Subatomic Physics

11.9. Weak Decays of Quarks and the CKM Matrix 355
In the electromagnetic case we have expressed the strength of the interaction by
making e 2 dimensionless as in Eq. (10.79):
α = e2 1
≈
�c 137 .
Comparison of Eqs. (11.15) and (11.16) makes it clear that the weak analog to the
electric charge is gw, notGF .Likee2 ,g2 w is made dimensionless by division by �c.
The connection with GF , as given in Eq. (11.21), then permits us to write g2 w/�c
in terms of GF and the mass m,
g 2 w
�c =
With mW ≈ 80 GeV/c 2 , we find
1
√ 24π
g 2 w
�c
1
�c
�
mW c
�
� 2
GF .
1
≈ . (11.56)
240
The coupling constants gw and e are of the same order of magnitude, suggesting
that the weak and electromagnetic interactions are related. The observed weakness
of the weak interactions at low energies is not caused by a small coupling constant,
but rather by a short range [Eq. (11.17)]. Actually, when these arguments were
first made, the mass of the W was not known and the formulation of a unified
electroweak theory led to the prediction of the correct mass of the W .
11.9 Weak Decays of Quarks and the CKM Matrix
In chapter 5 we introduced quarks which can be arranged in pairs:
� u
d
� � c
s
� � t
b
�
. (11.57)
Here the top row contains the q =2e/3 members and the bottom row contains the
q = −e/3 ones, grouped by family in order of increasing mass from left to right.
It turns out that all charged weak decays of quarks can be explained by assuming
that all transitions that change row are allowed. Thus, a down quark can change
into an up quark and emit a W − which may then decay into an electron and an
anti-neutrino. This is what happens in neutron beta decay. A different example
is a decay like: K + → π + eνe, where a strange quark decays to an up quark.
The situation can be better summarized by listing allowed parents and daughters
together:
� u
d ′
� � c
s ′
� � t
b ′
�
, (11.58)