296 CHAPTER 5. ELEMENTARY PARTICLES
1.Weakton confinement.The weak interaction potentials (5.3.15) and the weak charge
formula (5.3.16) can help us to understand why no freew∗,w 1 ,w 2 are found, while single
neutrinosνe,νμ,ντcan be detected.
In fact, by (5.3.15) the weak interaction potential reads
Φw=gse−kr[
1
r−
B
ρw( 1 + 2 kr)e−kr]
,
The bound energy to hold particles together is negative. Hence for weaktons, their weak
interaction bound energyEis the negative part ofgsΦw, i.e.
(5.3.28) E=−
B
ρwg^2 s( 1 + 2 kr)e−^2 kr.By (5.3.16),
(5.3.29) g^2 w= 0. 63 ×
(
ρn
ρw) 6
̄hc.It is estimated that ρ
n
ρw
= 104 ∼ 106.
Therefore, the bound energyEgiven by (5.3.28) and (5.3.29) is very large provided the weak
interaction constantB>0.
Thus, by the sufficiently large bound energy, the weaktons can form triplets confined in
the interior of charged leptons and quarks as (5.3.19), and doublets confined in mediators
as (5.3.24)-(5.3.26). They cannot be opened unless the exchange of weaktons between the
composite particles.
The free neutrinosνe,νμ,ντand antineutrinosνe,νμ,ντcan be found in Nature. The
reason is that in the weakton exchange process there appear pairs of different types of neutri-
nos such asνeandνμ, and between which the governing weak force is repelling because the
constantBin (5.3.28) is non-positive, i.e.
(5.3.30) B≤0 for different types of neutrinos.
2.Massless mediators.For the mass problem, we know that the mediators:(5.3.31) γ,gk,ν and their dual particles,
have no masses. To explain this, we note that these particlesin (5.3.31) consist of pairs as
(5.3.32) w 1 w 1 , w 2 w 2 , w∗w∗, νlνl.
The weakton pairs in (5.3.32) are bound in a circle with radiusR 0 as shown in Figure5.8.
Since the interacting force on each weakton pair is in the direction of their connecting line,
they rotate around the center 0 without resistance. As~F=0 in the moving direction, by the
relativistic motion law:
(5.3.33)
d
dt~P=
√
1 −
v^2
c^2