A Unified Mass theory of Elementary Fermions and Elementary Bosons

A Unified Mass theory of Elementary Fermions and Elementary Bosons

Dr. Shaoxu-ren

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Tongji University

A Unified Mass theory of Elementary Fermions and Elementary Bosons

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9AGZE

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10.34257/GJSFRA253432

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Abstract

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

--- abstract: | Base on photon generation , a unified mass theory of elementary fermions and elementary bosons is postulated. author: - Dr. Shaoxu-ren title: A Unified Mass theory of Elementary Fermions and Elementary Bosons --- **Keywords:** color-unit constant 0, critical pg, double helix structure, mass function mf (), photon pg q(q, scalar product-mass equation, table x, ξ), π running pg, ) **Contents** 1. **Introduction** (P.) 2. **Table X** (P.) 3. **Part A Unified mass theory of two Dirac Neutral Mass Bosons $`B = H, Z`$** (P.) 4. **Part B Unified mass theory of two Dirac Charged Mass Bosons $`B = W^{-}, W^{+}`$** (P.) 5. **Part C Unified mass theory of two Dirac Neutral Massless Bosons $`B = \gamma, g`$** (P.) 6. **Mass function of Photon $`B = \gamma`$** (P.) 7. **Mass function of Gluon $`B = g`$** (P.) 8. **Critical PG Mass Function $`\xi(\omega)`$ values** (P.) 9. **Chat** (P.) 10. **$`\Pi`$ Running PG Mass Function $`\xi(\omega)`$ values** (P.) 11. **Epilogue** (P.) 12. **References** (P.) # Introduction fter obtaining a unified mass theory of twelve elementary fermions \[1\], it is natural to ask about the other six elementary bosons: $`B = H, Z, W^{+}, W^{-}`$ and $`\gamma, g ? !`$. 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 $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi)`$, instead of zeroth generation $`0^{th}`$ of fermion $`\textbf{Q}(\Psi(0), \xi)`$ 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 ($`\textbf{Q}(\Psi(0), \xi), \pmb{\xi}(\Psi(0))`$) is the zeroth generation of fermion. ``` math (\textbf{Q}(\Psi(0), \xi), \xi(\Psi(0))) ``` In Table $`\pmb{\times}`$ column $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi), \xi(\gamma^{\mathsf{Q}})`$ is the generation of photon. ``` math (\textbf{Q}(\gamma^{\mathsf{Q}}, \xi), \xi(\gamma^{\mathsf{Q}})) ``` <div class="center"> | | | | |:--:|:--:|:--:| | $`\textbf{Q}(\Psi(0), \xi) = \begin{array}{|c|} \hline \textbf{Q}(\delta(0), \xi) \\ \textbf{Q}(\gamma(0), \xi) \\ \textbf{Q}(\beta(0), \xi) \\ \textbf{Q}(\alpha(0), \xi) \\ \hline \end{array}`$ | $`\Longrightarrow`$ | $`\textbf{Q}(\gamma^{\circ}, \xi) = \begin{array}{|c|} \hline \textbf{Q}(\gamma^{+\frac{2}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-\frac{1}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-e}, \xi) \\ \textbf{Q}(\gamma^{0e}, \xi) \\ \hline \end{array}`$ | | **Table 0** fermion zeroth generation | | **Table X** photon generation | | For twelve elementary fermions | | For twelve elementary bosons and six elementary bosons | </div> The color representation of particle $`\omega`$ is defined as below. And $`\xi(\omega)`$ is called as mass function. ``` math \textbf{Q}(\gamma^{0}, \xi) + i \xi(\omega) ``` Base on Scalar Product-Mass Equation, the mass value $`M(\omega)`$ of a particle $`\omega`$ could be obtained below: ``` math \begin{array}{lll} Q^{2}(\gamma^{0}, \xi) - \xi^{2}(\omega) = & Q^{2}(\omega) = & \frac{M(\omega)}{M(e^{-})} \end{array} ``` Here $`\omega = F, B`$ (fermion, boson). Charge of $`\omega`$ rely on photon generation $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi)`$ and mass of $`\omega`$ relate to mass function $`\xi(\omega)`$. And $`Q^{2}(\gamma^{\mathsf{Q}}, \xi)`$ is the scalar product of $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi)`$ that comprises four members, each one of $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi)`$ with different charge: $`Q(\gamma^{0}, \xi) = (0e, -e, -1/3e, +2/3e)`$ $`\tilde{Q}(\gamma^{Q}, \xi) = ( 0e,\; +e,\; +1/3e,\; -2/3e )`$. 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 $`\omega = H, Z, W^{+}, W^{-}`$ and $`\gamma, g`$ 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 $`\gamma, g`$ that all with same charge, $`0e`$. So, both $`H, Z`$ and $`\gamma, g`$ belong to the common photon generation members (A.1) (C.1) and (A.2) (C.2) ; But accompanied by the different mass function $`\xi(\omega) : \xi(Z), \xi(H)`$ by (A.7), (A.8) and photon $`\pmb{\xi}(\gamma)`$ by (C.4), gluon $`\xi(g)`$ by (C.24), (C.25), ..., (C.30), (C.31). Subsequently result in bosons $`Z, H`$ massive (A.13), (A.12), and $`\gamma, g`$ massless (C.9), (C.36). NOTICE: photon $`\gamma`$ is just $`\gamma^{0\mathsf{e}}`$. **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 $`\xi(W^{-})`$ (B.13), $`\xi(W^{+})`$ by (B.14). But at last, the two particles possess the same mass values (B.17), (B.18). Table X is defined as (more details see Table 2 and Table 3 & Table 4 (Chat)): ``` math \uline{\uline{\text{Table X}}} = \uline{\text{Table 0}} + \uline{\text{Part A} + \text{Part B} + \text{Part C}} ``` Before discussing Part A, Part B, Part C first, glance over Table 1, the archives of elementary fermion and elementary boson below: <div class="center"> <div class="adjustbox"> max width= <table> <thead> <tr> <th colspan="5" style="text-align: center;">Fermion</th> <th colspan="5" style="text-align: center;">Fermion</th> <th colspan="4" style="text-align: center;">Boson</th> </tr> </thead> <tbody> <tr> <td style="text-align: left;">q</td> <td style="text-align: center;">I3</td> <td style="text-align: center;">Y</td> <td style="text-align: right;">M(q) MeV</td> <td style="text-align: left;"></td> <td style="text-align: left;">l</td> <td style="text-align: center;">I3</td> <td style="text-align: center;">Y</td> <td style="text-align: right;">M(l) keV</td> <td style="text-align: left;"></td> <td style="text-align: left;">B</td> <td style="text-align: center;">I3</td> <td style="text-align: center;">Y</td> <td style="text-align: right;">M(B) MeV</td> </tr> <tr> <td style="text-align: left;">t</td> <td style="text-align: center;">+5/2</td> <td style="text-align: center;">−11/3</td> <td style="text-align: right;">173,000.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">ντ</td> <td style="text-align: center;">+5/2</td> <td style="text-align: center;">−5</td> <td style="text-align: right;">18,200.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">W+</td> <td style="text-align: center;">+1</td> <td style="text-align: center;">0</td> <td style="text-align: right;">80,400</td> </tr> <tr> <td style="text-align: left;">c</td> <td style="text-align: center;">+3/2</td> <td style="text-align: center;">−5/3</td> <td style="text-align: right;">1,280.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">νμ</td> <td style="text-align: center;">+3/2</td> <td style="text-align: center;">−3</td> <td style="text-align: right;">190.