A Mathematica based Version of the CKMfitter Package

50 Chapter 6. New Physics Beyond the Standard Model
theory predictions of the relevant observables are changed as follows [67]:
γ ⇒ γ (tree level dominated)
|Vud|, |Vus| ⇒ |Vud|, |Vus| (tree level dominated)
|Vub|, |Vcb| ⇒ |Vub|, |Vcb| (tree level dominated)
∆md ⇒ ∆m NP
d
sin 2β ⇒ sin(2β + 2ϑd)
= ∆mSM d · r 2 d
cos 2β ⇒ cos(2β + 2ϑd) (6.2)
α (= π − β − γ) ⇒ α NP (= π − β − γ − ϑd)
� �SM Γ12 sin 2ϑd
ASL ⇒ A NP
SL = −Re
M12
r 2 d
� �SM Γ12 cos 2ϑd
+ Im
M12 r2 d
The tree-level dominated constraints from |Vud|, |Vus|, |Vub|, |Vcb| and γ remain unchanged.
The other observables in Eqn. 6.2 have more important loop contributions
which are sensitive to possible New Physics effects. The only constraint on both NP
parameters r 2 d and 2ϑd comes from the semileptonic CP asymmetry ASL, where the
SM prediction of Γ12/M12 is used here at LO in QCD.
The observables in Eqn. 6.2 provide significant constraints in the (¯ρ,¯η) plane as well
as in the (r 2 d ,2ϑd) plane. The results of a global New Physics fit are shown in the
Figures 6.1 to 6.5, where the used input values are summarized in Table 5.1 & 5.2.
η
1.5
1
0.5
0
-0.5
-1
γ
α
-1.5
-1 -0.5 0 0.5 1 1.5 2
ρ
β
CKM
1-CL
f i t t e r
ICHEP 2006
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
(rad)
d
2 ϑ
3
2
1
0
-1
-2
CKM
1-CL
f i t t e r
ICHEP 2006
-3
0 1 2 3
r 2
d
4 5 6
Figure 6.1: Constraints within the framework of New Physics contributions to the B 0 - ¯ B 0
mixing amplitude on the (¯ρ,¯η) plane (left) and on the (r 2 d ,2ϑd) plane (right), obtained from
a global CKM fit including |Vud|, |Vus|, |Vub|, |Vcb|, ∆md and sin 2β.
Figure 6.1 shows the confidence level obtained from a global CKM fit in the (¯ρ,¯η)
and (r 2 d ,2ϑd) planes, assuming New Physics contributions to B 0 - ¯ B 0 oscillations.
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
.