A Mathematica based Version of the CKMfitter Package

32 Chapter 5. Probing the Standard Model
5.1.7 The UT angle γ
The extraction of the UT angle γ stems from measurements of direct CP violation
in B → D (∗) K (∗) decays. It is obtained from a combination of the Gronau-
London-Wyler (GLW) [31,32], Atwood-Dunietz-Soni (ADS) [33,34] and Giri-
Grossman-Soffer-Zupan (GGSZ) [35, 36] methods. Figure 5.1 shows the combined
result using a frequentist method, which is advocated by the CKMfitter
group [16]. Analogous to the UT angle α the corresponding χ 2 -contour is used
as a LUT input file (see Chapter 4).
5.1.8 |ɛK|
In the Standard Model, the absolute value of the CP-violating parameter in the
neutral Kaon system |ɛK| is defined by:
|ɛK| = G2 F m2 W mK
12 √ 2π2 f
∆mK
2 �
KBK
+ 2ηctS(xc, xt)Im[VcsV ∗ ∗
cdVtsVtd ]
ηccS(xc)Im[(VcsV ∗
cd )2 ] + ηttS(xt)Im[(VtsV ∗
td )2 ]
�
, (5.6)
where fK is the Kaon decay constant. The hadronic matrix element of the |∆S| = 2
box diagram is proportional to � √ �2, fK BK where BK is the bag parameter. It
has been obtained from Lattice QCD calculations and is the primary source of the
theoretical uncertainties for the prediction of |ɛK|. The parameters ηqiqj are nextto-leading
order (NLO) QCD corrections to the Inami-Lim functions S, which are
listed in Appendix A. The values of ηct and ηtt are shown in Table 5.2, while due to
large uncertainties, a parameterization [37–39] is used for ηcc. This is also shown in
Appendix A. The used average of |ɛK| is [40]:
5.1.9 ∆md
|ɛK| = (2.221 ± 0.008gauss) · 10 −3 . (5.7)
The B 0 - ¯ B 0 oscillation frequency is expressed through the mass difference ∆md between
the mass eigenstates BH and BL. It is predicted in the Standard Model as:
∆md = G2 F
6π 2 ηB mBd f 2 Bd Bd m 2 W S(xt) |VtdV ∗
tb |2 , (5.8)
where ηB is a perturbative QCD correction
√
to the Inami-Lim function. The hadronic
matrix element is proportional to fBd Bd, where the decay constant fBd and bag
parameter Bd are taken from LQCD (see also Section 5.1.12). ∆md has been measured
to high precision in many experiments. The WA is [29]:
∆md = 0.507 ± 0.004gauss . (5.9)