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">Z, H</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">91,200, 125,000</td> </tr> <tr> <td style="text-align: left;">u</td> <td style="text-align: center;">+1/2</td> <td style="text-align: center;">+1/3</td> <td style="text-align: right;">2.3</td> <td style="text-align: left;"></td> <td style="text-align: left;">νe</td> <td style="text-align: center;">+1/2</td> <td style="text-align: center;">−1</td> <td style="text-align: right;">0.002</td> <td style="text-align: left;"></td> <td style="text-align: left;">W−</td> <td style="text-align: center;">−1</td> <td style="text-align: center;">0</td> <td style="text-align: right;">80,400</td> </tr> <tr> <td style="text-align: left;">d</td> <td style="text-align: center;">−1/2</td> <td style="text-align: center;">+1/3</td> <td style="text-align: right;">4.8</td> <td style="text-align: left;"></td> <td style="text-align: left;">e−</td> <td style="text-align: center;">−1/2</td> <td style="text-align: center;">−1</td> <td style="text-align: right;">511.0</td> <td style="text-align: left;"></td> <td style="text-align: left;"></td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;">s</td> <td style="text-align: center;">−3/2</td> <td style="text-align: center;">+7/3</td> <td style="text-align: right;">95.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">μ−</td> <td style="text-align: center;">−3/2</td> <td style="text-align: center;">+1</td> <td style="text-align: right;">105,700.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">γ</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">0</td> </tr> <tr> <td style="text-align: left;">b</td> <td style="text-align: center;">−5/2</td> <td style="text-align: center;">+13/3</td> <td style="text-align: right;">4,700.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">τ−</td> <td style="text-align: center;">−5/2</td> <td style="text-align: center;">+3</td> <td style="text-align: right;">1,777,000.0</td> <td style="text-align: left;"></td> <td style="text-align: left;">g</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">0</td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> <td style="text-align: left;"></td> <td style="text-align: left;"></td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> <td style="text-align: left;"></td> <td style="text-align: left;"></td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;">t</td> <td style="text-align: center;">+5/2</td> <td style="text-align: center;">−11/3</td> <td style="text-align: right;">338,551.859 099 8043</td> <td style="text-align: left;">Q(t)</td> <td style="text-align: left;">ντ</td> <td style="text-align: center;">+5/2</td> <td style="text-align: center;">−5</td> <td style="text-align: right;">35.616 438 3562</td> <td style="text-align: left;">Q(ντ)</td> <td style="text-align: left;">H</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">244,618.395 303 3268</td> </tr> <tr> <td style="text-align: left;">c</td> <td style="text-align: center;">+3/2</td> <td style="text-align: center;">−5/3</td> <td style="text-align: right;">2,504.892 367 9061</td> <td style="text-align: left;">Q(c)</td> <td style="text-align: left;">νμ</td> <td style="text-align: center;">+3/2</td> <td style="text-align: center;">−3</td> <td style="text-align: right;">0.371 819 9609</td> <td style="text-align: left;">Q(νμ)</td> <td style="text-align: left;">Z</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">178,473.581 213 3072</td> </tr> <tr> <td style="text-align: left;">u</td> <td style="text-align: center;">+1/2</td> <td style="text-align: center;">+1/3</td> <td style="text-align: right;">4.500 978 4736</td> <td style="text-align: left;">Q(u)</td> <td style="text-align: left;">νe</td> <td style="text-align: center;">+1/2</td> <td style="text-align: center;">−1</td> <td style="text-align: right;">0.000 003 9139</td> <td style="text-align: left;">Q(νe)</td> <td style="text-align: left;">W±</td> <td style="text-align: center;">±1</td> <td style="text-align: center;">0</td> <td style="text-align: right;">157,338.551 859 0998</td> </tr> <tr> <td style="text-align: left;">d</td> <td style="text-align: center;">−1/2</td> <td style="text-align: center;">+1/3</td> <td style="text-align: right;">9.393 346 3796</td> <td style="text-align: left;">Q(d)</td> <td style="text-align: left;">e−</td> <td style="text-align: center;">−1/2</td> <td style="text-align: center;">−1</td> <td style="text-align: right;">1.000 000 0000</td> <td style="text-align: left;">Q(e−)</td> <td style="text-align: left;"></td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;">s</td> <td style="text-align: center;">−3/2</td> <td style="text-align: center;">+7/3</td> <td style="text-align: right;">185.909 980 4305</td> <td style="text-align: left;">Q(s)</td> <td style="text-align: left;">μ−</td> <td style="text-align: center;">−3/2</td> <td style="text-align: center;">+1</td> <td style="text-align: right;">206.849 315 0685</td> <td style="text-align: left;">Q(μ−)</td> <td style="text-align: left;">γ</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">0.000 000 0000</td> </tr> <tr> <td style="text-align: left;">b</td> <td style="text-align: center;">−5/2</td> <td style="text-align: center;">+13/3</td> <td style="text-align: right;">9,197.651 663 4051</td> <td style="text-align: left;">Q(b)</td> <td style="text-align: left;">τ−</td> <td style="text-align: center;">−5/2</td> <td style="text-align: center;">+3</td> <td style="text-align: right;">3,477.495 107 6321</td> <td style="text-align: left;">Q(τ−)</td> <td style="text-align: left;">g</td> <td style="text-align: center;">0</td> <td style="text-align: center;">0</td> <td style="text-align: right;">0.000 000 0000</td> </tr> </tbody> </table> </div> </div> Decompose the color scalar products $`Q^{2}(B)`$ of six bosons of the right column of Table 1, into three dimensional color space $`\textbf{Q}(B)`$ following: - Boson Ground States for massive particles $`B = H, Z, W^{-}, W^{+}`$: ``` math \begin{align*} \textbf{Q}(H) &= ( +201.915\, 161\, 76492, +201.915\, 161\, 76492, -403.830\, 323\, 50984 ) \tag{0.1} \\ \textbf{Q}^{2}(H) &= 244,618.395\, 303\, 3228 = \frac{124,999.999\, 999\, 9980}{0.511} = \frac{M(H)}{0.511} \tag{0.2} \\[10pt] \textbf{Q}(Z) &= ( +172.469\, 118\, 59486, +172.469\, 118\, 59486, -344.938\, 237\, 18972 ) \tag{0.3} \\ \textbf{Q}^{2}(Z) &= 178,473.581\, 213\, 3274 = \frac{91,200.000\, 000\, 0103}{0.511} = \frac{M(Z)}{0.511} \tag{0.4} \\[10pt] \textbf{Q}(W^{-}) &= ( -161.932\, 883\, 14360, -163.932\, 883\, 14360, +322.865\, 766\, 28720 ) \tag{0.5} \\ \textbf{Q}^{2}(W^{-}) &= 157,338.551\, 859\, 1929 = \frac{80,400.000\, 000\, 0476}{0.511} = \frac{M(W^{-})}{0.511} \tag{0.6} \\[10pt] \textbf{Q}(W^{+}) &= ( -159.932\, 883\, 14360, -161.932\, 883\, 14360, +321.865\, 766\, 28720 ) \tag{0.7} \\ \textbf{Q}^{2}(W^{+}) &= 157,338.551\, 859\, 