A Unified Mass Theory of Elementary Fermions and Elementary Bosons

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A Unified Mass Theory of Elementary Fermions and Elementary Bosons

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Abstract

Base on photon generation, a unified mass theory of elementary fermions and elementary bosons is postulated.

1. Introduction

After obtaining a unified mass theory of twelve elementary fermions [1], extravagant hopes naturally, subsequently what about the other six elementary bosons, B = H , Z , W + , W and γ , g ? ! . May these six bosons be merged into the existing unified mass theory of twelve elementary fermions mentioned?

Ahead of us, light; Genesis of mass, light.

In this paper, we will use photon generation Q ( γ Q , ξ ) , instead of zeroth generation Zth of fermion Q ( Ψ ( 0 ) , ξ ) of Table 0 [1], to make a new larger Table X below, in which six elementary bosons B are included. Further, all the masses of both twelve elementary fermions and six elementary bosons of Standard Model SM could be uniformly identified.

IN Table 0, column ( Q ( Ψ ( 0 ) , ξ ) , ξ ( Ψ ( 0 ) ) ) is the zeroth zh of generation of fermion.

( 00.1 ) ( Q ( Ψ ( 0 ) , ξ ) , ξ ( Ψ ( 0 ) )

IN Table X, column ( Q ( γ Q , ξ ) , ξ ( γ Q ) ) is the generation of photon.

( Q ( γ Q , ξ ) , ξ ( γ Q ) )

OR

( 00.2 ) Q ( Ψ ( 0 ) , ξ ) = [ Q ( δ ( 0 ) , ξ ) Q ( γ ( 0 ) , ξ ) Q ( β ( 0 ) , ξ ) Q ( α ( 0 ) , ξ ) ] Q ( γ Q , ξ ) = [ Q ( γ + 2 3 e , ξ ) Q ( γ 1 3 e , ξ ) Q ( γ e , ξ ) Q ( γ 0 e , ξ ) ] Table 0  fermion zeroth generation Table 0  photon generation For twelve elementary fermions For twelve elementary bosons and six elementary bosons

The color representation of particle ω is defined as below. And ξ ( ω ) is called as mass function.

( 00.3 ) Q ( γ Q , ξ ) + i ξ ( ω )

Base on ScalarProduct-Mass Equation, the mass value M ( ω ) of a particle ω could be obtained below

( 00.4 ) Q 2 ( γ Q , ξ ) ξ 2 ( ω ) = Q 2 ( ω ) = M ( ω ) M ( e )

Here ω = F , B fermion, boson. CHARGE of ω rely on photon generation Q ( γ Q , ξ ) and MASS of ω relate to mass function ξ ( ω ) .

AND Q 2 ( γ Q , ξ ) is the scalar product of Q ( γ Q , ξ ) that comprises four members, each one of Q ( γ Q , ξ ) with different charge: Q ( γ Q , ξ ) = ( 0 e , e , 1 e 3 2 e 3 ) Q ~ ( γ Q , ξ ) = ( 0 e , + e , 1 e 3 2 e 3 ) .

Analogy with what did for the masses of the twelves elementary fermions, NOW, the more detailed discussions for the masses of the six elementary bosons ω = H , Z , W + , W and γ , g are given in the next three parts Part A, Part B and Part C following

Part A and Part C are related to four neutral bosons H, Z and γ g , that all with same charge, 0e, So, both H, Z and γ g belong to the common photon generation members (A.1) (C.1) and (A.2) (C.2); But accompanied by the different mass function ξ ( ω ) : ξ ( Z ) , ξ ( H ) by (A.7), (A.8) and photon ξ ( γ ) by (C.4), gluon ξ ( g ) by (C.24), (C.25), ..... , (C.30), (C.31). Subsequently result in bosons Z, H massive (A.13), (A.12), and γ g massless (C.9), (C.36). NOTICE: photon γ is just γ 0 e .

Part B is related to two charged bosons W , W + that with different particle charge -e, +e, So they belong to different photon generation. W (B.1), W + (B.2); W accompanied by mass function ξ ( W ) (B.13), ξ ( W + ) by (B.14). BUT at last, the two particles possess the same mass valus (B.17) (B.18).

Table X is defined as ( more details see Table 2 and Table 3 Table 4 & Table 5 ) :

( 00.5 )  Table X  =  Table 0  +  Part A  +  Part B  +  Part C 

Before discuss Part A, Part B, Part C First, glance over Table 1, the archives of elementary fermion and elementary boson below

Table 10717: Table 1. Mass M and Color Scalar Products Q 2 of Twelve elementary fermions q, l and six elementary bosons B
FermionFermionBoson
qI3YM(q) MeV|lI3YM(l) keV||BI3YM(B) MeV
t+5/2-11/3173,000.0|ντ+5/2-518,200.0||W++1080,400
c+3/2-5/31,280.0|νμ+3/2-3190.0||Z, H0091,200,125,000
u+1/2+1/32.3|νe+1/2-10.002||W--1080,400
d-1/2+1/34.8|e--1/2-1511.0||
s-3/2+7/395.0|μ--3/2+1105,700.0||γ000
b-5/2+13/34,700.0|τ--5/2+31,777,000.0||g000
 
Q2(q)Q(q)Q2(l)Q(l)Q2(B)
t+5/2-11/3338,551.859099 8043Q(t)|ντ+5/2-535.616438 3562Q(ντ)||H00244,618.395303 3268
c+3/2-5/32,504.892367 9061Q(c)|νμ+3/2-30.371819 9609Q(νμ)||Z00178,473.581213 3072
u+1/2+1/34.500978 4736Q(u)|νe+1/2-10.000003 9139Q(νe)||W±±10157,338.551859 0998
d-1/2+1/39.393346 3796Q(d)|e--1/2-11.000000 0000Q(e-)||
s-3/2+7/3185.909980 4305Q(s)|μ--3/2+1206.849315 0685Q(μ-)||γ000.000000 0000
b-5/2+13/39,197.651663 4051Q(b)|τ--5/2+33,477.495107 6321Q(τ-)||g000.000000 0000

Decompose the color scalar products Q 2 ( B ) of Six Bosons of the right column of Table1, into three dimensional color space Q ( B ) following

