A Mathematica based Version of the CKMfitter Package

6.2. Charged Higgs Contributions to Leptonic B ± Decays 55
The prediction of the branching fraction B of purely leptonic B ± decays can be
written as [70]:
B (B → lν) = G2 F mBm2 l f 2 B
|Vub|
8π
2
�
1 − m2 l
m2 �2
· rH , (6.4)
B
where the factor rH contains the charged Higgs boson contributions. It is defined
by [69]:
�
rH = 1 − tan 2 β m2 B
m2 H ±
�2
1
1 + ɛ0 · tan β
. (6.5)
The factor 1/(1 + ɛ0 · tan β) combines corrections to the coupling H ± uidj which occur
at large tan β in SUSY models [69, 71]. Since a detailed discussion of this effect
occurring in SUSY models is beyond the scope of this thesis, they are neglected
by fixing ɛ0 to be zero. A discussion of the numerical impact of ɛ0 1 is provided in
Ref. [69].
Figure 6.8 shows the confidence level in the (tan β,m H +) plane obtained from the
constraints |Vud|, |Vus|, |Vcb|, |Vub|incl and B(B + → τ + ντ ). Their input values are the
same as summarized in Table 5.1, where for B(B + → τ + ντ ) the combined likelihood
function from BABAR [44] and Belle [45] is taken.
2
) GeV/c
+
m(H
350
300
250
200
150
100
50
0 10 20 30 40 50 60 70 80 90
tan( β )
CKM
1-CL
f i t t e r
ICHEP 2006
Figure 6.8: Confidence level in the (tan β,m H +) plane obtained from |Vud|, |Vus|, |Vcb|,
|Vub|incl and B(B + → τ + ντ ).
Since the constraint in Fig. 6.8 is very loose, only small m H + are exclude for large
tan β at 95 % CL. An experimental lower limit with m H + > 78.6 GeV/c 2 at 95 %
CL is obtained from the combined LEP results of searches in the decay channels
1 Varied in an interval −0.01 < ɛ0 < +0.01 which has been found in Ref. [71].
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0