1929 = \frac{80,400.000\, 000\, 0476}{0.511} = \frac{M(W^{+})}{0.511} \tag{0.8} \end{align*} ``` - Boson Ground States for massless photon, gluon, $`B = \gamma, g`$: ``` math \begin{align*} \textbf{Q}(\gamma, g) &= ( 0.000\, 000\, 0000, 0.000\, 000\, 0000, 0.000\, 000\, 0000 ) \tag{0.9} \\ \textbf{Q}^{2}(\gamma, g) &= 0.000\, 000\, 0000 = \frac{0.000\, 000\, 0000}{0.511} = \frac{M(\gamma, g)}{0.511} \tag{0.10} \end{align*} ``` The above six formulas $`\textbf{Q}^{2}`$ (0.2) (0.4) (0.6) (0.8) (0.10) will help us to use Scalar Product-Mass Equation (0.4) (0.11) to calculate the mass $`M(B)`$ of the above six boson particles $`\omega = B`$ ``` math \textbf{Q}^{2}(\gamma^{\mathsf{Q}}, \xi) - \xi^{2}(\omega = B) = \textbf{Q}^{2}(\omega = B) = \frac{M(\omega = B)}{M(e^{-})} \tag{0.11} ``` Later we will see the formulas $`\textbf{Q}^{2}`$ (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). <div class="center"> <div class="adjustbox"> max width= <table> <tbody> <tr> <td style="text-align: center;">Boson γQ</td> <td style="text-align: center;">Fermion</td> <td style="text-align: center;">Fermion</td> <td style="text-align: center;">Fermion</td> <td style="text-align: center;">Boson</td> <td style="text-align: center;">Q(ω)</td> </tr> <tr> <td style="text-align: center;"></td> <td style="text-align: center;">1st</td> <td style="text-align: center;">2nd</td> <td style="text-align: center;">3rd</td> <td style="text-align: center;">Force Carriers</td> <td style="text-align: center;">Charge</td> </tr> <tr> <td style="text-align: center;">$\gamma^{+\frac{2}{3}}$</td> <td style="text-align: center;">u</td> <td style="text-align: center;">c</td> <td style="text-align: center;">t</td> <td style="text-align: center;"></td> <td style="text-align: center;">$+\frac{2}{3}e$</td> </tr> <tr> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{2}{3}}, \xi), \xi(\delta(0)))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{2}{3}}, \xi), \xi(u))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{2}{3}}, \xi), \xi(c))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{2}{3}}, \xi), \xi(t))$</td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">$\gamma^{-\frac{2}{3}}$</td> <td style="text-align: center;">ũ</td> <td style="text-align: center;">c̃</td> <td style="text-align: center;">t̃</td> <td style="text-align: center;"></td> <td style="text-align: center;">$-\frac{2}{3}e$</td> </tr> <tr> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{2}{3}}, \xi), \xi(\tilde{\delta}(0)))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{2}{3}}, \xi), \xi(\tilde{u}))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{2}{3}}, \xi), \xi(\tilde{c}))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{2}{3}}, \xi), \xi(\tilde{t}))$</td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">$\gamma^{-\frac{1}{3}}$</td> <td style="text-align: center;">d</td> <td style="text-align: center;">s</td> <td style="text-align: center;">b</td> <td style="text-align: center;"></td> <td style="text-align: center;">−1/3e</td> </tr> <tr> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{1}{3}}, \xi), \xi(\gamma(0)))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{1}{3}}, \xi), \xi(d))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{1}{3}}, \xi), \xi(s))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{-\frac{1}{3}}, \xi), \xi(b))$</td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">$\gamma^{+\frac{1}{3}}$</td> <td style="text-align: center;">d̃</td> <td style="text-align: center;">s̃</td> <td style="text-align: center;">b̃</td> <td style="text-align: center;"></td> <td style="text-align: center;">+1/3e</td> </tr> <tr> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{1}{3}}, \xi), \xi(\tilde{\gamma}(0)))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{1}{3}}, \xi), \xi(\tilde{d}))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{1}{3}}, \xi), \xi(\tilde{s}))$</td> <td style="text-align: center;">$(\textbf{Q}(\gamma^{+\frac{1}{3}}, \xi), \xi(\tilde{b}))$</td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">γ−</td> <td style="text-align: center;">e</td> <td style="text-align: center;">μ</td> <td style="text-align: center;">τ</td> <td style="text-align: center;"></td> <td style="text-align: center;">−e</td> </tr> <tr> <td style="text-align: center;">(Q(γ−, ξ), ξ(γ−))</td> <td style="text-align: center;">(Q(γ−, ξ), ξ(e−))</td> <td style="text-align: center;">(Q(γ−, ξ), ξ(μ−))</td> <td style="text-align: center;">(Q(γ−, ξ), ξ(τ−))</td> <td style="text-align: center;">(Q(γ−, ξ), ξ(W−))</td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">γ+</td> <td style="text-align: center;">ẽ</td> <td style="text-align: center;">μ̃</td> <td style="text-align: center;">τ̃</td> <td style="text-align: center;"></td> <td style="text-align: center;">+e</td> </tr> <tr> <td style="text-align: center;">(Q(γ+, ξ), ξ(γ+))</td> <td style="text-align: center;">(Q(γ+, ξ), ξ(e+))</td> <td style="text-align: center;">(Q(γ+, ξ), ξ(μ+))</td> <td style="text-align: center;">(Q(γ+, ξ), ξ(τ+))</td> <td style="text-align: center;">(Q(γ+, ξ), ξ(W+))</td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">γ0</td> <td style="text-align: center;">νe</td> <td style="text-align: center;">νμ</td> <td style="text-align: center;">ντ</td> <td style="text-align: center;"></td> <td style="text-align: center;">0e</td> </tr> <tr> <td style="text-align: center;">(Q(γ0, ξ), ξ(γ0))</td> <td style="text-align: center;">(Q(γ0, ξ), ξ(νe))</td> <td style="text-align: center;">(Q(γ0, ξ), ξ(νμ))</td> <td style="text-align: center;">(Q(γ0, ξ), ξ(ντ))</td> <td style="text-align: center;">(Q(γ0, ξ), ξ(Z, H; γ, g))</td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">γ0</td> <td style="text-align: center;">ν̃e</td> <td style="text-align: center;">ν̃μ</td> <td style="text-align: center;">ν̃τ</td> <td style="text-align: center;"></td> <td style="text-align: center;">0e</td> </tr> <tr> <td style="text-align: center;">(Q(γ̃0, ξ), ξ(γ0))</td> <td style="text-align: center;">(Q(γ̃0, ξ), ξ(ν̃e))</td> <td style="text-align: center;">(Q(γ̃0, ξ), ξ(ν̃μ))</td> <td style="text-align: center;">(Q(γ̃0, ξ), ξ(ν̃τ))</td> <td style="text-align: center;">(Q(γ̃0, ξ), ξ(Z, H; γ, g))</td> <td style="text-align: center;"></td> </tr> <tr> <td style="text-align: center;">ZeroMass</td> <td colspan="3" style="text-align: center;">Non-Zero-Mass</td> <td style="text-align: center;"></td> <td style="text-align: center;"></td> </tr> </tbody> </table> </div> </div> <div class="center"> <div class="adjustbox"> max width= <table> <tbody> <tr> <td style="text-align: left;">Photon Generation</td> <td style="text-align: center;">MF ξ(γQ)</td> <td colspan="3" style="text-align: center;">MF ξ(F)</td> <td style="text-align: center;">MF ξ(B)</td> <td style="text-align: right;">Charge</td> </tr> <tr> <td style="text-align: left;">Q(γQ, ξ)</td> <td style="text-align: center;"></td> <td style="text-align: