Mathematical Principles of Theoretical Physics

5.4. MECHANISMS OF SUBATOMIC DECAYS AND ELECTRON RADIATIONS 305

which is rewritten in the weakton components as

(5.4.18) νμ+νew 1 w 2 →w 1 w 2 (W−)+νμ+νe

→νμw 1 w 2 +νe.

In (5.4.18) we can see that the transient vector bosonW−appears, and then capturesνμto
form the muonμ. The Feynman digram of (5.4.18) is given by Figure5.11.

W−

νμ

e−

νe

μ−

Figure 5.11

Replacing the Feynman diagram, we describe the scattering (5.4.18) by using Figure5.12.
It is clear that the scattering (5.4.18) is achieved by exchanging weaktonsνμandνe.

2.β-decay.Consider the classicalβ-decay process

(5.4.19) n→p+e−+νe.

with the quark constituents ofnandp:

n=udd, p=uud,

theβ-decay (5.4.19) is equivalent to the followingd-quark decay:

d→u+e−+νe,

whose complete form should be given by

(5.4.20) w∗w 1 w 2 (d)+νeνe(ν)+w 1 w 1 (γ)→w∗w 1 w 1 (u)+w 1 w 2 (W−)+νeνe(ν)

→w∗w 1 w 1 (u)+νew 1 w 2 (e−)+νe.

In theβ-decay (5.2.20),w∗ind-quark and photonγ=w 1 w 1 recombine to formu-quark and
charged vector bosonW−, thenW−capturesνefromν-mediator to yield an electrone−and
anνe.

3.Quark pair creations.Consider

gk+γ 0 +γ→u+u,

gk 0 +γ 0 +γ 0 →d+d.