### 0. INTRODUCTION The three-colors R, G, B of quarks is really a curious and excellent concept in monder particle physics. In Standard Model SM, R, G, B are used to treat strong interaction quark classification and weak interaction flavor-transitions among particles in different generations. To discuss hadronic constituents in strong interaction In previous papers [1] when discussing SM, Colous Spectrum Diagram of Flavour CSDF is introduced by Spin Topological Space STS math frame [2], in which the concretization of color values $q_{\mathrm{R}}, q_{\mathrm{G}}, q_{\mathrm{B}}$ of each quark can be selected from the third components $\pi_3(q)$ of one-sixth spin $\vec{\pi}(q)$ below $$ \pi_{3}(q) = \dots, \frac{-29}{6}, \frac{-23}{6}, \frac{-17}{ 6}, \frac{-11}{6}, \frac{-5}{6}, \frac{+1}{6}, \frac{+7}{6}, \frac{+13}{6}, \frac{+19}{6}, \frac{+25}{6}, \dots \subseteq q_{\mathrm{RGB}} \equiv q_{\mathrm{R}}, q_{\mathrm{G}}, q_{\mathrm{B}} \tag{00.1} $$ $$ \vec{\pi}(q) \times \vec{\pi}(q) = i\vec{\pi}(q) $$ To discuss hadronic constituents in strong interaction [3], colored quark, $q(\chi, \alpha) = q(\chi) + q_{\alpha}$ is introduced (where quark spin $q(\chi), \chi = \uparrow, \downarrow$ and quark color $q_{\alpha} = q_{\mathrm{RGB}}$ (00.1), $\alpha = \mathsf{R}, \mathsf{G}, \mathsf{B}$ ). We will again make use of quark color $q_{\alpha}$, turn to discuss weak interaction in this paper. Because these colors $q_{\alpha}$ or $q_{\mathbb{R}}, q_{\mathbb{G}}, q_{\mathbb{B}}$ can offer an unified isospin $I_{3}(q)$ representation [1] for all six quarks below, so we decide to use $I_{3}(q)$ (0.0) to research weak interaction following $$ I_{3}(q) = \frac{1}{3}(q_{\mathrm{R}} + q_{\mathrm{G}} + q_{\mathrm{B}}) \equiv I_{3}(q_{\mathrm{RGB}}) \tag{0.0} $$ Or $$ \vec {u} = \left(u _ {\mathrm {R}}, u _ {\mathrm {G}}, u _ {\mathrm {B}}\right) = \left(\frac {- 5}{6}, \frac {+ 1}{6}, \frac {+ 1 3}{6}\right), \quad I _ {3} (u) = \frac {1}{3} \left(\frac {- 5}{6} + \frac {+ 1}{6} + \frac {+ 1 3}{6}\right) = \frac {+ 1}{2} \tag {0.1} $$ $$ \vec {d} = \left(d _ {\mathrm {R}}, d _ {\mathrm {G}}, d _ {\mathrm {B}}\right) = \left(\frac {- 1 1}{6}, \frac {- 5}{6}, \frac {+ 7}{6}\right), \quad I _ {3} (d) = \frac {1}{3} \left(\frac {- 1 1}{6} + \frac {- 5}{6} + \frac {+ 7}{6}\right) = \frac {- 1}{2} \tag {0.2} $$ $$ \vec {c} = \left(c _ {\mathrm {R}}, c _ {\mathrm {G}}, c _ {\mathrm {B}}\right) = \left(\frac {+ 1}{6}, \frac {+ 7}{6}, \frac {+ 1 9}{6}\right), \quad I _ {3} (c) = \frac {1}{3} \left(\frac {+ 1}{6} + \frac {+ 7}{6} + \frac {+ 1 9}{6}\right) = \frac {+ 3}{2} \tag {0.3} $$ $$ \overrightarrow {s} = \left(s _ {\mathrm {R}}, s _ {\mathrm {G}}, s _ {\mathrm {B}}\right) = \left(\frac {- 1 7}{6}, \frac {- 1 1}{6}, \frac {+ 1}{6}\right), \quad I _ {3} (s) = \frac {1}{3} \left(\frac {- 1 7}{6} + \frac {- 1 1}{6} + \frac {+ 1}{6}\right) = \frac {- 3}{2} \tag {0.4} $$ $$ \vec {t} = \left(t _ {\mathrm {R}}, t _ {\mathrm {G}}, t _ {\mathrm {B}}\right) = \left(\frac {+ 7}{6}, \frac {+ 1 3}{6}, \frac {+ 2 5}{6}\right), \quad I _ {3} (t) = \frac {1}{3} \left(\frac {+ 7}{6} + \frac {+ 1 3}{6} + \frac {+ 2 5}{6}\right) = \frac {+ 5}{2} \tag {0.5} $$ $$ \vec {b} = \left(b _ {\mathrm {R}}, b _ {\mathrm {G}}, b _ {\mathrm {B}}\right) = \left(\frac {- 2 3}{6}, \frac {- 1 7}{6}, \frac {- 5}{6}\right), \quad I _ {3} (b) = \frac {1}{3} \left(\frac {- 2 3}{6} + \frac {- 1 7}{6} + \frac {- 5}{6}\right) = \frac {- 5}{2} \tag {0.6} $$ $$ V _ {C K M} = \left( \begin{array}{c c c c} & & & \\& V _ {\mathrm {u d}} & V _ {\mathrm {u s}} & V _ {\mathrm {u b}} \\& V _ {\mathrm {c d}} & V _ {\mathrm {c s}} & V _ {\mathrm {c b}} \\& V _ {\mathrm {t d}} & V _ {\mathrm {t s}} & V _ {\mathrm {t b}} \end{array} \right) = \left( \begin{array}{c c c c} & & & \\& 0. 9 7 5 & 0. 2 2 4 & 0. 0 0 4 \\& 0. 2 2 4 & 0. 9 7 4 & 0. 0 4 2 \\& 0. 0 0 9 & 0. 0 4 1 & 0. 9 9 9 \end{array} \right) \tag {0} $$ After that, CKM matrix is parameterized [5] to be written as a product of three rotation matrices, that called a smart Wolfenstein parametrization, one of its advantage is CP violation can be involved. (Ref [6],[7],...[12]) In this paper, CKM matrix is colorized by means of quark color $q_{\mathrm{R}}, q_{\mathrm{G}}, q_{\mathrm{B}}$. And scalar products of colors $q_{\mathrm{R}}, q_{\mathrm{G}}, q_{\mathrm{B}}$ and isospin broken $I_{3}(\xi_{rw})_{\mathrm{CKM}}$ are concerned about into Cabibbo-Kobayashi-Maskawa Matrix CKM. Outline Flowchart for Isospin Violated In CKM Matrix ## I. QUARKCOLOR SCALAR PRODUCTS IN CKM MATRIX $$ \mathrm {V} _ {C K M} = \mathrm {V} ^ {\mathrm {C K M}} \left(q _ {\mathrm {R G B}}\right) \quad \Rightarrow \quad \mathrm {V} (\vec {r} \cdot \vec {w}) \quad (1) \star \quad \Rightarrow \quad \mathrm {V} \left(\vec {r ^ {\prime}} \cdot \overrightarrow {w _ {\mathrm {r}} ^ {\prime}}\right) \quad (2) \star \quad \Rightarrow \quad \mathrm {V} \left(\vec {r ^ {\prime}} \cdot \overrightarrow {w} _ {\mathrm {r}}\right) \quad (3) \star $$ Here - 【1】 $\vec{r} \cdot \vec{w} = r_{\mathrm{R}} w_{\mathrm{R}} + r_{\mathrm{G}} w_{\mathrm{G}} + r_{\mathrm{B}} w_{\mathrm{B}}$ (1.0) - 【2】 $\overrightarrow{r^{\prime}}\cdot \overrightarrow{w_{\mathrm{r}}^{\prime}} = r_{\mathrm{R}}^{\prime}w_{\mathrm{rR}}^{\prime} + r_{\mathrm{G}}^{\prime}w_{\mathrm{rG}}^{\prime} + r_{\mathrm{B}}^{\prime}w_{\mathrm{rB}}^{\prime}$ (2.0) - 【3】 $\vec{r^{\prime}}\cdot \vec{W}_{\mathrm{r}} = r_{\mathrm{R}}^{\prime}\mathsf{W}_{\mathrm{rR}} + r_{\mathrm{G}}^{\prime}\mathsf{W}_{\mathrm{rG}} + r_{\mathrm{B}}^{\prime}\mathsf{W}_{\mathrm{rB}}$ (3.0) Symbols (1)★, (2)★, (3)★ respectively stand for the quarkcolor scalar products (1.0), (2.0), (3.0) of CKM Matrix in different interaction regions shown below 【1】Strong interaction color representation of flavor, when $I_{3}(q)$ is conserved $$ \vec{r} = \vec{r}(q) = \left(r_{\mathrm{R}}, r_{\mathrm{G}}, r_{\mathrm{B}}\right) \tag{1.1} $$ $$ \vec{w} = \vec{w}(q) = \left(w_{\mathrm{R}}, w_{\mathrm{G}}, w_{\mathrm{B}}\right) \tag{1.2} $$ 【2】Weak interaction color representation of flavor, when isospin $I_{3}(q)$ is conserved ( $\xi = 0$ ). $$ \vec {r} ^ {\prime} = \vec {r} (q) + \frac {1}{6} \vec {\Phi} _ {\mathrm {r}} \tag {2.1} $$ $$ \overrightarrow{w_{\mathrm{r}}^\prime} = \vec{w}(q) + \frac{1}{6} \overrightarrow{\Phi}_{\mathrm{r w}} = \left(w_{\mathrm{R}}, w_{\mathrm{G}}, w_{\mathrm{B}}\right) + \frac{1}{6} \left(\left(\Phi_{\mathrm{r w}}\right)_{\mathrm{R}}, \left(\Phi_{\mathrm{r w}}\right)_{\mathrm{G}}, \left(\Phi_{\mathrm{r w}}\right)_{\mathrm{B}}\right) \tag{2.2} $$ 【3】Weak interaction color representation of flavor, when isospin $I_{3}(q)$ is broken ( $\xi \neq 0$ ) $$ \vec {r} ^ {\prime} = \vec {r} (q) + \frac {1}{6} \vec {\Phi} _ {\mathrm {r}} \tag {3.1} $$ $$ \vec{W}_{\mathrm{r}} \equiv \vec{w}_{\mathrm{r}}^{\prime}(\xi) = \vec{w}(q) + \frac{1}{6} \vec{\Phi}_{\mathrm{r w}}(\xi) \tag{3.2} $$ Where $r = u, c, t$ are up-type quarks, quark charge $Q_{r} = \frac{+2}{3} e$ and $w = d, s, b$ are down-type quarks, quark charge $Q_{w} = \frac{-1}{3} e$. It will be shown that in case [3], the charge $Q_{w}$ of down-type quark will be a slight deviated from $\frac{-1}{3}$ due to isospin broken $I_{3}(q)$. Superscript " ' ", that written on the top right of $r$ and $w$, stands for quark being in weak interaction region. Detail Processes for Isospin Violated In CKM Matrix ## II. ISOSPIN $I_{3}$ BE CONSERVED IN CKM MATRIX For clear logical route to quark-colorization of Cabibbo-Kobayashi-Maskawa Matrix CKM, in following an example (labelled by mark "♦") of color scalar product $\vec{u'} \cdot \vec{d}_u$ is given, which (includes 2.1. $\vec{u} \cdot \vec{d}$ and 2.2. $\vec{u'} \cdot \vec{d}_u'$ ) arranged in the top left element $V_{11}$ of CKM matrix. 