218
H. Wittig
N f = 0
N f = 2
N f = 2+1
0.6
0.8
1.0
B K
RBC 2004, DWF, RI/MOM
CP-PACS 2001, DWF, pert.
BosMar 2003, overlap, RI/MOM
MILC 2003, overlap, RI/MOM
ALPHA 2007, tmQCD, SF, a=0
JLQCD 1997, stagg., pert., a=0
RBC 2006, DWF, RI/MOM
UKQCD 2004, SW/Wilson, pert.,
RBC/UKQCD 2007, DWF, RI/MOM
HPQCD/UKQCD 2006, stagg., pert.
SPQcdR 2004, SW/Wilson, RI/MOM
Fig. 5.19 Recent lattice results for the RGI kaon B-parameter ˆ
B K . From top to bottom, the
plotted values are taken from Refs. [144–154]. Dotted error bars (where shown) indicate the
quoted systematic error. The labels include information on the fermionic discretization and the
intermediate renormalization scheme, if non-perturbative renormalization was used. We also
indicate whether or not the results have been extrapolated to the continuum limit. The vertical
lines represent the (non-lattice) result from [130], with the quoted uncertainty (see text)
uncertainties. In this way one obtains ˆ
B
non − lattice
K
= 0.94 ± 0.17, which is shown
as the vertical band in Fig. 5.19. Clearly, within the rather large error margins, this
result is compatible with all lattice determinations, quenched or unquenched.
First Row Unitarity and the Value of |V us | In addition to Eq. (5.210), the unitarity
of the CKM matrix implies many other constraints on its elements, such as those
which appear in the first row:
|V ud |
2
+ |V us |
2
+ |V ub |
2
= 1.
(5.217)
Owing to the smallness of |V ub |, i.e. |V ub | 2 2 · 10 −5 , the direct verification of first
row unitarity with the current experimental and theoretical accuracy rests on the
precise knowledge of |V ud | and |V us |. The value of |V ud | can be determined with
high accuracy from super-allowed nuclear β-decays (0 + → 0 + transitions), and in
the current edition of the particle data book the best estimate is quoted as [61]
|V ud | = 0.97377 ± 0.00027.
(5.218)
H. Wittig
N f = 0
N f = 2
N f = 2+1
0.6
0.8
1.0
B K
RBC 2004, DWF, RI/MOM
CP-PACS 2001, DWF, pert.
BosMar 2003, overlap, RI/MOM
MILC 2003, overlap, RI/MOM
ALPHA 2007, tmQCD, SF, a=0
JLQCD 1997, stagg., pert., a=0
RBC 2006, DWF, RI/MOM
UKQCD 2004, SW/Wilson, pert.,
RBC/UKQCD 2007, DWF, RI/MOM
HPQCD/UKQCD 2006, stagg., pert.
SPQcdR 2004, SW/Wilson, RI/MOM
Fig. 5.19 Recent lattice results for the RGI kaon B-parameter ˆ
B K . From top to bottom, the
plotted values are taken from Refs. [144–154]. Dotted error bars (where shown) indicate the
quoted systematic error. The labels include information on the fermionic discretization and the
intermediate renormalization scheme, if non-perturbative renormalization was used. We also
indicate whether or not the results have been extrapolated to the continuum limit. The vertical
lines represent the (non-lattice) result from [130], with the quoted uncertainty (see text)
uncertainties. In this way one obtains ˆ
B
non − lattice
K
= 0.94 ± 0.17, which is shown
as the vertical band in Fig. 5.19. Clearly, within the rather large error margins, this
result is compatible with all lattice determinations, quenched or unquenched.
First Row Unitarity and the Value of |V us | In addition to Eq. (5.210), the unitarity
of the CKM matrix implies many other constraints on its elements, such as those
which appear in the first row:
|V ud |
2
+ |V us |
2
+ |V ub |
2
= 1.
(5.217)
Owing to the smallness of |V ub |, i.e. |V ub | 2 2 · 10 −5 , the direct verification of first
row unitarity with the current experimental and theoretical accuracy rests on the
precise knowledge of |V ud | and |V us |. The value of |V ud | can be determined with
high accuracy from super-allowed nuclear β-decays (0 + → 0 + transitions), and in
the current edition of the particle data book the best estimate is quoted as [61]
|V ud | = 0.97377 ± 0.00027.
(5.218)