Model of the Quark Mixing Matrix
Abstract
The structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is analyzed from the standpoint of a composite model. A model is constructed with three families of quarks, by taking tensor products of sufficient numbers of spin-1/2 representations and imagining the dominant terms in the mass matrix to arise from spin-spin interactions. Generic results then obtained include the familiar relation
|
V
us
|=(
m
d
/
m
s
)
1/2
−(
m
u
/
m
c
)
1/2
, and a less frequently seen relation
|
V
cb
|=
2
–
√
[(
m
s
/
m
b
)−(
m
c
/
m
t
)]
. The magnitudes of
V
ub
and
V
td
come out naturally to be of the right order. The phase in the CKM matrix can be put in by hand, but its origin remains obscure.