Subatomic Physics

408 The Electroweak Theory of the Standard Model
for the two families that contributes. For the neutral current, J nc , this sum is
〈d cos θC + s sin θC|J nc |d cos θC + s sin θC〉
+ 〈s cos θC − d sin θC|J nc |s cos θC − d sin θC〉
= 〈d|J nc |d〉(cos 2 θC +sin 2 θC)
+ 〈s|J nc |s〉(cos 2 θC +sin 2 θC)
+ 〈s|J nc |d〉(sin θC cos θC − sin θC cos θC)
+ 〈d|J nc |s〉(cos θC sin θC − sin θC cos θC)
= 〈d|J nc |d〉 + 〈s|J nc |s〉. (13.12)
There is thus no contribution for any process of a neutral current connecting the
strange and down quarks, or a neutral strangeness-changing current. The contribution
of this current is canceled by the symmetry between the second and first
families introduced by the charmed quark.
The existence of the c, t, andb quarks was later confirmed and their properties
are now fairly well known. Moreover, presently all direct evidence for CP violation
can be explained by a phase in the CKM matrix. (8)
13.3 The Electroweak Interaction
In this section, we concentrate on the interaction terms of the electroweak theory to
demonstrate the unity of the weak and electromagnetic interactions. We first need
to write the currents in a transparent manner. In the notation of chapter 11 [see
e.g., Eq. (11.37)], we can write,
jµ,em(e) =ψ ∗ eVµ,emψe = ψ ∗ eLVµ,emψeL + ψ ∗ eRVµ,emψeR, (13.13)
where we have generalized the operators 1 and p/m or vop by the relativistic Vµ,em
with µ =0...3;
V0,em =1 and Vi,em = vi,op
for i =1, 2, 3orx, y, z in the nonrelativistic limit. We have also replaced the
wavefunctions ψα and ψβ of Eq. (11.37) by ψe,ψeL or ψeR. The break-up into lefthanded
(L) and right-handed (R) currents in Eq. (13.13) is just a formal change
without importance for the electromagnetic interaction. For the weak interaction,
however, the break-up becomes useful. As discussed earlier, the weak current contains
both a vector and an axial vector operator in the combination Vµ −Aµ, with
A0 = σ·p/m and Ai = σi in the nonrelativistic approximation. Instead of using the
two operators between the complete wavefunction ψe, we can sandwich the operator
8 T.E. Browder, R. Faccini, Annu. Rev. Nucl. Part. Sci. 53, 353 (2003).