center;">Fermion 1st</td> <td style="text-align: center;">Fermion 2nd</td> <td style="text-align: center;">Fermion 3rd</td> <td style="text-align: center;">Force Carriers</td> <td style="text-align: right;">Q(ω)</td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">$\gamma^{+\frac{2}{3}}$</td> <td style="text-align: center;">u</td> <td style="text-align: center;">c</td> <td style="text-align: center;">t</td> <td style="text-align: center;"></td> <td style="text-align: right;">$+\frac{2}{3}e$</td> </tr> <tr> <td style="text-align: left;">$\textbf{Q}(\gamma^{+\frac{2}{3}}, \xi)$</td> <td style="text-align: center;">$\xi(\gamma^{+\frac{2}{3}})$</td> <td style="text-align: center;">ξ(u)</td> <td style="text-align: center;">ξ(c)</td> <td style="text-align: center;">ξ(t)</td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">$\gamma^{-\frac{2}{3}}$</td> <td style="text-align: center;">ũ</td> <td style="text-align: center;">c̃</td> <td style="text-align: center;">t̃</td> <td style="text-align: center;"></td> <td style="text-align: right;">$-\frac{2}{3}e$</td> </tr> <tr> <td style="text-align: left;">$\textbf{Q}(\gamma^{-\frac{2}{3}}, \xi)$</td> <td style="text-align: center;">$\xi(\gamma^{-\frac{2}{3}})$</td> <td style="text-align: center;">ξ(ũ)</td> <td style="text-align: center;">ξ(c̃)</td> <td style="text-align: center;">ξ(t̃)</td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">$\gamma^{-\frac{1}{3}}$</td> <td style="text-align: center;">d</td> <td style="text-align: center;">s</td> <td style="text-align: center;">b</td> <td style="text-align: center;"></td> <td style="text-align: right;">$-\frac{1}{3}e$</td> </tr> <tr> <td style="text-align: left;">$\textbf{Q}(\gamma^{-\frac{1}{3}}, \xi)$</td> <td style="text-align: center;">$\xi(\gamma^{-\frac{1}{3}})$</td> <td style="text-align: center;">ξ(d)</td> <td style="text-align: center;">ξ(s)</td> <td style="text-align: center;">ξ(b)</td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">$\gamma^{+\frac{1}{3}}$</td> <td style="text-align: center;">d̃</td> <td style="text-align: center;">s̃</td> <td style="text-align: center;">b̃</td> <td style="text-align: center;"></td> <td style="text-align: right;">$+\frac{1}{3}e$</td> </tr> <tr> <td style="text-align: left;">$\textbf{Q}(\gamma^{+\frac{1}{3}}, \xi)$</td> <td style="text-align: center;">$\xi(\gamma^{+\frac{1}{3}})$</td> <td style="text-align: center;">ξ(d̃)</td> <td style="text-align: center;">ξ(s̃)</td> <td style="text-align: center;">ξ(b̃)</td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">γ−</td> <td style="text-align: center;">e</td> <td style="text-align: center;">μ</td> <td style="text-align: center;">τ</td> <td style="text-align: center;"></td> <td style="text-align: right;">−e</td> </tr> <tr> <td style="text-align: left;">Q(γ−, ξ)</td> <td style="text-align: center;">ξ(γ−)</td> <td style="text-align: center;">ξ(e−)</td> <td style="text-align: center;">ξ(μ−)</td> <td style="text-align: center;">ξ(τ−)</td> <td style="text-align: center;">ξ(W−)</td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">γ+</td> <td style="text-align: center;">ẽ</td> <td style="text-align: center;">μ̃</td> <td style="text-align: center;">τ̃</td> <td style="text-align: center;"></td> <td style="text-align: right;">+e</td> </tr> <tr> <td style="text-align: left;">Q(γ+, ξ)</td> <td style="text-align: center;">ξ(γ+)</td> <td style="text-align: center;">ξ(e+)</td> <td style="text-align: center;">ξ(μ+)</td> <td style="text-align: center;">ξ(τ+)</td> <td style="text-align: center;">ξ(W+)</td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">γ0</td> <td style="text-align: center;">νe</td> <td style="text-align: center;">νμ</td> <td style="text-align: center;">ντ</td> <td style="text-align: center;"></td> <td style="text-align: right;">0e</td> </tr> <tr> <td style="text-align: left;">Q(γ0, ξ)</td> <td style="text-align: center;">ξ(γ0)</td> <td style="text-align: center;">ξ(νe)</td> <td style="text-align: center;">ξ(νμ)</td> <td style="text-align: center;">ξ(ντ)</td> <td style="text-align: center;">ξ(Z, H; γ, g)</td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">γ0</td> <td style="text-align: center;">ν̃e</td> <td style="text-align: center;">ν̃μ</td> <td style="text-align: center;">ν̃τ</td> <td style="text-align: center;"></td> <td style="text-align: right;">0e</td> </tr> <tr> <td style="text-align: left;">Q(γ̃0, ξ)</td> <td style="text-align: center;">ξ(γ0)</td> <td style="text-align: center;">ξ(ν̃e)</td> <td style="text-align: center;">ξ(ν̃μ)</td> <td style="text-align: center;">ξ(ν̃τ)</td> <td style="text-align: center;">ξ(Z, H; γ, g)</td> <td style="text-align: right;"></td> </tr> <tr> <td style="text-align: left;"></td> <td style="text-align: center;">ZeroMass</td> <td style="text-align: center;">Non-ZeroMass</td> <td style="text-align: center;">Non-ZeroMass</td> <td style="text-align: center;">Non-ZeroMass</td> <td style="text-align: center;"></td> <td style="text-align: right;"></td> </tr> </tbody> </table> </div> </div> # Part A: Unified Mass Theory of Two Dirac Neutral Mass Bosons B = H, Z B = H, Z Detailed values of $`\textbf{Q}(\gamma^{0}, \xi)`$ of particles $`B = Z, H`$ below: ``` math \begin{array}{rlr} \pmb{Q}(\gamma^{0}, \xi) = & ( & +236.53965485315, \qquad +238.53965485315, \qquad -475.07930970630 ) \\ & & \\ \pmb{Q}(\tilde{\gamma}^{0}, \xi) = & ( & +238.53965485315, \qquad +236.53965485315, \qquad -475.07930970630 ) \end{array} ``` The charges of particles $`B = Z, H`$ are zero: ``` math \begin{array}{llll} Q = & \frac{1}{3} ( 236.53965485315 + 238.53965485315 - 475.07930970630 ) = 0 \\ Q = & \frac{1}{3} ( 238.53965485315 + 236.53965485315 - 475.07930970630 ) = 0 \end{array} ``` $`\pmb{\lozenge}`$ Detailed values of mass function $`\xi(B)`$ of particles $`B = Z, H`$ below: ``` math \begin{align*} \bullet \text{ 1} \qquad \xi(Z) &= ( +163.339\, 597\, 441044, \quad +163.339\, 597\, 441044, \quad -326.679\, 194\, 882088 ) \tag{A.5} \\ \bullet \text{ 2} \qquad \xi(H) &= ( +125.122\, 693\, 427295, \quad +125.122\, 693\, 427295, \quad -250.245\, 386\, 854590 ) \tag{A.6} \\ & \\ \bullet \text{ 1} \qquad \xi(Z) &= 163.339\, 597\, 441044 \, (+1, \quad +1, \quad -2) = 163.339\, 597\, 441044 \pmb{\xi}_{0} \tag{A.7} \\ \bullet \text{ 2} \qquad \xi(H) &= 125.122\, 693\, 427295 \, (+1, \quad +1, \quad -2) = 125.122\, 693\, 427295 \pmb{\xi}_{0} \tag{A.8} \end{align*} ``` Where $`\pmb{\xi}_{0}`$ called as Color-Unit Constant that is a three dimensional colore vector, with which $`\xi(\omega)`$ could be limpid. see following ``` math \begin{align*} \pmb{\xi}_{0} &= ( +1, \quad +1, \quad -2 ) \tag{00.6} \\ \pmb{\xi}_{0}^{2} &= 6 \tag{00.7} \end{align*} ``` Expressions of the color scalar products of the above are given below: ``` math \textbf{Q}^{2}(\gamma^{0}, \xi) = \textbf{Q}^{2}(\tilde{\gamma}^{0}, \xi) = 338,552.5257665218 ``` ``` math \begin{array}{rlr} \xi^{2}(Z) & = & 160,078.9445532138 \\ \xi^{2}(H) & = & 93,934.1304630052 \end{array} ``` 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 $`\textbf{Q}^{2}(\gamma^{0}, \xi)`$ of photon generation of particle $`\gamma^{0}`$ and color scalar product $`\xi^{2}(Z), \xi^{2}(H)`$ of mass function $`\xi(Z), \xi(H)`$ of particles $`Z, H`$. - $`\textbf{Q}^{2}(\gamma^{0}, \xi) - \xi^{2}(Z) =`$ ``` math \begin{align*} & 338, 552. 