4.6. WEAK INTERACTION THEORY 249
Under the transformation (4.6.68),(4.6.70)
Zμ=cosθwWμ^3 +sinθwBμ,
Aμ=−sinθwWμ^3 +cosθwBμ,whereθwis called the Weinberg angle, defined by
cosθw=g 1
|g|, sinθw=g 2
|g|.
- The Higgs field equation governedH^0 boson is given by (4.6.61), and at the ground
stateφ=awhich can be written as
∂μ∂μφ−(mHc
h ̄) 2
φ=1
4
(4.6.71) (φ+a)(g^21 WμaWμa+g 22 BμBμ− 2 g 1 g 2 Wμ^3 Bμ)
+λ φ(φ^2 + 2 aφ)+Gl(lLR+RlL),4.2.3 Higgs mechanism and mass generation
(4.6.72)
mHc
̄h=
√
2 λa.4.6.6 Problems in WS theory
The classical electroweak theory provides a model with someexperimental supports. How-
ever, this theory faces a number of problems, which are difficult, if not impossible, to resolve.
1.Lack of weak force formulas. This problem is that all weak interaction theories have
to face, and it is also that all existed theories cannot solve.
In fact, in the original field equations (4.6.60) there are four gauge field components:
(4.6.73) Wμ^1 ,Wμ^2 ,Wμ^3 ,Bμ,
and we don’t know which of these potentials plays the role of weak interaction potential. In
fact, with the mixed fields
Wμ±,Zμ,Aμ,
it is even more difficult to determine the weak force.
If we combine the classical electroweak theory with PRI, andtake
Wμ=ω 1 Wμ^1 +ω 2 Wμ^2 +ω 3 Wμ^3as the weak interaction potential, then from the field equations (4.6.60), we can only deduce
the weak force potential in the following form:
Φw=g 1
r
e−kr or Φw=−g 1
r
e−kr, k=1
√
2
ag 1.It implies that the weak force is only repulsive or attractive, which is not consistent with
experiments.