  • Boson Ground States for massive particles B = H , Z , W , W + :
( 0.1 ) Q ( H ) = ( + 2 0 1. 9 1 5 1 6 1 7 6 4 9 2 , + 2 0 1. 9 1 5 1 6 1 7 6 4 9 2 , 4 0 3. 8 3 0 3 2 3 5 0 9 8 4 )
( 0.2 ) Q 2 ( H ) = 2 4 4 , 6 1 8. 3 9 5 3 0 3 3 2 2 8 = 1 2 4 , 9 9 9 . 9 9 9 9 9 9 9 8 0 0 . 5 1 1 = M ( H ) 0 . 5 1 1
( 0.3 ) Q ( Z ) = ( + 1 7 2. 4 6 9 1 1 8 5 9 4 8 6 , + 1 7 2. 4 6 9 1 1 8 5 9 4 8 6 , 3 4 4. 9 3 8 2 3 7 1 8 9 7 2 )
( 0.4 ) Q 2 ( Z ) = 1 7 8 , 4 7 3. 5 8 1 2 1 3 3 2 7 4 = 9 1 , 2 0 0 . 0 0 0 0 0 0 0 1 0 3 0 . 5 1 1 = M ( Z ) 0 . 5 1 1
( 0.5 ) Q ( W ) = ( 1 6 1. 9 3 2 8 8 3 1 4 3 6 0 , 1 6 3. 9 3 2 8 8 3 1 4 3 6 0 , + 3 2 2. 8 6 5 7 6 6 2 8 7 2 0 )
( 0.6 ) Q 2 ( W ) = 1 5 7 , 3 3 8. 5 5 1 8 5 9 1 9 2 9 = 8 0 , 4 0 0 . 0 0 0 0 0 0 0 4 7 6 0 . 5 1 1 = M ( W ) 0 . 5 1 1
( 0.7 ) Q ( W + ) = ( 1 5 9. 9 3 2 8 8 3 1 4 3 6 0 , 1 6 1. 9 3 2 8 8 3 1 4 3 6 0 , + 3 2 4. 8 6 5 7 6 6 2 8 7 2 0 )
( 0.8 ) Q 2 ( W + ) = 1 5 7 , 3 3 8. 5 5 1 8 5 9 1 9 2 9 = 8 0 , 4 0 0 . 0 0 0 0 0 0 0 4 7 6 0 . 5 1 1 , = M ( W + ) 0 . 5 1 1
  • Boson Ground States for massless photon, gluon, B = γ , g :
( 0.9 ) Q ( γ , g ) = ( 0. 0 0 0 0 0 0 0 0 0 0 , 0. 0 0 0 0 0 0 0 0 0 0 , 0. 0 0 0 0 0 0 0 0 0 0 )
( 0.10 ) Q 2 ( γ , g ) = 0. 0 0 0 0 0 0 0 0 0 0 = 0 . 0 0 0 0 0 0 0 0 0 0 0 . 5 1 1 , = M ( γ , g ) 0 . 5 1 1

The above six formulas Q 2 (0.2) (0.4) (0.6) (0.8) (0.10) will help us to use ScalarProduct-Mass Equation (00.4) (0.11) to calculate the mass M ( B ) of the above six boson particle ω = B

( 0.11 ) Q 2 ( γ Q , ξ ) ξ 2 ( ω = B ) = Q 2 ( ω = B ) = M ( ω = B ) M ( e )

Later we will see the formulas Q 2 (0.2) (0.4) (0.6) (0.8) (0.10) are just formulas (A.13) (A.12) (B.17) (B.18) (C.9) (C.36).

Table 10716: Table X. Unified Mass Theory of Elementary Fermion and Elementary Boson
Boson γαFermionFermionFermionBosonQ(ω)
|1st2nd3rd|Force CarriersCharge
γ+2/3|uct|+2/3e
(Q+2/3, ξ), ξ(δ(0)))|(Q+2/3, ξ), ξ(u))(Q+2/3, ξ), ξ(c))(Q+2/3, ξ), ξ(t))|
γ-2/3||-2/3e
(Q-2/3, ξ), ξ(δ̃(0)))|(Q-2/3, ξ), ξ(ũ))(Q-2/3, ξ), ξ(c̃))(Q-2/3, ξ), ξ(t̃))|
γ-1/3|dsb|-1/3e
(Q-1/3, ξ), ξ(γ(0)))|(Q-1/3, ξ), ξ(d))(Q-1/3, ξ), ξ(s))(Q-1/3, ξ), ξ(b))|
γ+1/3||+1/3e
(Q+1/3, ξ), ξ(γ̃(0)))|(Q+1/3, ξ), ξ(d̃))(Q+1/3, ξ), ξ(s̃))(Q+1/3, ξ), ξ(b̃))|
γ-|eμτ|-e
(Q-, ξ), ξ(γ-))|(Q-, ξ), ξ(e-))(Q-, ξ), ξ(μ-))(Q-, ξ), ξ(τ-))|(Q-, ξ), ξ(W-))
γ+|μ̃τ̃|+e
(Q+, ξ), ξ(γ+))|(Q+, ξ), ξ(e+))(Q+, ξ), ξ(μ+))(Q+, ξ), ξ(τ+))|(Q+, ξ), ξ(W+))
γ0|νeνμντ|0e
(Q0, ξ), ξ(γ0))|(Q0, ξ), ξ(νe))(Q0, ξ), ξ(νμ))(Q0, ξ), ξ(ντ))|(Q0, ξ), ξ(Z, H; γ, g))
γ̃0|ν̃eν̃μν̃τ|0e
(Q(γ̃0, ξ), ξ(γ̃0))|(Q(γ̃0, ξ), ξ(ν̃e))(Q(γ̃0, ξ), ξ(ν̃μ))(Q(γ̃0, ξ), ξ(ν̃τ))|(Q(γ̃0, ξ), ξ(Z, H; γ, g))
ZeroMassNon-Zero-MassNon-Zero-MassNon-Zero-Mass
Table 10715: Table 2. Photon Generation Q ( γ Q , ξ ) and Mass Function MF ξ ( ω ) of Elementary Fermion and Elementary Boson
Photon GenerationMF ξ(γQ)MF ξ(F)MF ξ(F)MF ξ(F)MF ξ(B)Charge
QQ, ξ)Fermion 1stFermion 2ndFermion 3rdForce CarriersQ(ω)
||γ+2/3|uct|||  +2/3 e
Q+2/3, ξ)||ξ(γ+2/3)|ξ(u)ξ(c)ξ(t)|||
||γ-2/3|ũ|||  -2/3 e
Q-2/3, ξ)||ξ(γ-2/3)|ξ(ũ)ξ(c̃)ξ(t̃)|||
||γ-1/3|dsb|||  -1/3 e
Q-1/3, ξ)||ξ(γ-1/3)|ξ(d)ξ(s)ξ(b)|||
||γ+1/3||||  +1/3 e
Q+1/3, ξ)||ξ(γ+1/3)|ξ(d̃)ξ(s̃)ξ(b̃)|||
||γ-|eμτ|||  -e
Q-, ξ)||ξ(γ-)|ξ(e-)ξ(μ-)ξ(τ-)|ξ(W-)||
||γ+|μ̃τ̃|||  +e
Q+, ξ)||ξ(γ+)|ξ(e+)ξ(μ+)ξ(τ+)|ξ(W+)||
||γ0|νeνμντ|||  0e
Q0, ξ)||ξ(γ0)|ξ(νe)ξ(νμ)ξ(ντ)|ξ(Z, H; γ, g)||
||γ̃0|ν̃eν̃μν̃τ|||  0e
Q(γ̃0, ξ)||ξ(γ̃0)|ξ(ν̃e)ξ(ν̃μ)ξ(ν̃τ)|ξ(Z, H; γ, g)||
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMass
  1. Part A: Unified Mass Theory of Two Dirac Neutral Mass Bosons B = H, Z B = H, Z