525\, 766\, 5218 - 160, 078. 944\, 553\, 2146 = 178, 473. 581\, 213\, 3072 = \frac{91,200.000\, 000\, 0000}{0.511} = \frac{M(Z)}{M(e^{-})} \\ & 338, 552. 525\, 766\, 5218 - 160, 078. 944\, 553\, 2138 = 178, 473. 581\, 213\, 3080 = \frac{91,200.000\, 000\, 0004}{0.511} \tag{A.12} \end{align*} ``` - $`\textbf{Q}^{2}(\gamma^{0}, \xi) - \xi^{2}(H) =`$ ``` math \begin{align*} & 338, 552. 525\, 766\, 5218 - 93, 934. 130\, 463\, 1950 = 244, 618. 395\, 303\, 3268 = \frac{125,000.000\, 000\, 0000}{0.511} = \frac{M(H)}{M(e^{-})} \\ & 338, 552. 525\, 766\, 5218 - 93, 934. 130\, 463\, 0052 = 244, 618. 395\, 303\, 5166 = \frac{125,000.000\, 000\, 0097}{0.511} \tag{A.13} \end{align*} ``` # Part B: Unified Mass Theory of Two Dirac Charged Mass Bosons B = W^ - , W^ + B = W-, W+ - Detailed values of photon generation $`\textbf{Q}(\gamma^{-}, \xi), \textbf{Q}(\gamma^{+}, \xi)`$ of particle $`\gamma^{-}`$ and anti-particle $`\gamma^{+}`$: - ``` math \textbf{Q}(\gamma^{-}, \xi) = ( +236.539\, 654\, 85315, \quad +238.539\, 654\, 85315, \quad -478.079\, 309\, 70630 ) \tag{B.1} ``` - ``` math \textbf{Q}(\gamma^{+}, \xi) = ( +238.539\, 654\, 85315, \quad +236.539\, 654\, 85315, \quad -472.079\, 309\, 70630 ) \tag{B.2} ``` The charges of particles $`B = W^{-}, W^{+}`$: ``` math \begin{align*} Q(W^{-}) &= \frac{1}{3} ( 236.53965485315 + 238.53965485315 - 478.07930970630 ) = -e \tag{B.3} \\ Q(W^{+}) &= \frac{1}{3} ( 238.53965485315 + 236.53965485315 - 472.07930970630 ) = +e \tag{B.4} \end{align*} ``` And the color scalar products of (B.1) (B.2) are below: - ``` math \textbf{Q}^{2}(\gamma^{-}, \xi) = 341,412.001\, 624\, 7596 \tag{B.5} ``` - ``` math \textbf{Q}^{2}(\gamma^{+}, \xi) = 335,711.049\, 908\, 2840 \tag{B.6} ``` Because of requirement of final results (B.7) (B.8) below, Then having color scalar products (B.9) (B.10) - $`\textbf{Q}^{2}(\gamma^{-}, \xi) - \xi^{2}(W^{-}) =`$ ``` math \begin{align*} & 341, 412. 001\, 624\, 7596 - 184, 073. 449\, 765\, 6598 = 157, 338. 551\, 859\, 0998 = \frac{80,400.000\, 000\, 0000}{0.511} \tag{B.7} \end{align*} ``` - $`\textbf{Q}^{2}(\gamma^{+}, \xi) - \xi^{2}(W^{+}) =`$ ``` math \begin{align*} & 335, 711. 049\, 908\, 2840 - 178, 372. 498\, 049\, 1842 = 157, 338. 551\, 859\, 0998 = \frac{80,400.000\, 000\, 0000}{0.511} \tag{B.8} \end{align*} ``` OR ``` math \begin{align*} \xi^{2}(W^{-}) &= 184, 073. 449\, 765\, 6598 \tag{B.9} \\ \xi^{2}(W^{+}) &= 178, 372. 498\, 049\, 1842 \tag{B.10} \end{align*} ``` FURTHER, Discompose color scalar products (B.9) and (B.10) into their mass function (B.11) (B.13) and (B.12) (B.14) below: - ``` math \xi(W^{-}) = ( +175.153\, 955\, 97667, \quad +175.153\, 955\, 97667, \quad -350.307\, 911\, 95334 ) \tag{B.11} ``` - ``` math \xi(W^{+}) = ( +172.420\, 270\, 48716, \quad +172.420\, 270\, 48716, \quad -344.840\, 540\, 97432 ) \tag{B.12} ``` OR - ``` math \xi(W^{-}) = 175.153\, 955\, 97667 ( +1, \quad +1, \quad -2 ) = 175.153\, 955\, 97667 \pmb{\xi}_{0} \tag{B.13} ``` - ``` math \xi(W^{+}) = 172.420\, 270\, 48716 ( +1, \quad +1, \quad -2 ) = 172.420\, 270\, 48716 \pmb{\xi}_{0} \tag{B.14} ``` 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: ``` math \begin{align*} \xi^{2}(W^{-}) &= 184, 073. 449\, 765\, 6635 \tag{B.15} \\ \xi^{2}(W^{+}) &= 178, 372. 498\, 049\, 1924 \tag{B.16} \end{align*} ``` - $`\textbf{Q}^{2}(\gamma^{-}, \xi) - \xi^{2}(W^{-}) =`$ ``` math \begin{align*} & 341, 412. 001\, 624\, 7596 - 184, 073. 449\, 765\, 6635 = 157, 338. 551\, 859\, 0961 = \frac{80,399.999\, 999\, 9981}{0.511} = \frac{M(W^{-})}{M(e^{-})} \tag{B.17} \end{align*} ``` - $`\textbf{Q}^{2}(\gamma^{+}, \xi) - \xi^{2}(W^{+}) =`$ ``` math \begin{align*} & 335, 711. 049\, 908\, 2840 - 178, 372. 498\, 049\, 1924 = 157, 338. 551\, 859\, 0916 = \frac{80,399.999\, 999\, 9958}{0.511} = \frac{M(W^{+})}{M(e^{-})} \tag{B.18} \end{align*} ``` # Part C: Unified Mass Theory of Two Dirac Neutral Massless Bosons B = , g B = gamma, g Both Boson photon $`\gamma`$ and Boson gluon $`g`$ are massless particles. Photon $`\gamma`$ is mediating particle in electromagnetic interation, And gluon $`g`$ in strong interaction. $`\pmb{\lozenge}`$ Detailed values of photon generation of particles $`B = \gamma, g`$ below ``` math \begin{align*} \bullet \text{ 0} \qquad \textbf{Q}(\gamma^{0}, \xi) = ( +236.539\, 654\, 85315, \quad +238.539\, 654\, 85315, \quad -475.079\, 309\, 70630 ) \tag{C.1, A.1} \\ \bullet \text{ 0} \qquad \textbf{Q}(\tilde{\gamma}^{0}, \xi) = ( +238.539\, 654\, 85315, \quad +236.539\, 654\, 85315, \quad -475.079\, 309\, 70630 ) \tag{C.2, A.2} \end{align*} ``` $`\pmb{\lozenge}`$ Next two paragraphs search for detailed values of mass function of particles $`B = \gamma, g`$ respectively. <div class="center"> </div> The color representation of mass function of photon is given below - $`\gamma`$ ``` math \xi(\gamma) = ( +237.540\, 356\, 489349, \quad +237.540\, 356\, 489349, \quad -475.080\, 712\, 978698 ) \tag{C.3} ``` - ``` math = \kappa ( +1, \quad +1, \quad -2 ) = \kappa \pmb{\xi}_{0} \tag{C.4} ``` Where ``` math \begin{equation} \kappa = 237.540\, 356\, 489349 \tag{C.5} \end{equation} ``` From (C.4), having ``` math \begin{equation} \xi^{2}(\gamma) = 338, 552. 525\, 766\, 5220 \tag{C.6} \end{equation} ``` Further the expressions of the color scalar products of photon generation and mass function of photon $`\gamma`$ are given below: ``` math \begin{align*} \textbf{Q}^{2}(\gamma^{0}, \xi) = \textbf{Q}^{2}(\bar{\gamma}^{0}, \xi) &= 338, 552. 525\, 766\, 5218 \tag{C.7} \\ \xi^{2}(\gamma) &= 338, 552. 525\, 766\, 5220 \tag{C.8} \end{align*} ``` Last making subtraction, using ScalarProduct-Mass Equation: ``` math \begin{align*} | \textbf{Q}^{2}(\gamma^{0}, \xi) - \xi^{2}(\gamma) | &= \\ = | 338, 552. 525\, 766\, 5218 &- 338, 552. 