300 CHAPTER 5. ELEMENTARY PARTICLES
5.4 Mechanisms of Subatomic Decays and Electron Radia-
tions
5.4.1 Weakton exchanges
We conclude that all particle decays are caused by weakton exchange. The exchanges occur
between composite particles as mediators, charged leptons, and quarks.
1.Weakton exchange in mediators. First we consider one of the most important decay
processes in particle physics, the electron-positron paircreation and annihilation:
(5.4.1)
2 γ→e++e−,
e++e−→ 2 γ.In fact, the reaction formulas in (5.4.1) are not complete, and the correct formulas should be
as follows
(5.4.2) 2 γ+ν⇄e++e−,
whereνis theν-mediator as in (5.3.27).
Note that the weakton components ofγandνare
γ=cosθww 1 w 1 −sinθww 2 w 2 ,
ν=α 1 νeνe+α 2 νμνμ+α 3 ντντ,which imply that the probability of the photonγat the statew 1 w 1 is cos^2 θwand at the state
−w 1 w 2 is sin^2 θw, and the probability ofνatνiνiisαi^2. Namely, for photon, the densities of
thew 1 w 1 (⇈)and−w 2 w 2 ()particle states are cos^2 θwand sin^2 θw, and the densities of the
statesνeνe,νμνμ,ντντareα 12 ,α 22 ,α 32. Hence the formula (5.4.2) can be written as
(5.4.3) w 1 w 1 (⇈)+w 2 w 2 ()+νeνe(↓↑)⇄νew 1 w 2 (↓↑↓)+νew 1 w 2 (⇈↓).
It is then clear to see from (5.4.3) that the weakton constituentsw 1 ,w 1 ,w 2 ,w 2 ,νe,νecan
regroup due to the weak interaction, and we call this processweakton exchange. The mech-
anism of this exchanging process can be explained using the layered formulas in (5.3.15) of
weak interaction potentials.
The layered potential formulas in (5.3.15) indicate that each composite particle has an
exchange radiusR, which satisfies
(5.4.4) ρ<R<ρ 1 ,
whereρis the radius of this particle andρ 1 is its repelling radius of weak force. If two
composite particlesAandBare in a distance less than their common exchange radius, then
the weaktons inAandBare attracting to each other by their weak interacting forces generated
byΦw 0 in (5.3.15), given by
(5.4.5) Φw 0 =gwe−kr
[
1
r−
Bw
ρw( 1 + 2 kr)e−kr