◆ Detailed values of Q ( γ 0 , ξ ) of particles B=Z,H bwlow

( A.2 ) 0 Q ( γ ~ 0 , ξ ) = ( + 238.53965485315 ,   + 236.53965485315 ,   475.07930970630 )
( A.2 ) 0 Q ( γ ~ 0 , ξ ) = ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 )

The charges of particles B = Z , H are zero

( A.3 ) Q = 1 3 ( 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 ) = 0
( A.4 ) Q = 1 3 ( 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 ) = 0

AND below

◆ Detailed values of mass function ξ ( B ) of particles B = Z, H below

( A.5 ) 1 ξ ( Z ) = ( + 1 6 3. 3 3 9 5 9 7 4 4 1 0 4 4 , + 1 6 3. 3 3 9 5 9 7 4 4 1 0 4 4 , 3 2 6. 6 7 9 1 9 4 8 8 2 0 8 8 )
( A.6 ) 2 ξ ( H ) = ( + 1 2 5. 1 2 2 6 9 3 4 2 7 2 9 5 , + 1 2 5. 1 2 2 6 9 3 4 2 7 2 9 5 , 2 5 0. 2 4 5 3 8 6 8 5 4 5 9 0 )
( A.7 ) 1 ξ ( Z ) = 1 6 3. 3 3 9 5 9 7 4 4 1 0 4 4 ( + 1 , + 1 , 2 ) = 1 6 3. 3 3 9 5 9 7 4 4 1 0 4 4 ξ 0
( A.8 ) 2 ξ ( H ) = 1 2 5. 1 2 2 6 9 3 4 2 7 2 9 5 ( + 1 , + 1 , 2 ) = 1 2 5. 1 2 2 6 9 3 4 2 7 2 9 5 ξ 0

Where ξ 0 called as Color-Unit Constant that is a three dimensional colore vector, with which ξ ( ω ) could be limpid. see following

( 00.6 ) ξ 0 = ( + 1 , + 1 , 2 )
( 00.7 ) ξ 0 2 = 6

Expressions of the color scalar products of the above 0, 1, 2 are given below

( A.9 ) 1 Q 2 ( γ 0 , ξ ) = Q 2 ( γ ~ 0 , ξ ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8
( A.10 ) 2 ξ 2 ( Z ) = 1 6 0 , 0 7 8. 9 4 4 5 5 3 2 1 3 8
( A.11 ) 3 ξ 2 ( H ) = 9 3 , 9 3 4. 1 3 0 4 6 3 0 0 5 2

Finally using ScalarProduct-Mass Equation (0.11): The masses of two neutral Dirac leptons Z, H are obtained by using a common color scalar product Q 2 ( γ 0 , ξ ) of photon generation of particle γ 0 and color scalar product ξ 2 ( Z ) , ξ 2 ( H ) of mass function ξ ( Z ) , ξ ( H ) of particles Z, H

( A.12 ) 1 Q 2 ( γ 0 , ξ ) ξ 2 ( Z ) = = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 1 6 0 , 0 7 8. 9 4 4 5 5 3 2 1 4 6 = 1 7 8 , 4 7 3. 5 8 1 2 1 3 3 0 7 2 = 9 1 , 2 0 0 . 0 0 0 0 0 0 0 0 0 0 0 . 5 1 1 = M ( Z ) M ( e ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 1 6 0 , 0 7 8. 9 4 4 5 5 3 2 1 3 8 = 1 7 8 , 4 7 3. 5 8 1 2 1 3 3 0 8 0 = 9 1 , 2 0 0 . 0 0 0 0 0 0 0 0 4 0 . 5 1 1
( A.13 ) 2 Q 2 ( γ 0 , ξ ) ξ 2 ( H ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 9 3 , 9 3 4. 1 3 0 4 6 3 1 9 5 0 = 2 4 4 , 6 1 8. 3 9 5 3 0 3 3 2 6 8 = 1 2 5 , 0 0 0 . 0 0 0 0 0 0 0 0 0 0 0 . 5 1 1 = M ( H ) M ( e ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 9 3 , 9 3 4. 1 3 0 4 6 3 0 0 5 2 = 2 4 4 , 6 1 8. 3 9 5 3 0 3 5 1 6 6 = 1 2 5 , 0 0 0 . 0 0 0 0 0 0 0 9 7 0 . 5 1 1
  1. Part B: Unified Mass Theory of Two Dirac Charged Mass Bosons B = W , W +

• Detailed values of photon generation Q ( γ , ξ ) Q ( γ + , ξ ) of particle γ and anti-particle γ +

( B.1 ) 0 Q ( γ , ξ ) = ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 8. 0 7 9 3 0 9 7 0 6 3 0 )
( B.2 ) 0 Q ( γ + , ξ ) = ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 4 7 2. 0 7 9 3 0 9 7 0 6 3 0 )

The charges of particles B = W , W +

( B.3 ) Q ( W ) = 1 3 ( 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 4 7 8. 0 7 9 3 0 9 7 0 6 3 0 ) = e
( B.4 ) Q ( W + ) = 1 3 ( 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 4 7 2. 0 7 9 3 0 9 7 0 6 3 0 ) = + e

And the color scalar products of (B.1) (B.2) are below

( B.5 ) 0 Q 2 ( γ , ξ ) = 3 4 1 , 4 1 2. 0 0 1 6 2 4 7 5 9 6
( B.6 ) 0 Q 2 ( γ + , ξ ) = 3 3 5 , 7 1 1. 0 4 9 9 0 8 2 8 4 0

Because of requirement of final results (B.7) (B.8) below, Then having color scalar products (B.9) (B.10)

( B.7 ) 1 Q 2 ( γ , ξ ) ξ 2 ( W ) = = 3 4 1 , 4 1 2. 0 0 1 6 2 4 7 5 9 6 1 8 4 , 0 7 3. 4 4 9 7 6 5 6 5 9 8 = 1 5 7 , 3 3 8. 5 5 1 8 5 9 0 9 9 8 = 8 0 , 4 0 0 . 0 0 0 0 0 0 0 0 0 0 . 5 1 1
( B.8 ) 1 Q 2 ( γ + , ξ ) ξ 2 ( W + ) = = 3 3 5 , 7 1 1. 0 4 9 9 0 8 2 8 4 0 1 7 8 , 3 7 2. 4 9 8 0 4 9 1 8 4 2 = 1 5 7 , 3 3 8. 5 5 1 8 5 9 0 9 9 8 = 8 0 , 4 0 0 . 0 0 0 0 0 0 0 0 0 0 0 . 5 1 1

OR

( B.9 ) ξ 2 ( W ) = 1 8 4 , 0 7 3. 4 4 9 7 6 5 6 5 9 8
( B.10 ) ξ 2 ( W + ) = 1 7 8 , 3 7 2. 4 9 8 0 4 9 1 8 4 2

FURTHER, Discompose color scalar products (B.9) and (B.10) into their mass function (B.11) (B.13) and (B.12) B.14) below

