Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

186 11. The CKM quark-mixing matrix
1.5
η
1.0
0.5
0.0
-0.5
-1.0
excluded area has CL > 0.95
sin 2β
εK
α
γ
Vub
γ
α
γ
excluded at CL > 0.95
ρ
β
α
Δmd
& Δms
Δmd
εK
sol. w/ cos 2β
< 0
(excl. at CL > 0.95)
-1.5
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0
Figure 11.2: 95% CL constraints on the ¯ρ, ¯η plane.
is obtained subtracting the sum of the first row from the measurement
of �
u,c,d,s,b |Vij| 2 from the W leptonic branching ratio [35], yielding
|Vcd| 2 + |Vcs| 2 + |Vcb| 2 =1.002 ± 0.027. The sum of the three angles,
α + β + γ = (183 +22
−25 )◦ , is also consistent with the SM expectation.
The CKM matrix elements can be most precisely determined by a
global fit that uses all available measurements and imposes the SM
constraints. There are several approaches to combining the experimental
data [6,95,102,118], which provide similar results. The results for the
Wolfenstein parameters are
λ =0.2253 ± 0.0007 , A =0.808 +0.022
−0.015 ,
¯ρ =0.132 +0.022
−0.014 , ¯η =0.341 ± 0.013 . (11.26)
The allowed ranges of the magnitudes of all nine CKM elements are
⎛
0.97428 ± 0.00015 0.2253 ± 0.0007 0.00347
VCKM = ⎝
+0.00016
−0.00012
0.2252 ± 0.0007 0.97345 +0.00015
−0.00016 0.0410 +0.0011
−0.0007
0.00862 +0.00026
−0.00020 0.0403 +0.0011
−0.0007 0.999152 +0.000030
⎞
⎠,
−0.000045
(11.27)
and the Jarlskog invariant is J =(2.91 +0.19
−0.11 ) × 10−5 . Fig. 11.2 illustrates
the constraints on the ¯ρ, ¯η plane from various measurements and the global
fit result. The shaded 95% CL regions all overlap consistently around the
global fit region.