298 CHAPTER 5. ELEMENTARY PARTICLES
Actually, in the weakton exchange theory in the next section, we can see that the particles in
(5.3.36) are in some transition states in the weakton exchange procedure. At the moment of
exchange, the weaktons in (5.3.36) are at a speedvwithv<c. Hence, the particles in (5.3.35)
are massive, and their life-times are very short(τ≃ 10 −^25 s).
5.3.6 Quantum rules for weaktons
By carefully examining the quantum numbers of weaktons, thecomposite particles in (5.3.19)
and (5.3.24)-(5.3.26) are well-defined.
In the last subsection, we solved the free weakton problem and the mass problem. In this
subsection, we propose a few rules to resolve the remainningproblems.
- Weak color neutral rule: All composite particles by weaktons must be weak color
neutral.
Based on this rule, many combinations of weaktons are ruled out. For example, it is clear
that there are no particles corresponding to the followingwwwandwwcombinations, because
they all violate the weak color neutral rule:
νew 1 w 2 ,w∗w 2 w 2 ,w∗w 1 w 2 , etc.,νew 1 ,w∗w 1 ,w∗w 2 etc.2.BL= 0 ,LiLj= 0 (i 6 =j), where B is the baryon number, and L=Lj=Le,Lμ,Lτare
the lepton numbers.
The following combinations of weaktonsw∗νi, νiνj, νiνk(i 6 =k),are not observed in Nature, and are ruled out by this rule.
3.L+Qe= 0 ,|B+Qe| ≤ 1 for L,B 6 = 0.
The following combinations of weaktons(5.3.37) νiw 1 w 1 ,νiw 2 w 2 ,νiw 1 w 2 ,w∗w∗ etc
cannot be found in Nature, and are ruled out this rule.
4.Spin selection.In reality, there are no weakton composites with spinJ=^32 as(5.3.38) w∗w 1 w 1 (↑↑↑,↓↓↓),w∗w 2 w 2 (↑↑↑,↓↓↓),w∗w 1 w 2 (↑↑↑,↓↓↓),
and as
(5.3.39) νw 1 w 2 (↑↑↑,↓↓↓).
The cases (5.3.38) are excluded by the Angular Momentum Rule5.8. The reasons for this
exclusion are two-fold. First, the composite particles in (5.3.38) carry one strong charge, and
consequently, will be confined in a small ball by the strong interaction potential as the quarks
confined in hadrons, as shown in Figure5.7(b). Second, due to the uncertainty principle, the