( B.11 ) 1 ξ ( W ) = ( + 1 7 5. 1 5 3 9 5 5 9 7 6 6 7 , + 1 7 5. 1 5 3 9 5 5 9 7 6 6 7 , 3 5 0. 3 0 7 9 1 1 9 5 3 3 4 )
( B.12 ) 2 ξ ( W + ) = ( + 1 7 2. 4 2 0 2 7 0 4 8 7 1 6 , + 1 7 2. 4 2 0 2 7 0 4 8 7 1 6 , 3 4 4. 8 4 0 5 4 0 9 7 4 3 2 )

OR

( B.13 ) 1 ξ ( W ) = 1 7 5. 1 5 3 9 5 5 9 7 6 6 7 ( + 1 , + 1 , 2 ) = 1 7 5. 1 5 3 9 5 5 9 7 6 6 7 ξ 0
( B.14 ) 2 ξ ( W + ) = 1 7 2. 4 2 0 2 7 0 4 8 7 1 6 ( + 1 , + 1 , 2 ) = 1 7 2. 4 2 0 2 7 0 4 8 7 1 6 ξ 0

NOW USING (B.13) and (B.14), obtain (B.15) and (B.16); Finally the masses (B.17) and (B.18) of charged bosons W and W + are given

( B.15 ) ξ 2 ( W ) = 1 8 4 , 0 7 3. 4 4 9 7 6 5 6 6 3 5
( B.16 ) ξ 2 ( W + ) = 1 7 8 , 3 7 2. 4 9 8 0 4 9 1 9 2 4
( B.17 ) 1 Q 2 ( γ , ξ ) ξ 2 ( W ) = = 3 4 1 , 4 1 2. 0 0 1 6 2 4 7 5 9 6 1 8 4 , 0 7 3. 4 4 9 7 6 5 6 6 3 5 = 1 5 7 , 3 3 8. 5 5 1 8 5 9 0 9 6 1 = 8 0 , 3 9 9 . 9 9 9 9 9 9 9 9 8 1 0 . 5 1 1 = M ( W ) M ( e )
2 Q 2 ( γ + , ξ ) ξ 2 ( W + ) = = 3 3 5 , 7 1 1. 0 4 9 9 0 8 2 8 4 0 1 7 8 , 3 7 2. 4 9 8 0 4 9 1 9 2 4 = 1 5 7 , 3 3 8. 5 5 1 8 5 9 0 9 1 6 = 8 0 , 3 9 9 . 9 9 9 9 9 9 9 9 5 8 0 . 5 1 1 = M ( W + ) M ( e ) ( B . 1 8 )
  1. Part C: Unified Mass Theory of Two Dirac Neutral Massless Bosons B = γ , g

Both Boson photon γ and Boson gluon g are massless particles. Photon γ is mediating particle in electromagnetic interaction, And gluon g in strong interaction.

◆ Detailed values of photon generation of particles B = γ , g bwlow

( C.1) (A.1 ) 0 Q ( γ 0 , ξ ) = ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 )
( C.2) (A.2 ) 0 Q ( γ ~ 0 , ξ ) = ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 )

◆ Next two paragraphs search for detailed values of mass function of particles B = γ , g respectively

FIRST discuss mass function ξ ( γ ) of photon B = γ following:

The color representation of mass function of photon is given below

( C.3 ) ■ γ ξ ( γ ) = ( + 2 3 7. 5 4 0 3 5 6 4 8 9 3 4 9 , + 2 3 7. 5 4 0 3 5 6 4 8 9 3 4 9 , 4 7 5. 0 8 0 7 1 2 9 7 8 6 9 8 )
( C.4 ) = κ ( + 1 , + 1 , 2 ) = κ ξ 0

Where

( C.5 ) κ = 2 3 7. 5 4 0 3 5 6 4 8 9 3 4 9

From (C.4), having

( C.6 ) ξ 2 ( γ ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 2 0

Further the expressions of the color scalar products of photon generation and mass function of photon γ are given below

( C.7 ) Q 2 ( γ 0 , ξ ) = Q 2 ( γ ~ 0 , ξ ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8
( C.8 ) ξ 2 ( γ ) = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 2 0

Last making subtraction, using ScalarProduct-Mass Equation:

( C.9 ) | Q 2 ( γ 0 , ξ ) ξ 2 ( γ ) | = = | 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 2 0 | = 0. 0 0 0 0 0 0 0 0 0 2 = 0 . 0 0 0 0 0 0 0 0 0 1 0 . 5 1 1 = M ( γ ) 0 . 5 1 1 0

(C.9) shows from photon generation (C.1) and mass function (C.4), we could obtain mass of photon γ

SECOND discuss mass function ξ ( g ) of gluons B = g following:

In contrast with photon γ , the pictures of color representation of mass function ξ ( g ) of gluon is rough to be revealed.

Because of: The gluons are considered as the mediating particles in strong interaction, which both carry color charge and anti-color charge simultaneously. So a gluon actually is a mixture of element color and element anti-color. There are six colored gluons R G ~ , G B ~ , B R ~ & G R ~ , B G ~ , R B ~ and two color neutral gluons R R ~ , G G ~ (see following).

In the expedition to explore the color representations of twelve elementary fermions and six elementary bosons, the color representations of photon and gluon are the rather life of hardship, we could even not write down "the real ground states of photon and gluon." But the trivial ground state, Q ( γ ) = Q ( g ) = ( 0.0000000000 , 0.0000000000 , 0.0000000000 ) ! ! (see: (0.9)).

The way to the mass function of gluons B = g following :

THEN six mass function states of colored gluons

( C.24 ) ■ R G̃ ξ ( g R G ~ ) = 3 κ ( + 1 , 1 , 0 )
( C.25 ) ■ G B̃ ξ ( g G B ~ ) = 3 κ ( 0 , + 1 , 1 )
( C.26 ) ■ B R̃ ξ ( g B R ~ ) = 3 κ ( 1 , 0 , + 1 )
( C.27 ) ■ G R̃ ξ ( g G R ~ ) = 3 κ ( 1 , + 1 , 0 )
( C.28 ) ■ B G̃ ξ ( g B G ~ ) = 3 κ ( 0 , 1 , + 1 )
( C.29 ) ■ R B̃ ξ ( g R B ~ ) = 3 κ ( + 1 , 0 , 1 )

AND three mass function states of color neutral gluons

( C.30 ) ■ R R̃ ξ ( g R R ~ ) = κ ( + 2 , 1 , 1 )
( C.31 ) ■ G G̃ ξ ( g G G ~ ) = κ ( 1 , + 2 , 1 )
( C.32 ) ■ B B̃ ξ ( g B B ~ ) = κ ( 1 , 1 , + 2 )

Due to the color representation of mass function of photon is given by (C.4), and compare it with (C.32)

( C.4 ) ■ γ ξ ( γ ) = κ ( + 1 , + 1 , 2 ) = + κ ξ 0
( C.32 ) ■ B B̃ ξ ( g B B ~ ) = κ ( 1 , 1 , + 2 ) = κ ξ 0

Having

( C.33 ) ξ ( g B B ~ ) = ξ ( γ )