525\, 766\, 5220 | = 0.000\, 000\, 0002 = \frac{0.000\, 000\, 0001}{0.511} = \frac{M(\gamma)}{0.511} \approx 0 \tag{C.9} \end{align*} ``` (C.9) shows from photon generation (C.1) and mass function (C.4), we could obtain mass of photon $`\gamma`$. $`\dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots \qquad \dots`$ <div class="center"> </div> In contrast with photon $`\gamma`$, the pictures of color representation of mass function $`\xi(g)`$ 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 $`R\tilde{G},\; G\tilde{B},\; B\tilde{R} \;\&\; \tilde{G}R,\; \tilde{B}G,\; \tilde{R}B`$ and two color neutral gluons $`R\tilde{R},\; G\tilde{G}`$ (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, $`\textbf{Q}(\gamma) = \textbf{Q}(g) = (0.0000000000, 0.0000000000, 0.0000000000)`$ !! (see: (0.9)). - The way to the mass function of gluons $`B = g`$ following: THEN six mass function states of colored gluons: - $`R\tilde{G}`$ ``` math \xi(g_{R\tilde{G}}) = \sqrt{3} \kappa ( +1, \quad -1, \quad 0 ) \tag{C.24} ``` - $`G\tilde{B}`$ ``` math \xi(g_{G\tilde{B}}) = \sqrt{3} \kappa ( 0, \quad +1, \quad -1 ) \tag{C.25} ``` - $`B\tilde{R}`$ ``` math \xi(g_{B\tilde{R}}) = \sqrt{3} \kappa ( -1, \quad 0, \quad +1 ) \tag{C.26} ``` - $`G\tilde{R}`$ ``` math \xi(g_{G\tilde{R}}) = \sqrt{3} \kappa ( -1, \quad +1, \quad 0 ) \tag{C.27} ``` - $`B\tilde{G}`$ ``` math \xi(g_{B\tilde{G}}) = \sqrt{3} \kappa ( 0, \quad -1, \quad +1 ) \tag{C.28} ``` - $`R\tilde{B}`$ ``` math \xi(g_{R\tilde{B}}) = \sqrt{3} \kappa ( +1, \quad 0, \quad -1 ) \tag{C.29} ``` AND three mass function states of color neutral gluons: - $`R\tilde{R}`$ ``` math \xi(g_{R\tilde{R}}) = \kappa ( +2, \quad -1, \quad -1 ) \tag{C.30} ``` - $`G\tilde{G}`$ ``` math \xi(g_{G\tilde{G}}) = \kappa ( -1, \quad +2, \quad -1 ) \tag{C.31} ``` - $`B\tilde{B}`$ ``` math \xi(g_{B\tilde{B}}) = \kappa ( -1, \quad -1, \quad +2 ) \tag{C.32} ``` Due to the color representation of mass function of photon is given by (C.4), and compare it with (C.32) - $`\gamma`$ ``` math \xi(\gamma) = \kappa ( +1, \quad +1, \quad -2 ) = +\kappa \pmb{\xi}_{0} \tag{C.4} ``` - $`B\tilde{B}`$ ``` math \xi(g_{B\tilde{B}}) = \kappa ( -1, \quad -1, \quad +2 ) = -\kappa \pmb{\xi}_{0} \tag{C.32} ``` Having ``` math \begin{equation} \xi(g_{B\tilde{B}}) = -\xi(\gamma) \tag{C.33} \end{equation} ``` Last, (C.30) and (C.31) are chosen as two color neutral candidates of eight color states of boson gluon $`g`$. - $`R\tilde{R} \qquad \xi(g R\tilde{R}) = \kappa \, ( +2,\,-1,\,-1 ) \hfill (C.30)`$ - $`G\tilde{G} \qquad \xi(g G\tilde{G}) = \kappa \, ( -1,\,+2,\,-1 ) \hfill (C.31)`$ Because of the color scalar products of the eight color states of boson gluon $`g`$ are the same math value below: ``` math \begin{equation} \xi^{2}(g) = \xi^{2}(g_{R\tilde{G}}) = \xi^{2}(g_{G\tilde{B}}) = \xi^{2}(g_{B\tilde{R}}) = \xi^{2}(g_{G\tilde{R}}) = \xi^{2}(g_{B\tilde{G}}) = \xi^{2}(g_{R\tilde{B}}) = \xi^{2}(g_{R\tilde{R}}) = \xi^{2}(g_{G\tilde{G}}) \tag{C.34} \end{equation} ``` ``` math \begin{equation} = 6 \kappa^{2} = 338, 552. 525\, 766\, 5220 \tag{C.35} \end{equation} ``` Where ``` math \begin{equation} \kappa = 237.540\, 356\, 489349 \tag{C.5} \end{equation} ``` Then making subtraction, using ScalarProduct-Mass Equation: ``` math \begin{equation} | \textbf{Q}^{2}(\gamma^{0}, \xi) - \xi^{2}(g) | = | 338, 552. 525\, 766\, 5218 - 338, 552. 525\, 766\, 5220 | = 0.000\, 000\, 0002 = \frac{0.000\, 000\, 0001}{0.511} = \frac{M(g)}{0.511} \approx 0 \tag{C.36} \end{equation} ``` (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 $`g`$. <div class="center"> **Table 3 Critical PG and Mass Function MF $`\xi(\omega)`$ values of Elementary Fermion and Elementary Boson (Color-Unit Constant $`\xi_0`$)** </div> <div class="scriptsize"> | | | | | | | | | |:---|:--:|:--:|:--:|:--:|:--:|:--:|:--:| | $`Q(\gamma^{Q}, \xi)`$ | Photon | Fermion | Fermion | Fermion | Boson | Boson | Boson | | | Generation | 1st | 2nd | 3rd | Force Carriers | Force Carriers | Force Carriers | | $`Q(\gamma^{+\frac{2}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{+\frac{2}{3}})`$ | $`\xi(u)`$ | $`\xi(c)`$ | $`\xi(t)`$ | | | | | $`|`$ | 236.890997571510 | 236.889414215465 | 236.008183479106 | 0.0000000000 | | | | | $`Q(\gamma^{-\frac{2}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{\bar{-\frac{2}{3}}})`$ | $`\xi(\tilde{u})`$ | $`\xi(\tilde{c})`$ | $`\xi(\tilde{t})`$ | | | | | $`|`$ | 238.224230106917 | 238.222655612254 | 237.346375048611 | 18.040896875322 | | | | | | | | | | | | | | $`Q(\gamma^{-\frac{1}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{-\frac{1}{3}})`$ | $`\xi(d)`$ | $`\xi(s)`$ | $`\xi(b)`$ | | | | | $`|`$ | 237.873805614775 | 237.870514860345 | 237.808667632002 | 234.629506784110 | | | | | $`Q(\gamma^{+\frac{1}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{\bar{+\frac{1}{3}}})`$ | $`\xi(\tilde{d})`$ | $`\xi(\tilde{s})`$ | $`\xi(\tilde{b})`$ | | | | | $`|`$ | 237.207141245477 | 237.203841242341 | 237.141820143797 | 233.953597779454 | | | | | | | | | | | | | | $`Q(\gamma^{-}, \xi) \quad |`$ | $`\xi(\gamma^{-})`$ | $`\xi(e^{-})`$ | $`\xi(\mu^{-})`$ | $`\xi(\tau^{-})`$ | | $`\xi(W^{-})`$ | | | $`|`$ | 238.541401586377 | 238.541052240755 | 238.469128788085 | 237.323445434400 | | 175.15395597667 | | | $`Q(\gamma^{+}, \xi) \quad |`$ | $`\xi(\gamma^{+})`$ | $`\xi(e^{+})`$ | $`\xi(\mu^{+})`$ | $`\xi(\tau^{+})`$ | | $`\xi(W^{+})`$ | | | $`|`$ | 236.541416355320 | 236.541064055935 | 236.468532294544 | 235.313108715690 | | 172.42027048716 | | | | | | | | | | | | $`Q(\gamma^{0}, \xi) \quad |`$ | $`\xi(\gamma^{0})`$ | $`\xi(\nu_e)^{\clubsuit}`$ | $`\xi(\nu_\mu)`$ | $`\xi(\nu_\tau)`$ | $`\xi(\gamma)^{*}`$ | $`\xi(Z)`$ | $`\xi(H)`$ | | $`|`$ | 237.540356489349 | 237.540356487976 | 237.540226048334 | 237.527861287950 | 237.540356489349 | 163.339597441044 | 125.122693427295 | | $`Q(\tilde{\gamma}^{0}, \xi) \quad |`$ | $`\xi(\tilde{\gamma}^{0})`$ | $`\xi(\tilde{\nu}_e)^{\clubsuit}`$ | $`\xi(\tilde{\nu}_\mu)`$ | $`\xi(\tilde{\nu}_\tau)`$ | $`\xi(g)^{***}`$ | $`\xi(Z)`$ | $`\xi(H)`$ | | $`|`$ | 237.540356489349 | 237.540356487976 | 237.540226048334 | 237.527861287950 | | 163.339597441044 | 125.122693427295 | | | ZeroMass | Non-ZeroMass | Non-ZeroMass | Non-ZeroMass | ZeroMass | Non-ZeroMass | Non-ZeroMass | </div> Next, the detailed examples ($`\xi(\nu_e)^{\clubsuit} \xi(\tilde{\nu}_e)^{\clubsuit}`$ and $`\xi(\gamma)^{*} \xi(g)^{***}`$) of characteristic values of Function-$`\xi(\omega)`$ are given. <div class="center"> </div> <div class="center"> $`\Downarrow \qquad \qquad \Downarrow`$ </div> ``` math \begin{align*} \xi(\nu_e)^{\clubsuit} = \xi(\tilde{\nu}_e)^{\clubsuit} = &( +237.540\, 356\, 487976, \quad +237.540\, 356\, 487976, \quad -475.080\, 712\, 975952 ) \\ \xi(\gamma)^{*} = &( +237.540\, 356\, 489349, \quad +237.540\, 356\, 489349, \quad -475.080\, 712\, 978698 ) \\ & \\ \xi(g)^{***} = \xi(g_{R\tilde{R}}) = &( +475.080\, 712\, 978698, \quad -237.540\, 356\, 489349, \quad -237.540\, 356\, 489349 ) \\ \xi(g_{G\tilde{G}}) = &( -237.540\, 356\, 489349, \quad +475.080\, 712\, 978698, \quad -237.540\, 356\, 489349 ) \\ & \\ \xi(g_{R\tilde{G}}) = \sqrt{3} &( +237.540\, 356\, 489349, \quad -237.540\, 356\, 489349, \quad 0.000\, 000\, 000000 ) \\ \xi(g_{G\tilde{B}}) = \sqrt{3} &( 0.000\, 000\, 000000, \quad +237.540\, 356\, 489349, \quad -237.540\, 356\, 489349 ) \\ \xi(g_{B\tilde{R}}) = \sqrt{3} &( -237.540\, 356\, 489349, \quad 0.000\, 000\, 000000, \quad +237.540\, 356\, 489349 ) \\ & \\ \xi(g_{G\tilde{R}}) = \sqrt{3} &( -237.540\, 356\, 489349, \quad +237.540\, 356\, 489349, \quad 0.000\, 000\, 000000 ) \\ \xi(g_{B\tilde{G}}) = \sqrt{3} &( 0.000\, 000\, 000000, \quad -237.540\, 356\, 489349, \quad +237.540\, 356\, 489349 ) \\ \xi(g_{R\tilde{B}}) = \sqrt{3} &( +237.540\, 356\, 489349, \quad 0.000\, 000\, 000000, \quad -237.540\, 356\, 489349 ) \end{align*} ``` ``` math \begin{align*} \xi(\nu_e)^{2\clubsuit} = \xi(\tilde{\nu}_e)^{2\clubsuit} &= 338, 552. 