Mathematical Principles of Theoretical Physics

5.3. WEAKTON MODEL OF ELEMENTARY PARTICLES 293

Table 5.8: Weakton quantum numbers

Weakton Qe Qw Qs Qc Le Lμ Lτ B J m

w∗ 2 / 3 1 1 0 0 0 0 1 / 3 ± 1 / 2 0

w 1 − 1 / 3 1 0 1 0 0 0 0 ± 1 / 2 0

w 2 − 2 / 3 1 0 -1 0 0 0 0 ± 1 / 2 0

νe 0 1 0 0 1 0 0 0 − 1 / 2 0

νμ 0 1 0 0 0 1 0 0 − 1 / 2 0

ντ 0 1 0 0 0 0 1 0 − 1 / 2 0

4) The weakton confinement theory given by the layered formulas of weak interaction

potentials (5.3.15)-(5.3.16); and

5) The duality (5.3.17) for the mediators.

The weaktons consist of the following 6 elementary particles and their antiparticles:

(5.3.18)

w∗, w 1 , w 2 , νe, νμ, ντ,

w∗, w 1 , w 2 , νe, νμ, ντ,

whereνe,νμ,ντare the three flavor neutrinos, andw∗,w 1 ,w 2 are three new elementary parti-
cles, which we callw-weaktons.
These weaktons in (5.3.18) are endowed with the quantum numbers: electric chargeQe,
weak chargeQw, strong chargeQs, weak color chargeQc, baryon numberB, lepton numbers
Le,Lμ,Lτ,spinJ, and massm. The quantum numbers of weaktons are listed in Table5.8.
A few remarks are now in order.

Remark 5.9.For the weaktons and antiweaktons, the quantum numbersQe,Qc,B,Le,Lμ,Lτ
have opposite signs, andQw,Qs,mhave the same values. The neutrinosνe,νμ,ντpossess left-
hand helicity with spinJ=−^12 , and the antineutrinosνe,νμ,ντpossess right-hand helicity
with spinJ=^12.

Remark 5.10.The weak color chargeQcis a new quantum number introduced for the weak-
tons only, which will be used to rule out some unrealistic combinations of weaktons.

Remark 5.11.Since the fundamental composite particles as quarks only contain onew∗-
weakton, there is no strong interaction between the constituent weaktons of a composite
particle, except the gluons. Therefore, for the weaktons (5.3.18), there is no need to introduce
the classical strong interaction quantum numbers as strange numberS, isospin(I,I 3 )and
parityπetc.

Remark 5.12.It is known that the quark model is based on the irreducible representations
ofSU( 3 )as

meson= 3 ⊗ 3 = 8 ⊕ 1 ,

baryon= 3 ⊗ 3 ⊗ 3 = 10 ⊕ 8 ⊕ 8 ⊕ 1.

However, the weakton model is based on the aforementioned theories and observational facts
1)-5), different from the quark model.