Last, (C.30) and (C.31) are chosen as two color neutral candidates of eight color states of boson gluon (g)

( C.30 ) ■ R R̃ ξ ( g R R ~ ) = κ ( + 2 , 1 , 1 )
( C.31 ) ■ G G̃ ξ ( g G G ~ ) = κ ( 1 , + 2 , 1 )

Because of the color scalar products of the eight color states of boson gluon (g) are the same math value below

( C.34 ) ξ 2 ( g ) ξ 2 ( g R G ~ ) = ξ 2 ( g G B ~ ) = ξ 2 ( g B R ~ ) = ξ 2 ( g G R ~ ) = ξ 2 ( g B G ~ ) = ξ 2 ( g R B ~ ) = ξ 2 ( g R R ~ ) = ξ 2 ( g G G ~ )
( C.35 ) = 6 κ 2 = 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 2 0

Where κ = 237.540   356   489349 (C.5)

Then making subtraction, using ScalarProduct-Mass Equation:

( C.36 ) | Q 2 ( γ 0 , ξ ) ξ 2 ( g ) | = = | 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 1 8 3 3 8 , 5 5 2. 5 2 5 7 6 6 5 2 2 0 | = 0. 0 0 0 0 0 0 0 0 0 2 = 0 . 0 0 0 0 0 0 0 0 0 1 0 . 5 1 1 = M ( g ) 0 . 5 1 1 0

(C.36) shows from photon generation (C.1) and the eight color states ( (C.24), (C.25), ..... , (C.30), (C.31) ), we could obtain mass of gluon g

Photon Generation Charge Q ( γ Q , ξ ) and Particle Mass Function ξ ( ω ) of Table X

♦ Photon Generation Charge Q ( γ Q , ξ ) : In Part A & Part C, neutral particles H , Z & γ , g are related to charges Q ( γ 0 e , ξ ) & Q ( γ ~ 0 e , ξ ) AND In Part B charged particles W , W + related to charges Q ( γ e , ξ ) and Q ( γ + e , ξ ) shown in Table Y below

◆ Particle Mass Function ξ ( ω ) : H, Z & γ , g and W , W + are listed in Table3 below

For Particle:

( 1.1 ) Q ( γ Q , ξ ) = [ Q ( γ + 2 3 e , ξ ) Q ( γ 1 3 e , ξ ) Q ( γ e , ξ ) Q ( γ 0 e , ξ ) ] = [ ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 3. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 6. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 8. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 ) ] Table 0 photon generation Table Y1 values of photon generation ( Critical PG )

For Anti-Particle:

( 1.2 ) Q ( γ Q , ξ ) = [ Q ( γ 2 3 e , ξ ) Q ( γ + 1 3 e , ξ ) Q ( γ + e , ξ ) Q ( γ ~ 0 e , ξ ) ] = [ ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 7. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 4. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 2. 0 7 9 3 0 9 7 0 6 3 0 ) ( + 2 3 8. 5 3 9 6 5 4 8 5 3 1 5 , + 2 3 6. 5 3 9 6 5 4 8 5 3 1 5 , 4 7 5. 0 7 9 30970630 ) ] Table 0 photon generation Table Y1 values of photon generation ( Critical PG )
Table 10714: Table 3. Critical PG and Mass Function MF ξ ( ω ) values of Elementary Fermion and Elementary Boson (Color-Unit Constant ξ 0 )
QQ, ξ)Photon
Generation
Fermion
1st
Fermion
2nd
Fermion
3rd
Boson
Force Carriers
Boson
Force Carriers
Boson
Force Carriers
Q+2/3, ξ)ξ(γ+2/3)ξ(u)ξ(c)ξ(t)
236.890997571510236.889414215465236.0081834791060.0000000000
Q-2/3, ξ)ξ(γ-2/3)ξ(ũ)ξ(c̃)ξ(t̃)
238.224230106917238.222655612254237.34637504861118.040896875322
Q-1/3, ξ)ξ(γ-1/3)ξ(d)ξ(s)ξ(b)
237.873805614775237.870514860345237.808667632002234.629506784110
Q+1/3, ξ)ξ(γ+1/3)ξ(d̃)ξ(s̃)ξ(b̃)
237.207141245477237.203841242341237.141820143797233.953597779454
Q-, ξ)ξ(γ-)ξ(e-)ξ(μ-)ξ(τ-)ξ(W-)
238.541401586377238.541052240755238.469128788085237.323445434400175.15395597667
Q+, ξ)ξ(γ+)ξ(e+)ξ(μ+)ξ(τ+)ξ(W+)
236.541416355320236.541064055935236.468532294544235.313108715690172.42027048716
Q0, ξ)ξ(γ0)ξ(νe)ξ(νμ)ξ(ντ)ξ(γ)*ξ(Z)ξ(H)
237.540356489349237.540356487976237.540226048334237.527861287950237.540356489349163.339597441044125.122693427295
Q(γ̃0, ξ)ξ(γ̃0)ξ(ν̃e)ξ(ν̃μ)ξ(ν̃τ)ξ(g)***ξ(Z)ξ(H)
237.540356489349237.540356487976237.540226048334237.527861287950✉ ✉ ✉163.339597441044125.122693427295
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassZeroMassNon-ZeroMassNon-ZeroMass

Next, the detailed examples ( ξ ( υ e ) ξ ( υ ~ e ) and ξ ( γ ) ξ ( g ) ※※※ ) of characteristic vlues of Function- ξ ( ω ) are given

( 1.3 ) ξ ( ν e ) ξ ( γ ) 237.540356487976 237.540356489349 ξ ( ν ~ e ) ξ ( g ) 237.540356487976 ※※※
ξ ( ν e ) = ξ ( ν ~ e ) = ( + 237.540 356 487976 , + 237.540 356 487976 , 475.080 712 975952 ) ξ ( γ ) = ( + 237.540 356 489349 , + 237.540 356 489349 , 475.080 712 978698 ) ξ ( g ) = ξ ( g R R ~ ) = ( + 475.080 712 978698 , 237.540 356 489349 , 237.540 356 489349 ) ξ ( g G G ~ ) = ( 237.540 356 489349 , + 475.080 712 978698 , 237.540 356 489349 ) ξ ( g R G ~ ) = 3 ( + 237.540 356 489349 , 237.540 356 489349 , 0.000 000 000000 ) ξ ( g G B ~ ) = 3 ( 0.000 000 000000 , + 237.540 356 489349 , 237.540 356 489349 ) ξ ( g B R ~ ) = 3 ( 237.540 356 489349 , 0.000 000 000000 , + 237.540 356 489349 ) ξ ( g G R ~ ) = 3 ( 237.540 356 489349 , + 237.540 356 489349 , 0.000 000 000000 ) ξ ( g B G ~ ) = 3 ( 0.000 000 000000 , 237.540 356 489349 , + 237.540 356 489349 ) ξ ( g R B ~ ) = 3 ( + 237.540 356 489349 , 0.000 000 000000 , 237.540 356 489349 ) ξ ( ν e ) 2 = ξ ( ν ~ e ) 2 = 338 , 552.525 762 6079 (1.11) [1] ξ ( γ ) 2 = ξ ( g ) 2 = 338 , 552.525 766 5220 (C.6) (C.35)

