324
20. Introduction to the Phenomenology of Weak Interactions
FIGURE 20.12
Effective four-fermion non-leptonic weak transition at the quark level.
FIGURE 20.13
Non-leptonic weak decay of Λ
0 using the process of figure 20.12, with the
addition of two ‘spectator’ quarks.
20.8 Non-leptonic weak interactions
The CKM 6-quark charged weak current, which replaces the GIM current
(20.101), is
μ
(1 − γ 5 )
(1 − γ 5 ) ′ ¯ (1 − γ 5 )
ˆ
¯
d ˆ ′ ¯
ˆ
ˆ b
′
j
(u, d, s, c, t, b) = ˆ
+ cγ
μ
s tγ
μ
uγ
μ
ˆ
ˆ +
,
CKM
2
2
2
(20.184)
and the effective weak Hamiltonian of (20.92) (as modified by CKM) clearly
contains the term
G F μ
†
H ˆ q (x) = √ ˆ j
(x) ˆ j
(x)
(20.185)
CC
CKM
μCKM
2
in which no lepton fields are present (just as there are no quarks in (20.40)).
This interaction is responsible, at the quark level, for transitions involving
four quark (or antiquark) fields at a point. For example, the process shown in
figure 20.12 can occur. By ‘adding on’ another two quark lines u and d, which
undergo no weak interaction, we arrive at figure 20.13, which represents the
non-leptonic decay Λ
0
→ pπ
− .