525\, 762\, 6079 \qquad \qquad (1.11) \: [1] \\ \xi(\gamma)^{2*} = \xi(g)^{2***} &= 338, 552. 525\, 766\, 5220 \qquad \qquad (C.6) \: (C.35) \end{align*} ``` $`\pmb{\star} \quad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup \qquad \cup \cup \cup`$ # Chat with Boson Particle Q(B) = Q( ) Q(B) = Q(Pi) The photon generation $`\textbf{Q}(\gamma^{\mathbb{Q}}, \xi)`$ is an essential family tree of unified mass theory in this paper. The four massless particles $`\gamma^{0\text{e}}, \gamma^{-\text{e}}, \gamma^{-\frac{1}{3}\text{e}}, \gamma^{+\frac{2}{3}\text{e}}`$ and massless anti-particles $`\tilde{\gamma}^{0\text{e}}, \gamma^{+\text{e}}, \gamma^{+\frac{1}{3}\text{e}}, \gamma^{-\frac{2}{3}\text{e}}`$ of photon generation, as $`\textbf{Q}(\Psi(0), \xi)`$ \[1\], satisfy relation ($`\pi.1`$), ($`\pi.2`$) below ``` math \begin{align*} \textbf{Q}(\gamma^{0\text{e}}, \xi) + \textbf{Q}(\tilde{\gamma}^{0\text{e}}, \xi) = \textbf{Q}(\gamma^{-\text{e}}, \xi) + \textbf{Q}(\gamma^{+\text{e}}, \xi) = \textbf{Q}(\gamma^{-\frac{1}{3}\text{e}}, \xi) + \textbf{Q}(\gamma^{+\frac{1}{3}\text{e}}, \xi) = \textbf{Q}(\gamma^{+\frac{2}{3}\text{e}}, \xi) + \textbf{Q}(\gamma^{-\frac{2}{3}\text{e}}, \xi) \tag{$\pi.1$} \\ = ( +475.079\, 309\, 70630, \quad +475.079\, 309\, 70630, \quad -950.158\, 619\, 41260 ) \quad = \textbf{Q}(\Pi) \tag{$\pi.2$} \end{align*} ``` ``` math \begin{equation} \textbf{Q}^{2}(\Pi) = 1354, 202. 103\, 066\, 0872 = \frac{691, 997. 274\, 666\, 7706 \text{ MeV}}{0.511} = \frac{M(\Pi)}{0.511} \tag{$\pi.3$} \end{equation} ``` The above particle $`\Pi`$ is an amazing boson named as Heaven particle with mass $`M(\Pi) = 692 \text{ GeV}`$, its debut appears unexpected in the discussion of "Production and Decay of Higgs Boson" \[2\]. Where in order to ensure quark genera $`(t, b), (c, s), (u, d)`$ to be harmony flavor symmetry, then boson particle $`\Pi`$ is required instead of God particle $`H`$ with $`M(H) = 125 \text{ GeV}`$. This $`M(\Pi)`$ is as four times as heavy as ground state $`\textbf{Q}^{2}(t)`$ of $`t`$ top quark. ``` math \begin{equation} \textbf{Q}^{2}(\Pi) = 4 \: \frac{173, 000.}{0.511} = 4 \: \frac{M(t)}{0.511} \tag{$\pi.4$} \end{equation} ``` Boson $`\Pi`$, is a bound state, a color-pair of quark $`q`$ and an antiquark $`\tilde{q}`$ in complex field $`\mathbb{C}`$, that shown below \[2\] ``` math \begin{equation} \underline{\textbf{Q}(B, \xi(B)) \: + \: i\xi(B)} = \underline{\textbf{Q}(q, \xi) \: + \: i\xi(q)} + \underline{\textbf{Q}(\tilde{q}, \xi) \: + \: i\xi(\tilde{q})} \tag{$\pi.5$} \end{equation} ``` ``` math \begin{equation} \xi(q) + \xi(\tilde{q}) = 0 \tag{$\pi.6$} \end{equation} ``` $`\textbf{Q}(B = \Pi) = \textbf{Q}(f\bar{f}) \: [2]`$ is the prototype of $`\textbf{Q}(\Pi)`$ ($`\pi.1`$), ($`\pi.2`$). What’s about particle $`\textbf{Q}(B = \Pi)`$ ! A Physical Boson, or A Math Boson? $`\Longrightarrow`$ From Critical PG to $`\Pi`$ Running PG # Chat with Photon Generation Q( ^ Q , ) Q(gamma, xi) PG Now **BACK TO** paragraph **Introduction**. The detailed values of Photon Generation $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi)`$, that appear at the most left column of Table 3 are given below <div class="center"> For Particle: $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi) = \left[ \begin{array}{c} \textbf{Q}(\gamma^{+\frac{2}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-\frac{1}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-e}, \xi) \\ \textbf{Q}(\gamma^{0e}, \xi) \end{array} \right] = \fbox{ \begin{minipage}{0.65\textwidth} \begin{align*} ( +236.\, 53965485315, \quad +238.\, 53965485315, \quad -473.\, 07930970630 ) \\ ( +236.\, 53965485315, \quad +238.\, 53965485315, \quad -476.\, 07930970630 ) \\ ( +236.\, 53965485315, \quad +238.\, 53965485315, \quad -478.\, 07930970630 ) \\ ( +236.\, 53965485315, \quad +238.\, 53965485315, \quad -475.\, 07930970630 ) \end{align*} \end{minipage} }`$\ Table X photon generation Table Y detailed values of photon generation ( Critical PG ) </div> We find out: The value $`-475.\, 07930970630`$ appears in **Table Y** also appear in expression $`\textbf{Q}(\Pi)`$ ($`\pi.2`$) ! THEN making following transformation <div class="center"> For Particle: $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi) = \left[ \begin{array}{c} \textbf{Q}(\gamma^{+\frac{2}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-\frac{1}{3}e}, \xi) \\ \textbf{Q}(\gamma^{-e}, \xi) \\ \textbf{Q}(\gamma^{0e}, \xi) \end{array} \right] = \fbox{ \begin{minipage}{0.65\textwidth} \begin{align*} ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -948.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -951.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -953.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -950.\, 15861941260 ) \end{align*} \end{minipage} }`$\ Table X photon generation Table Z detailed values of photo generation ( $`\Pi`$ Running PG ) </div> **AND in the same way, below** <div class="center"> For Anti-Particle: $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi) = \left[ \begin{array}{c} \textbf{Q}(\gamma^{-\frac{2}{3}e}, \xi) \\ \textbf{Q}(\gamma^{+\frac{1}{3}e}, \xi) \\ \textbf{Q}(\gamma^{+e}, \xi) \\ \textbf{Q}(\tilde{\gamma}^{0e}, \xi) \end{array} \right] = \fbox{ \begin{minipage}{0.65\textwidth} \begin{align*} ( +238.\, 53965485315, \quad +236.\, 53965485315, \quad -477.\, 07930970630 ) \\ ( +238.\, 53965485315, \quad +236.\, 53965485315, \quad -474.\, 07930970630 ) \\ ( +238.\, 53965485315, \quad +236.\, 53965485315, \quad -472.\, 07930970630 ) \\ ( +238.\, 53965485315, \quad +236.\, 53965485315, \quad -475.\, 07930970630 ) \end{align*} \end{minipage} }`$\ Table X photon generation Table Y detailed values of photon generation ( Critical PG ) </div> **THEN making following transformation** <div class="center"> For Anti-Particle: $`\textbf{Q}(\gamma^{\mathsf{Q}}, \xi) = \left[ \begin{array}{c} \textbf{Q}(\gamma^{-\frac{2}{3}e}, \xi) \\ \textbf{Q}(\gamma^{+\frac{1}{3}e}, \xi) \\ \textbf{Q}(\gamma^{+e}, \xi) \\ \textbf{Q}(\tilde{\gamma}^{0e}, \xi) \end{array} \right] = \fbox{ \begin{minipage}{0.65\textwidth} \begin{align*} ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -952.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -949.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -947.\, 15861941260 ) \\ ( +475.\, 07930970630, \quad +475.\, 07930970630, \quad -950.