Next Q ( γ Q , ξ ) -Running: increasing the values of Q ( γ Q , ξ ) from Critical PG, (1.1) and (1.2) to (2.1) and (2.2) below

For Particle:

( 2.1 ) Q ( γ Q , ξ ) = [ Q ( γ + 2 3 e , ξ ) Q ( γ 1 3 e , ξ ) Q ( γ e , ξ ) Q ( γ 0 e , ξ ) ] = [ ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 4 8. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 5 1. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 5 3. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 5 0. 1 5 8 6 1 9 1 4 1 2 6 0 ) ] Table 0 photon generation Table Y2 values of photon generation ( Running PG )

For Anti-Particle:

( 2.2 ) Q ( γ Q , ξ ) = [ Q ( γ 2 3 e , ξ ) Q ( γ + 1 3 e , ξ ) Q ( γ + e , ξ ) Q ( γ ~ 0 e , ξ ) ] = [ ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 5 2. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 4 9. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , 9 4 7. 1 5 8 6 1 9 4 1 2 6 0 ) ( + 4 7 5. 0 7 9 3 0 9 7 0 6 3 0 , + 4 7 5. 0 7 9 3 0 9 7 0 6 3 , 950.15861941260 ) ] Table 0 photon generation Table Y2 values of photon generation ( Running PG )

SUBSEQUENTLY, Table Y2 instead of Table Y1, Table4 instead of Table3. see below

Table 10713: Table 4. Q ( γ Q , ξ ) -Running and Mass Function MF ξ ( ω ) values of Elementary Fermion and Elementary Boson (Color-Unit Constant ξ 0 )
QQ, ξ)Photon
Generation
Fermion
1st
Fermion
2nd
Fermion
3rd
Boson
Force Carriers
Boson
Force Carriers
Boson
Force Carriers
Q+2/3, ξ)ξ(γ+2/3)ξ(u)ξ(c)ξ(t)
474.412877247312474.412086624059473.972674356608410.660770281391
Q-2/3, ξ)ξ(γ-2/3)ξ(ũ)ξ(c̃)ξ(t̃)
475.746209924251475.745421516814475.307241893043412.200371672955
Q-1/3, ξ)ξ(γ-1/3)ξ(d)ξ(s)ξ(b)
475.412701468404475.411054940622475.380112878891473.797736142317
Q+1/3, ξ)ξ(γ+1/3)ξ(d̃)ξ(s̃)ξ(b̃)
474.746034883786474.744386043845474.713400528296473.128793981064
Q-, ξ)ξ(γ-)ξ(e-)ξ(μ-)ξ(τ-)ξ(W-)
476.079834828600476.079659787898476.043626408948475.470742120363447.692882625925
Q+, ξ)ξ(γ+)ξ(e+)ξ(μ+)ξ(τ+)ξ(W+)
474.079837043933474.079661264787474.043475860345473.468171447314445.565483307544
Q0, ξ)ξ(γ0)ξ(νe)ξ(νμ)ξ(ντ)ξ(γ)*ξ(Z)ξ(H)
475.079309706300475.079309705614475.079244485613475.073062210388475.079309706300442.667768921716430.035600805864
Q(γ̃0, ξ)ξ(γ̃0)ξ(ν̃e)ξ(ν̃μ)ξ(ν̃τ)ξ(g)**ξ(Z)ξ(H)
475.079309706300475.079309705614475.079244485613475.073062210388⊛⊛⊛⊛442.667768921716430.035600805864
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassZeroMassNon-ZeroMassNon-ZeroMass
Q ( γ Q , ξ ) -Running increasing continuously following

For Particle:

( 3.1 ) Q ( γ Q , ξ ) = [ Q ( γ + 2 3 e , ξ ) Q ( γ 1 3 e , ξ ) Q ( γ e , ξ ) Q ( γ 0 e , ξ ) ] = [ ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 8 9 8. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 9 0 1. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 9 0 3. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 9 0 0. 3 1 7 2 3 8 8 2 5 2 ) ] Table 0 photon generation Table Y3 values of photon generation ( Running PG )

For Anti-Particle:

( 3.2 ) Q ( γ Q , ξ ) = [ Q ( γ 2 3 e , ξ ) Q ( γ + 1 3 e , ξ ) Q ( γ + e , ξ ) Q ( γ ~ 0 e , ξ ) ] = [ ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 9 0 2. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 8 9 9. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 8 9 7. 3 1 7 2 3 8 8 2 5 2 ) ( + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , + 9 5 0. 1 5 8 6 1 9 4 1 2 6 0 , 1 9 0 0. 3 1 7 2 3 8 8 2 5 2 ) ] Table 0 photon generation Table Y3 values of photon generation ( Running PG )

SUBSEQUENTLY, Table Y3 instead of Table Y2, Table5 instead of Table4. see below

Table 10712: Table 5. Q ( γ Q , ξ ) -Running and Mass Function MF ξ ( ω ) values of Elementary Fermion and Elementary Boson (Color-Unit Constant ξ 0 )
QQ, ξ)Photon
Generation
Fermion
1st
Fermion
2nd
Fermion
3rd
Boson
Force Carriers
Boson
Force Carriers
Boson
Force Carriers
Q+2/3, ξ)ξ(γ+2/3)ξ(u)ξ(c)ξ(t)
949.492069767572949.491674733607949.272199366541919.298580822107
Q-2/3, ξ)ξ(γ-2/3)ξ(ũ)ξ(c̃)ξ(t̃)
950.825402936807950.825008456794950.605840929154920.675641591529
Q-1/3, ξ)ξ(γ-1/3)ξ(d)ξ(s)ξ(b)
950.491981970565950.491158418953950.475682378879949.685245671655
Q+1/3, ξ)ξ(γ+1/3)ξ(d̃)ξ(s̃)ξ(b̃)
949.825315324411949.824491194761949.809004292115949.018012309153
Q-, ξ)ξ(γ-)ξ(e-)ξ(μ-)ξ(τ-)ξ(W-)
951.158882249902951.158794637476951.140759507781950.854161669888937.272707010274
Q+, ξ)ξ(γ+)ξ(e+)ξ(μ+)ξ(τ+)ξ(W+)
949.158882803734949.158795006698949.140721873942948.853519931973935.243012713122
Q0, ξ)ξ(γ0)ξ(νe)ξ(νμ)ξ(ντ)ξ(γ)*ξ(Z)ξ(H)
950.158619412600950.158619412257950.158586802258950.155495680049950.158619412600934.374552936441928.456606144576
Q(γ̃0, ξ)ξ(γ̃0)ξ(ν̃e)ξ(ν̃μ)ξ(ν̃τ)ξ(g)*×××ξ(Z)ξ(H)
950.158619412600950.158619412257950.158586802258950.155495680049⊛⊗⊗⊗934.374552936441928.456606144576
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassZeroMassNon-ZeroMassNon-ZeroMass

Table Z 4th, 5th of Elementary Fermion

If Q ( γ Q , ξ ) -Running increasing continuously and approaching to Table Z, we seem to run out "the despairing plateau" ! Finally the first light of morning, Table 6. below. Further Table 7, Ahead of us, light; Genesis of mass, light.

