Version of the CKMfitter Package

5.2. Standard Model Fit Results 43
1 - CL
1
0.8
0.6
0.4
0.2
CKM
f i t t e r
ICHEP 2006
CKM fit
prediction
measurement
0
0 0.5 1 1.5 2 2.5 3
+ +
4
BR(B → τ ν τ ) × 10
1 - CL
1
0.8
0.6
0.4
0.2
CKM
f i t t e r
ICHEP 2006
0
0.2 0.3 0.4 0.5 0.6 0.7
+ +
6
BR(B → μ ν μ ) × 10
Figure 5.6: Confidence level on B(B + → τ + ντ ) and B(B + → µ + νµ) obtained from the SM
prediction (red curve). Furthermore, the results of the direct measurement (green shaded)
and the fit (blue curve) are given for the decay B + → τ + ντ .
Since the SM prediction of the branching fraction of purely leptonic B-meson decays
depends also on the decay constant fBd , a precise measurement can help to reduce
theoretical uncertainties in the Standard Global CKM Fit. Figure 5.7 shows the
constraint on (¯ρ,¯η) coming from the individual constraints B(B + → τ + ντ ), ∆md
and a combination of both inputs. Since B(B + → τ + ντ ) depends on the matrix
element |Vub|, its 95 % CL belt is to a very good approximation a ring around
(¯ρ, ¯η) = (0, 0). In the combination with ∆md, the theoretical uncertainties are
reduced due to the cancelation of the decay constant contribution. The remaining
theoretical uncertainty stems from the bag factor Bd in the SM prediction of ∆md.
η
1.5
1
0.5
0
-0.5
-1
excluded area has CL > 0.95
+ + B → τ ντ
CKM fit
γ
α
CKM
+ +
f i t t e r Constraint from B → τ ντ
and Δmd
ICHEP 06
-1.5
-1 -0.5 0 0.5 1 1.5 2
Figure 5.7: Confidence level in the (¯ρ,¯η) plane obtained from B(B + → τ + ντ ) (blue ring),
∆md (yellow ring) and a combination of both (green area).
ρ
β
Δmd