A Mathematica based Version of the CKMfitter Package

52 Chapter 6. New Physics Beyond the Standard Model
A much better constraint stems from the observable γ. Since it is tree-level dominated,
it directly constrains the CKM matrix parameters (¯ρ,¯η) and thereby the
allowed range in the (r 2 d ,2ϑd) plane. Figure 6.3 shows the two allowed regions remain
in the (¯ρ,¯η) plane and in the (r 2 d ,2ϑd) plane. Since a one-dimensional scan
in ¯η results ¯η �= 0 at a CL of at most 99.9 %, a real CKM matrix is also excluded
assuming New Physics contributions in B 0 - ¯ B 0 oscillations. The first solution in the
(r 2 d ,2ϑd) plane is in agreement with the SM values (r 2 d = 1, 2ϑd = 0), whereas the
second solution would be a clear sign of New Physics effects. Another major input
stems from measurements of the UT angle α. It decreases the allowed regions in the
(¯ρ,¯η) plane as well as in the (r 2 d ,2ϑd) plane as shown in Figure 6.4.
Finally, the inclusion of ASL in the fit gives an additional hard constraint in both
planes. As shown in Figure 6.5, the non-SM solution almost vanishes, which highlights
the importance of the observable ASL in constraining possible New Physics
contributions to B 0 - ¯ B 0 mixing. Additional fits have been performed to describe the
effects from the individual constraints. The results are shown in the Figures B.1
to B.5 , given in Appendix B.
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
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 6.4: 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, sin 2β, cos 2β, γ and α.
Figure 6.6 shows the confidence level obtained from one-dimensional scans of the
New Physics parameters r 2 d and 2ϑd, using constraints from |Vud|, |Vub|, |Vcb|, ∆md,
sin 2β, cos 2β, γ, α and ASL. The results
r 2 d
+0.50 +1.28
= 1.02 −0.42 (1σ)
−0.57 (2σ) and 2ϑd = −0.094 +0.049
−0.123
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
+0.11
(1σ) −0.16 (2σ) , (6.3)
are in good agreement with the Standard Model, nevertheless, the r2 d constraint shows
that NP contributions of order O(100 %) are still possible. The non-SM solution is
0