For Particle:

( 4.1 ) Q ( γ Q , ξ ) = [ Q ( γ 2 3 e , ξ ) Q ( γ 1 3 e , ξ ) Q ( γ e , ξ ) Q ( γ 0 e , ξ ) ] = [ ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 5 9 9. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 2. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 4. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 1. 2 6 8 9 5 5 3 0 0 8 ) ] Table 0 photon generation Table Z values of photon generation (Light PG)

For Anti-Particle:

( 4.2 ) Q ( γ Q , ξ ) = [ Q ( γ 2 3 e , ξ ) Q ( γ + 1 3 e , ξ ) Q ( γ + e , ξ ) Q ( γ ~ 0 e , ξ ) ] = [ ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 3. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 0. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 5 9 8. 2 6 8 9 5 5 3 0 0 8 ) ( + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , + 3 8 0 0. 6 3 4 4 7 7 6 5 0 4 , 7 6 0 1 . 2689553008 ) ] Table 0 photon generation Table Z values of photon generation (Light PG)
Table 10710: Table6   Photon Generation QQ, ξ) and Mass Function MF ξ(ω) values of Elementary Fermion
QQ, ξ)Photon
Generation
Fermion
1st
Fermion
2nd
Fermion
3rd
Fermion
4th
Fermion
5th
Q+2/3, ξ)ξ(γ+2/3)ξ(u)ξ(c)ξ(t)||ξ(q4+2/3)ξ(q5+2/3)
3799.9678402237473799.9677415172423799.9129075116203792.536127301197||3790.0406447548003786.324837743850
Q-2/3, ξ)ξ(γ-2/3)ξ(ũ)ξ(c̃)ξ(t̃)||ξ(q4-2/3)ξ(q5-2/3)
3801.3011735468243801.3010748749413801.2462601030133793.872072455593||3791.3774667253003787.662965515700
Q-1/3, ξ)ξ(γ-1/3)ξ(d)ξ(s)ξ(b)||ξ(q4-1/3)ξ(q5-1/3)
3800.9678182918143800.9676123498223800.9637423544703800.766161413529||3800.6977211029003800.596995634700
Q+1/3, ξ)ξ(γ+1/3)ξ(d̃)ξ(s̃)ξ(b̃)||ξ(q4+1/3)ξ(q5+1/3)
3800.3011516264293800.3009456483093800.2970749740643800.099459370670||3800.0310070534003799.930263914600
Q-, ξ)ξ(γ-)ξ(e-)ξ(μ-)ξ(τ-)||ξ(l4-)ξ(l5-)
3801.6345434115873801.6345214911923801.6300091900563801.558314578680||3801.5314081741003801.493304717900
Q+, ξ)ξ(γ+)ξ(e+)ξ(μ+)ξ(τ+)||ξ(l4+)ξ(l5+)
3799.6345434462023799.6345215142683799.6300068380063799.558274488192||3799.5313539209003799.493230407900
Q0, ξ)ξ(γ0)ξ(νe)ξ(νμ)ξ(ντ)||ξ(ν40e)ξ(ν50e)
3800.6344776504003800.6344776503143800.6344694978153800.633696718466||3800.6334316903003800.633041224300
Q(γ̃0, ξ)ξ(γ̃0)ξ(ν̃e)ξ(ν̃μ)ξ(ν̃τ)||ξ(ν̃4)ξ(ν̃5)
3800.6344776504003800.6344776503143800.6344694978153800.633696718466||3800.6334316903003800.633041224300
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMass
Table 10711: Table7   Mass values of Photon and Mass values of Elementary Fermion   Mev
PhotonFermionFermionFermionFermionFermion
Charge1st2nd3rd4th5th
γ+2/3|uct||q4+2/3q5+2/3
0+2/32. 300 000 00841279. 999 999 9969173000. 000 000 0008||231015. 428 381 58422317330. 416 904 2517
γ-2/3|ũ||q4-2/3q5-2/3
0-2/32. 999 999 99821280. 000 000 0002172999. 999 999 9978||231015. 486 558 1882317330. 606 538 0023
γ-1/3|dsb||q4-1/3q5-1/3
0-1/34. 799 999 998694. 999 999 98444699. 999 999 9872||6295. 075 920 32498642. 540 330 1016
γ+1/3|||q4+1/3q5+1/3
0+1/34. 799 999 998194. 999 999 99974700. 000 000 0127||6295. 075 897 72858642. 540 258 2346
γ-|e-μ-τ-||l4-l5-
0-10. 510 999 9898105. 699 999 99571776. 999 999 9938||2404. 217 163 74083292. 442 021 4139
γ+|e+μ+τ+||l4+l5+
0+10. 510 999 9969105. 699 999 99061776. 999 999 9969||2404. 217 150 15343292. 441 987 5652
γ0|νeνμντ||ν4ν5
000. 000 002 02870. 189 999 999618. 200 000 0020||24. 376 609 954533. 476 608 6728
γ̃0|ν̃eν̃μν̃τ||ν̃4ν̃5
000. 000 002 02870. 189 999 999618. 200 000 0020||24. 376 609 954533. 476 608 6728
ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMassNon-ZeroMass

3. Epilogue

" Double Helix Structure " of elementary particle : Two so-called " Double Helix Structure " , Photon Generation PG Q ( γ Q , ξ ) and Mass Function MF ξ ( ω ) , of a unified mass theory of elementary fermions and elementary bosons, with which the mass-values of particles of Standard Model SM could be uniformly identified. We are amazed to see a wide variety of particle masses of SM, go so far as to be trace back to a regular digital arrangement of Table Y1, Y2, Y3 and Table3, 4, 5 !!

STUNNING ! Due to Table Z and Table 6, 4th, 5th generations, Table 7, of elementary fermion are wondering hazily from the far horizon.

Mass Spectrum of 1st, 2nd, 3rd of Elementary Fermion

We arrange 1st, 2nd, 3rd of Elementary Fermion by THE ORDER of PARTICLE CHARGE ARITHMETIC PROGRESSION, Instead of by CURRENT PARTICLE FLAVOR.

