Mathematical Principles of Theoretical Physics

5.3. WEAKTON MODEL OF ELEMENTARY PARTICLES 295

we takeα 1 ,α 2 ,β 1 ,β 2 in (5.3.22) as follows

α 1 =cosθw, α 2 =−sinθw, β 1 =sinθw, β 2 =cosθw.

There is a natural duality in the spin arrangements:

(5.3.23) (⇈,)↔(↑↓,↓↑),

which not only yields new mediators with spinJ=0, but also gives the same conclusions as
in (5.3.17).
Thus, based on (5.3.23), the weakton model also leads to the dual mediators as follows:

γ=cosθww 1 w 1 −sinθww 2 w 2 (⇈,),

Z=sinθww 1 w 1 +cosθww 2 w 2 (⇈,),

(5.3.24) W−=w 1 w 2 (⇈,),

W+=w 1 w 2 (⇈,),

gk=w∗w∗(⇈,),

and their dual particles

γ 0 =cosθww 1 w 1 −sinθww 2 w 2 (↑↓,↓↑),

H^0 =sinθww 1 w 1 +cosθww 2 w 2 (↑↓,↓↑),

(5.3.25) H−=w 1 w 2 (↑↓,↓↑),

H+=w 1 w 2 (↑↓,↓↑),

gk 0 =w∗w∗(↑↓,↓↑).

3.Theν-mediator.By the weak interaction potential formulaΦwmin (5.3.15), the neutrino
pairs

(5.3.26) νeνe, νμνμ, ντντ (↓↑)

should be bounded by the weak interacting force to form a new mediator, although they have
not been discovered. The three pairs in (5.3.26) may be indistinguishable. Hence, they will
be regarded as a particle, i.e. their linear combination

(5.3.27) ν=∑
l

αlνlνl(↓↑), ∑

l

αl= 1 ,

is an additional mediator, and we call it theν-mediator. We believe thatνis an independent
new mediator.

5.3.5 Weakton confinement and mass generation

Since the weaktons are assumed to be massless and no freew-weaktons are found, we have
to explain: i) thew-weakton confinement, and ii) the mass generation mechanismfor the
massive composite particles, including the charged leptonse,μ,τ, the quarksu,d,s,c,t,b,
and the bosonsW±,Z,H±,H^0.