5.3. WEAKTON MODEL OF ELEMENTARY PARTICLES 299
bounding particles will rotate, at high speed with almost zero moment of force, which must
be excluded for composite particles withJ 6 =^12 based on the angular momentum rule.
The exclusion for (5.3.39) is based on the observation that by the left-hand helicity of
neutrinos with spinJ=−^12 , one ofw 1 andw 2 must be in the state withJ= +^12 to combine
withνj( 1 ≤j≤ 3 ), i.e. in the manner as
νjw 1 w 2 (↓⇈,↓↑↓,↑).
In summary, under the above rules 1-4, only the weakton constituents in (5.3.19) and
(5.3.24)-(5.3.26) are allowed.
5.Eight quantum states of gluons.It is known that the gluons have eight quantum states
gk:g^1 ,···,g^8.In (5.3.24) and (5.3.25), the vector and scalar gluons have the forms
w∗w∗(⇈,) and w∗w∗(↑↓,↓↑).According toQCD, quarks have three colors
red(r), green(g), blue(b),and anticolorr,g,b. They obey the rules
bb=rr=gg=w (white).Based on (5.3.19),w∗is endowed with three colors and anticolors:
w∗r,w∗g,w∗b and w∗r,w∗g,w∗b,which form the bases ofSU( 3 )andSU( 3 ). By the irreducible representation:
3 × 3 = 8 ⊕ 1 ,we can derive the eight-multiple states as
(5.3.40) g^1 = (w∗w)w, g^2 =w∗bw∗r, g^3 =wb∗w∗g, g^4 =w∗rw∗g,
(5.3.41) g^5 = (w∗w)w, g^6 =w∗rw∗b, g^7 =wg∗w∗b, g^8 =w∗gw∗r.
where(w∗w∗)wis a linear combination ofw∗bw∗b,w∗rw∗r,w∗gw∗g. Namely, the gluons in (5.3.41)
are the antigluons of these in (5.3.40).
In summary, the quantum rules presented above can be simply expressed in the following
formulas for quantum numbersQc,Qe,LandB:
(5.3.42)
weak color neutral: Qc= 0 ,
mutual exclusion of leptons and baryons: BL= 0 ,LiLj= 0 (i 6 =j),
relation of leptons and charges: L+Qe= 0 (L 6 = 0 ),
relation of baryons and charges: |B+Qe| ≤ 1 (B 6 = 0 ).These relations are summed up from realistic particle data.Based on (5.3.42), together with
the mass generation mechanism, the Angular Momentum Rule5.8and the layered formulas
of weak and strong interaction potentials, all of the most basic problems in the weakton model
have a reasonable explanation.