( 5.2 ) n = 1 , 2 , 3
( 5.3 ) AND ξ 2 ( ω , n , R ) = ξ 2 ( ν n ) ± m R n

Where ξ 2 ( v n ) ± m R n is Arithmetic Progression

( 5.4 ) When υ n = υ 1 , υ 2 , υ 3 = υ e , υ μ , υ τ y i e l d ξ 2 ( v n ) + m R n
( 5.5 ) v ~ n = v ~ 1 , v ~ 2 , v ~ 3 = v ~ e , v ~ μ , v ~ τ y i e l d ξ 2 ( v ~ n ) m R n
( 5.6 ) m = 1 , 2 , 3 , 4 , 5 , 6 , 7

AND R n

( 5.7 )  When  n = 1 , R 1 = 1 5 , 1 9 0 1 5 , 2 1 1
( 5.8 )  When  n = 2 , R 2 = 1 2 , 8 8 0 1 7 , 5 5 1
( 5.9 )  When  n = 3 , R 3 = ? ?
Table 10708: Table R1   Mass Spectrum of 1st of Elementary Fermion for Charge Q < 0 and Q > 0
ChargeQ2Q, ξ)ξ2Q)Mass  M(ω)Mass  M(ω)ξ2Q)Q2Q, ξ)Charge
Q ≤ 01st1stQ > 0
-7/3Q2-7/3, ξ)ξ2(q-7/3)ξ2(q+7/3)Q2+7/3, ξ)+7/3
86775, 369. 678 830 460016.189 897 176716.189 860 502386562, 534. 148 153 8000
-2Q2-2e, ξ)ξ2(q-2)ξ2(q+2)Q2+2e, ξ)+2
86760, 163. 951 681 880011.176 597 779411.176 567 773586577, 733. 496 813 3900
-5/3Q2-5/3, ξ)ξ2(q-5/3)ξ2(q+5/3)Q2+5/3, ξ)+5/3
86744, 958. 224 533 30007.185 298 38727.185 275 049886592, 932. 845 472 9600
-4/3Q2-4/3, ξ)ξ2(q-4/3)ξ2(q+4/3)Q2+4/3, ξ)+4/3
86729, 752. 497 383 82004.215 999 44984.215 982 315986608, 132. 194 132 5400
-1Q2-e, ξ)ξ2(e-)ξ2(e+)Q2+e, ξ)+1
86714, 550. 209 961 38000.511 000 00000.511 000 000086623, 334. 982 497 7800
-2/3Q2-2/3, ξ)ξ2(ũ)ξ2(u)Q2+2/3, ξ)+2/3
86699, 339. 171 072 29642.300 000 00002.300 000 000086699, 339. 171 072 2964
-1/3Q2-1/3, ξ)ξ2(d)ξ2(d̃)Q2+1/3, ξ)+1/3
86684, 128. 740 793 80044.800 000 00004.800 000 000086653, 723. 664 972 6104
0Q20, ξ)ξ2e)ξ2(ν̃e)Q20, ξ)0
86668, 934. 596 225 68610.000 002 00000.000 002 000086668, 934. 596 225 6861
0Q20, ξ)ξ20)ξ20)Q20, ξ)0
86668, 934. 596 229 60000.000 000 00000.000 000 000086668, 934. 596 229 6000
R1 = 15, 190~15, 211R1 = 15, 190~15, 211
Table 10709: Table R2   Mass Spectrum of 1st 2nd 3rd of Elementary Fermion for Charge Q < 0
ChargeQ2Q, ξ)||ξ2Q)ξ2Q)|Q2Q, ξ)
Q ≤ 01st2nd3rd
-7/3Q2-7/3, ξ)||ξ2(q-7/3)|ξ2(q+7/3)|
||86775, 369. 678 830 4600|86562, 534. 148 153 8000|
-2Q2-2e, ξ)||ξ2(q-2)|ξ2(q+2)|
||86760, 163. 951 681 8800|86577, 733. 496 813 3900|
-5/3Q2-5/3, ξ)||ξ2(q-5/3)|ξ2(q+5/3)|
||86744, 958. 224 533 3000|86592, 932. 845 472 9600|
-4/3Q2-4/3, ξ)||ξ2(q-4/3)|ξ2(q+4/3)|
||86729, 752. 497 383 8200|86608, 132. 194 132 5400|
-1Q2-e, ξ)||ξ2(e-)|ξ2-)|ξ2-)
||86714, 550. 209 961 3800|86714, 344. 360 646 3115|86711, 073. 714 853 7479
-2/3Q2-2/3, ξ)||ξ2(ũ)|ξ2(c̃)|ξ2(t̃)
||86699, 339. 171 072 2964|86696, 838. 779 682 8639|86360#, 791. 812 950 9657
-1/3Q2-1/3, ξ)||ξ2(d)|ξ2(s)|ξ2(b)
||86684, 128. 740 793 8004|86683, 952. 224 159 7495|86674, 940. 482 476 7749
0Q20, ξ)||ξ2e)|ξ2μ)|ξ2τ)
||86668, 934. 596 225 6861|86668, 934. 224 409 6391|86668, 898. 979 791 2438
0Q20, ξ)||ξ20)|ξ20)|ξ20)
||86668, 934. 596 229 6000|86668, 934. 596 229 6000|86668, 934. 596 229 6000
R1 = 15, 190~15, 211R2 = 12, 880 ~ 17, 551R3 = ? ?

Table R3. Mass Spectrum of 1st 2nd 3rd of Elementary Fermion for Charge Q ≤ 0 Mev

Table 10707: Table R3   Mass Spectrum of 1st 2nd 3rd of Elementary Fermion for Charge Q < 0   Mev
ChargeQ2Q, ξ)||ξ2Q)ξ2Q)|Q2Q, ξ)
Q < 01st2nd3rd
-7/3Q2-7/3, ξ)||ξ2(q-7/3)|ξ2(q+7/3)|
||16.189 897 1767|1210.883 000 0610|
-2Q2-2e, ξ)||ξ2(q-2)|ξ2(q+2)|
||11.176 597 7794|1055.620 000 0456|
-5/3Q2-5/3, ξ)||ξ2(q-5/3)|ξ2(q+5/3)|
||7.185 298 3872|901.379 000 0353|
-4/3Q2-4/3, ξ)||ξ2(q-4/3)|ξ2(q+4/3)|
||4.215 999 4498|748.160 000 0199|
-1Q2-e, ξ)||ξ2(e-)|ξ2-)|ξ2-)
||0.511 000 0000|105.700 000 0000|1777.000 000 0000
-2/3Q2-2/3, ξ)||ξ2(ũ)|ξ2(c̃)|ξ2(t̃)
||2.300 000 0000|1280.000 000 0000|173000.000 000 0000
-1/3Q2-1/3, ξ)||ξ2(d)|ξ2(s)|ξ2(b)
||4.800 000 0000|95.000 000 0000|4700.000 000 0000
0Q20, ξ)||ξ2e)|ξ2μ)|ξ2τ)
||0.000 002 0000|0.190 000 0000|18.200 000 0000
0Q20, ξ)||ξ20)|ξ20)|ξ20)
||0.000 000 0000|0.000 000 0000|0.000 000 0000
R1 = 15, 190~15, 211R2 = 12, 880 ~ 17, 551R3 = ? ?

■ ACKNOWLEDGEMENTS

Thanks to GJSFR, offering a academic platform for researchers all over the world.

References

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Conflict of Interest

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How to Cite This Article

Dr. ShaoXu Ren. 2026. "A Unified Mass Theory of Elementary Fermions and Elementary Bosons". Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 26 (GJSFR Volume 26 Issue A1).

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Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

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Issue date
April 10, 2026

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A Unified Mass Theory of Elementary Fermions and Elementary Bosons

ShaoXu Ren
ShaoXu Ren Tongji University