Letter of Intent for KEK Super B Factory Part I: Physics

η
1.5
1
0.5
0
-0.5
-1
excluded area has < 0.05 CL
ε K
|V ub /V cb |
C K M
f i t t e r
LP 2003
Δm d
φ 3
φ 2
Δm s & Δm d
sin 2φ 1 (WA)
-1.5
-1 -0.5 0 0.5 1 1.5 2
Figure 2.2: A fit of the parameters (ρ, η) using several experimental constraints as of Lepton-
Photon 2003. The plot is taken from the CKM fitter page http://ckmfitter.in2p3.fr/.
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ρ
φ 1
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ε K
¡¢¡ £
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Figure 2.3: Box diagrams to produce the ∆B = 2 four-quark operator
where the ∆B = 2 effective four-quark operator is
¥¦
Q ∆B=2 = dγµ(1 − γ5)b dγµ(1 − γ5)b. (2.12)
The operator is defined at the renormalization scale µb and the corresponding Wilson coefficient
C∆B=2 (µb) is calculated using the renormalization group technique as C∆B=2 (µb) =
[α (5)
s (µb)] −6/23 to leading order. The function S0(m2 t /M 2 W ) is called the Inami-Lim function [8]
and represents the loop effect through the box diagrams.
The ∆B = 1 transitions are described by the following effective Hamiltonian
H ∆B=1
eff
= 4GF
√2 VCKM
Ci(µb)Oi(µb) + h.c.,
i
where VCKM is the corresponding CKM matrix element. The operators Oi(µb) defined at the
scale µb are listed below, and the couplings Ci(µb) are the Wilson coefficients.
The effective operators representing the tree-level W exchange diagram depicted in Fig. 2.4
are
O q
1 = dα γµ(1 − γ5)q β q β γµ(1 − γ5)b α , q = u, c, (2.13)
O q
2 = dα γµ(1 − γ5)q α q β γµ(1 − γ5)b β , q = u, c. (2.14)
31
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