\, 15861941260 ) \end{align*} \end{minipage} }`$\ Table X photon generation Table Z detailed values of photo generation ( $`\Pi`$ Running PG ) </div> <div class="center"> **SUBSEQUENTLY, Table Z instead of Table Y, Table 4 instead of Table 3. see below** </div> <div class="center"> <div class="scriptsize"> | | | | | | | | | |:---|:--:|:--:|:--:|:--:|:--:|:--:|:--:| | $`Q(\gamma^{Q}, \xi)`$ | Photon | Fermion | Fermion | Fermion | Boson | Boson | Boson | | | Generation | 1st | 2nd | 3rd | Force Carriers | Force Carriers | Force Carriers | | $`Q(\gamma^{+\frac{2}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{+\frac{2}{3}})`$ | $`\xi(u)`$ | $`\xi(c)`$ | $`\xi(t)`$ | | | | | $`|`$ | 474.412877247312 | 474.412086624059 | 473.972674356608 | 410.660770281391 | | | | | $`Q(\gamma^{-\frac{2}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{\bar{-\frac{2}{3}}})`$ | $`\xi(\tilde{u})`$ | $`\xi(\tilde{c})`$ | $`\xi(\tilde{t})`$ | | | | | $`|`$ | 475.746209924251 | 475.745421516814 | 475.307241893043 | 412.200371672955 | | | | | | | | | | | | | | $`Q(\gamma^{-\frac{1}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{-\frac{1}{3}})`$ | $`\xi(d)`$ | $`\xi(s)`$ | $`\xi(b)`$ | | | | | $`|`$ | 475.412701468404 | 475.411054940622 | 475.380112878891 | 473.797736142317 | | | | | $`Q(\gamma^{+\frac{1}{3}}, \xi) \quad |`$ | $`\xi(\gamma^{\bar{+\frac{1}{3}}})`$ | $`\xi(\tilde{d})`$ | $`\xi(\tilde{s})`$ | $`\xi(\tilde{b})`$ | | | | | $`|`$ | 474.746034883786 | 474.744386043840 | 474.713400528296 | 473.128793981064 | | | | | | | | | | | | | | $`Q(\gamma^{-}, \xi) \quad |`$ | $`\xi(\gamma^{-})`$ | $`\xi(e^{-})`$ | $`\xi(\mu^{-})`$ | $`\xi(\tau^{-})`$ | | $`\xi(W^{-})`$ | | | $`|`$ | 476.079834828600 | 476.079659787898 | 476.043626408948 | 475.470742120363 | | 447.692882625925 | | | $`Q(\gamma^{+}, \xi) \quad |`$ | $`\xi(\gamma^{+})`$ | $`\xi(e^{+})`$ | $`\xi(\mu^{+})`$ | $`\xi(\tau^{+})`$ | | $`\xi(W^{+})`$ | | | $`|`$ | 474.079837043933 | 474.079661264787 | 474.043475860345 | 473.468171447314 | | 445.565483307544 | | | | | | | | | | | | $`Q(\gamma^{0}, \xi) \quad |`$ | $`\xi(\gamma^{0})`$ | $`\xi(\nu_e)^{\clubsuit}`$ | $`\xi(\nu_\mu)`$ | $`\xi(\nu_\tau)`$ | $`\xi(\gamma)^{*}`$ | $`\xi(Z)`$ | $`\xi(H)`$ | | $`|`$ | 475.079309706300 | 475.079309705614 | 475.079244485613 | 475.073062210388 | 475.079309706300 | 442.667768921716 | 430.035600805864 | | $`Q(\tilde\gamma^{{0}}, \xi) \quad |`$ | $`\xi(\tilde{\gamma}^{0})`$ | $`\xi(\tilde{\nu}_e)^{\clubsuit}`$ | $`\xi(\tilde{\nu}_\mu)`$ | $`\xi(\tilde{\nu}_\tau)`$ | $`\xi(g)^{***}`$ | $`\xi(Z)`$ | $`\xi(H)`$ | | $`|`$ | 475.079309706300 | 475.079309705614 | 475.079244485613 | 475.073062210388 | | 442.667768921716 | 430.035600805864 | | | ZeroMass | Non-ZeroMass | Non-ZeroMass | Non-ZeroMass | ZeroMass | Non-ZeroMass | Non-ZeroMass | </div> **Table 4 $`\Pi`$ Running PG and Mass Function MF $`\xi(\omega)`$ values of Elementary Fermion and Elementary Boson (Color-Unit Constant $`\xi_0`$)** </div> # Epilogue "Double Helix Structure" of elementary particle: Two so-called "Double Helix Structure", Photon Generation PG $`\textbf{Q}(\gamma^{\mathbb{Q}}, \xi)`$ and Mass Function MF $`\xi(\omega)`$, 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 Z** and **Table 4** !! Thanks to GJSFR, offering a academic platform for researchers all over the world. <div class="gjthebibliography"> 99 Shao-Xu Ren. The Zeroth of Generation Zh of Fermion, A Unified Mass Theory of Twelve Elementary Fermions. *GLOBAL JOURNAL OF SCIENCE FRONTIER RESEARCH: A PHYSICS AND SPACE SCIENCE* Volume 25 ISSUE 6 Version 1.0 Year 2025 27-61. Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Shao-Xu Ren. Production and Decay of Higgs Boson, From God Particle H to Heaven Particle $`\Pi`$. *GLOBAL JOURNAL OF SCIENCE FRONTIER RESEARCH: A PHYSICS AND SPACE SCIENCE* Volume 25 ISSUE 5 Version 1.0 Year 2025 36-58. Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Shao-Xu Ren. Colorization of Gell-mann-Nishijima Relation and Mass Principle, Origins of Mass; Fermions and Charges, Bosons and Color-Pairs. *GLOBAL JOURNAL OF SCIENCE FRONTIER RESEARCH: A PHYSICS AND SPACE SCIENCE* Volume 25 ISSUE 3 Version 1.0 Year 2025 93-128. Online ISSN: 2249-4626 & Print ISSN: 0975-5896 Ian J.R.Aitchison, Anthony J.G.Hey.(2013). Gauge Theories in Particle Physics A Practical Introduction 4th Edition Volume2. ISBN 978-7-5192-8371-1 Antonio Ereditato. (2017). Ever Smaller. ISBN: 978-0-262-04386-1 Paul Langacker. (2017). The Standard Model and Beyond Second Edition ISBN: 978-7-5192-9614-8. Richard A Dunlap (2018). Particle Physics. IOP Concise Physics. Morgan & Claypoo Publishers Daniel Denegri. Claude Guyot. Andreas Hoecker. Lydia Roos (2021). The Adventure of the LARGE HADRON COLLIDER From the Big Bang to the Higgs Boson. World Scientific. ISBN: 978-981-3236-08-0 Ikaros l Bigi. Giulia Ricciardi. Marco Pallavicini (2021). New Era for CP Asymmetries, Axions and Rare Decays of Hadrons and Leptons. World Scientific. ISBN: 978-981-3233-07-2 Andre Rubbia (2022). PHENOMENOLOGY OF PARTICLE PHYSICS. CAMBRIDGE UNIVERSITY PRESS ISBN 978-1-316-51934-9 Pierre Baldi, Peter Sadowski and Daniel Whiteson. Deep Learning from Four Vectors, ARTIFICIAL INTELLIGENCE for HIGH ENERGY PHYSICS 59-83, © 2022 World Scientific Publishing Company, https://doi.org/10.1142/9789811234026_0003. ISBN 978-981-123-402-6 Andrea Banfi. Hadron Jets: An Introduction. University of Sussex, Brighton, UK. © 2022 IOP Publishing Bristol, UK. ISBN 978-0-7503-4735-8 Dong-Sheng Du, Mao-Zhi Yang. (2023). Introduction to Particle Physics. ISBN: 978-981-125-945-6 Regina Demina. Aran Garcia-Bellido (2023). Electroweak Symmetry and its Breaking. University of Rochester, USA. World Scientific. ISBN: 978-981-122-224-5 PASCAL PAGANINI (2023). FUNDAMENTALS OF PARTICLE PHYSICS. CAMBRIDGE UNIVERSITY PRESS ISBN 978-1-009-17158-8 W.N. Cottingham and D.A. Greenwood. (2023). An Introduction to the Standard Model of Particle Physics. CAMBRIDGE UNIVERSITY PRESS ISBN 978-1-009-40170-8 ALESSANDRO BETTINI (2024). INTRODUCTION TO ELEMENTARY PARTICLE PHYSICS. CAMBRIDGE UNIVERSITY PRESS ISBN 978-1-009-44073-8 Guido Tonelli (2025). Matter: The Magnificent Illusion. SEPS Segretariato Europeo per le Pubblicazioni Scientifiche ISBN 978-1-509-56414-9 </div>

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How to Cite This Article

Dr. Shaoxu-ren. 2026. \u201cA Unified Mass theory of Elementary Fermions and Elementary Bosons\u201d. Global Journal of Science Frontier Research, Global Journal of Science Frontier Research - A: Physics & Space Science GJSFR-A Volume 26 (GJSFR Volume 26 Issue A1).

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GJSFR Volume 26 Issue A1

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Journal Specifications

Crossref Journal DOI 10.17406/GJSFR

Print ISSN 0975-5896

e-ISSN 2249-4626

Keywords

Color-Unit Constant 0 Critical PG Double Helix Structure Mass Function MF ()Photon PG Q(Q Scalar Product-Mass Equation Table X ξ)Π Running PG )

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MSC 81V05

81V25

Submission ReceivedMarch 2, 2026
Peer Review Double Blind
Handling Editor
Accepted March 9, 2026
Published April 10, 2026

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v1.2

Issue date

April 10, 2026

Language

English

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