2.1. In【1】Strong interaction color representation of flavor, (4) is color scalar product of $u$ quark and $d$ quark $$ \vec {u} \cdot \vec {d} \updownarrow = u _ {\mathrm {R}} d _ {\mathrm {R}} + u _ {\mathrm {G}} d _ {\mathrm {G}} + u _ {\mathrm {B}} d _ {\mathrm {B}} = (\frac {- 5}{6}) (\frac {- 1 1}{6}) + (\frac {+ 1}{6}) (\frac {- 5}{6}) + (\frac {+ 1 3}{6}) (\frac {+ 7}{6}) = \frac {1}{3 6} \{+ 5 5 - 5 + 9 1 \} = \frac {+ 1 4 1}{3 6} \updownarrow \tag {4} $$ obtain isospin $I_{3}(q_{\mathrm{RGB}})$ $$ I _ {3} (u) = \frac {1}{3} \left(\frac {- 5}{6} + \frac {+ 1}{6} + \frac {+ 1 3}{6}\right) = \frac {+ 1}{2} \tag {0.1} $$ $$ I _ {3} (d) = \frac {1}{3} \left(\frac {- 1 1}{6} + \frac {- 5}{6} + \frac {+ 7}{6}\right) = \frac {- 1}{2} \tag {0.2} $$ In this way, for CKM Matrix we get following $$ \text{Matrix} (1) \star \quad \mathrm{V} ^ {\mathrm{C K M}} \left(q _ {\mathrm{R G B}}\right) = \left( \begin{array}{c c c c c} & & & & \\& \vec{u} \cdot \vec{d} \updownarrow & \vec{u} \cdot \vec{s} & \vec{u} \cdot \vec{b} \\& \vec{c} \cdot \vec{d} & \vec{c} \cdot \vec{s} & \vec{c} \cdot \vec{b} \\& \vec{t} \cdot \vec{d} & \vec{t} \cdot \vec{s} & \vec{t} \cdot \vec{b} \\& & & & \end{array} \right) = \frac{1}{3 6} \left( \begin{array}{c c c c c} & + 1 4 1 \updownarrow & + 8 7 & + 3 3 \\& + 8 7 & - 7 5 & - 2 3 7 \\& + 3 3 & - 2 3 7 & - 5 0 7 \\& & & & \end{array} \right) \tag{5} $$ Matrix (5) always appears in strong interaction. 2.2. In【2】Weak interaction color representation of flavor, (10) is color scalar product of $u'$ quark and $d_{\mathrm{u}}'$ quark To research for the properties of quark color scalar product and quark isospin in Weak Interaction, so-called "weak interaction pairing $\vec{\Phi}$ " of CSDF is introduced and $\vec{\Phi}$ be attached to each of the six flavors $\vec{t},\vec{c},\vec{u},\vec{d},\vec{s},\vec{b}$ of strong interaction. (6),(7) are the concrete expressions of weak interaction pairing, for up-type quark $u$ and down-type quark $d$, by which, $\overrightarrow{u'}$ and $\overrightarrow{d_u'}$ of express (2.1) and (2.2) are obtained. $$ \overrightarrow {\Phi} _ {U} = \left(\frac {+ 1}{2}, \frac {+ 1 6}{2}, \frac {- 1 7}{2}\right) \tag {6} $$ $$ \vec{\Phi}_{ud} = \left(\frac{+5}{2}, \frac{+10}{2}, \frac{-15}{2}\right) \tag{7} $$ $$ \overrightarrow {u ^ {\prime}} = \overrightarrow {u} + \frac {1}{6} \overrightarrow {\Phi_ {U}} = \left(\frac {- 5}{6}, \frac {+ 1}{6}, \frac {+ 1 3}{6}\right) + \frac {1}{6} \left(\frac {+ 1}{2}, \frac {+ 1 6}{2}, \frac {- 1 7}{2}\right) = \left(\frac {- 9}{1 2}, \frac {+ 1 8}{1 2}, \frac {+ 9}{1 2}\right) \tag {8} $$ $$ \overrightarrow{d_{\mathrm{u}}^\prime} = \overrightarrow{d} + \frac{1}{6} \overrightarrow{\Phi}_{\mathrm{ud}} = \left(\frac{-11}{6}, \frac{-5}{6}, \frac{+7}{6}\right) + \frac{1}{6} \left(\frac{+5}{2}, \frac{+10}{2}, \frac{-15}{2}\right) = \left(\frac{-17}{12}, \frac{0}{12}, \frac{-1}{12}\right) \tag{9} $$ $$ \overrightarrow{u^\prime} \cdot \overrightarrow{d_{u}^\prime} \diamondsuit = (\overrightarrow{u} + \frac{1}{6} \overrightarrow{\Phi_{u}}) \cdot (\overrightarrow{d} + \frac{1}{6} \overrightarrow{\Phi_{ud}}) = (\frac{-9}{12}, \frac{+18}{12}, \frac{+9}{12}) \cdot (\frac{-17}{12}, \frac{0}{12}, \frac{-1}{12}) = 1.000\diamondsuit $$ Formulas (11) (12) show in case [2], isospin $I_{3}$ is conserved too, as that $I_{3}$ (0.1) and (0.2) in strong interaction. (11) (12) are $I_{3}$ crucial pion states of weak interaction. $$ I _ {3} \left(u ^ {\prime}\right) = \frac {1}{3} \left(\frac {- 9}{1 2} + \frac {+ 1 8}{1 2} + \frac {+ 9}{1 2}\right) = \frac {+ 1}{2} \tag {11} $$ $$ I _ {3} \left(d _ {\mathrm{u}} ^ {\prime}\right) = \frac{1}{3} \left(\frac{- 17}{1 2} + \frac{0}{1 2} + \frac{- 1}{1 2}\right) = \frac{- 1}{2} \tag{12} $$ There are nine weak interaction pairings $\vec{\Phi}$. in Matrix (2)★ below. Similar to pairing $\vec{\Phi}$ (6)-(7), after deliberate calculations, at last the eight other weak interaction pairings $\vec{\Phi}$ are found out, and using them, further previous Matrix (1)★ and (5) of CKM Matrix of strong interaction could be reconstructed into Matrix (2)★ and (13) of weak interaction. we get following $$ \begin{array}{r l r} & & {\Downarrow \quad \Downarrow \quad \Downarrow} \\& & {\mathsf{Matrix}(2)\star\quad \mathsf{V}^{\mathsf{CKM}}(q_{\mathsf{RGB}},\Phi) = \left( \begin{array}{c c c c c} & & & & \\& \overrightarrow{u^{'}} \cdot \overrightarrow{d_{\mathrm{u}}^{'}} \blacklozenge & \overrightarrow{u^{'}} \cdot \overrightarrow{s_{\mathrm{u}}^{'}} & \overrightarrow{u^{'}} \cdot \overrightarrow{b_{\mathrm{u}}^{'}} \\& \overrightarrow{c^{'}} \cdot \overrightarrow{d_{\mathrm{c}}^{'}} & \overrightarrow{c^{'}} \cdot \overrightarrow{s_{\mathrm{c}}^{'}} & \overrightarrow{c^{'}} \cdot \overrightarrow{b_{\mathrm{c}}^{'}} \\& \overrightarrow{t^{'}} \cdot \overrightarrow{d_{\mathrm{t}}^{'}} & \overrightarrow{t^{'}} \cdot \overrightarrow{s_{\mathrm{t}}^{'}} & \overrightarrow{t^{'}} \cdot \overrightarrow{b_{\mathrm{t}}^{'}} \end{array} \right) = \left( \begin{array}{c c c c c} & & & & \\& 1.000 \blacklozenge & 0.000 & 0.000 \\& 0.000 & 1.000 & 0.000 \\& 0.000 & 0.000 & 1.000 \\& & & & \end{array} \right)} \\& & {(13)} \end{array} $$ ## III. ISOSPIN $I_{3}$ BE BROKEN IN CKM MATRIX Taking broken parameter $\xi_{\mathrm{ud}} = \xi = 0.2$ into (7) of pairing- $\vec{\Phi}$ (6)-(7) obtain (14) and (15) $$ \overrightarrow{\Phi}_{ud}(\xi) = \left(\frac{+5}{2}, \frac{+10-\xi}{2}, \frac{-15}{2}\right) = \left(\frac{+5}{2}, \frac{+10-0.2}{2}, \frac{-15}{2}\right) = \left(\frac{+5}{2}, \frac{+9.8}{2}, \frac{-15}{2}\right) \tag{14} $$ $$ \vec{d}_{u} \equiv \vec{d}_{u}^\prime(\xi) = \vec{d} + \frac{1}{6} \vec{\Phi}_{ud}(\xi) = \left(\frac{-11}{6}, \frac{-5}{6}, \frac{+7}{6}\right) + \frac{1}{6} \left(\frac{+5}{2}, \frac{+9.8}{2}, \frac{-15}{2}\right) = \left(\frac{-17}{12}, \frac{-0.2}{12} \updownarrow, \frac{-1}{12}\right) \tag{15} $$ When broken parameter $\xi$ appears in $\vec{\Phi}$, we call $\vec{\Phi}$ be "Color-Broken" and call the colors of down-type quark $\vec{d}$ (15), or quarkcolor scalar products (16) of CKM be "Color-Broken". From $\vec{\mathbf{d}}_{\mathfrak{u}}$, simultaneously & respectively obtain two physical quantities $\vec{u^{\prime}}\cdot \vec{\mathbf{d}}_{\mathfrak{u}}$ (16) and $I_{3}(\vec{\mathbf{d}}_{\mathfrak{u}})$ (18) below: $$ \overrightarrow {u ^ {\prime}} \cdot \overrightarrow {d} _ {u} \downarrow = \left(\frac {- 9}{1 2}, \frac {+ 1 8}{1 2}, \frac {+ 9}{1 2}\right) \left(\frac {- 1 7}{1 2}, \frac {- 0 . 2}{1 2} \downarrow , \frac {- 1}{1 2}\right) = \frac {1}{1 4 4} \left\{+ 1 4 4 - 3. 6 \right\} = \frac {1}{1 4 4} \left\{+ 1 4 0. 4 \right\} = 0. 9 7 5 \downarrow \tag {16} $$ $$ I _ {3} \left(u ^ {\prime}\right) = \frac {1}{3} \left(\frac {- 9}{1 2} + \frac {+ 1 8}{1 2} + \frac {+ 9}{1 2}\right) = \frac {+ 1}{2} \tag {17} $$ $$ I_{3}(\vec{d}_{u}) = \frac{1}{3} \left( \frac{-18}{12} + \frac{-0.2}{12} \right) = \frac{-1}{3} \left( \frac{3}{2} + \frac{0.1}{6} \right) = \frac{-1}{2} \left( 1 + \frac{0.1}{9} \right) = \frac{-1}{2} \left( 1 + \frac{1}{90} \right) = \frac{-1}{2} (1.011) \tag{18} $$ - Formula (18) shows in case [3] $\xi \neq 0$, isospin $I_{3}$ is not conserved in weak interaction, there is a deviation 0.011 from $I_{3}(d) = \frac{-1}{2}$ (0.2) There are nine independent real parameters $\xi_{rw}$ (19) in CKM matrix, in which the third components $I_3$ are broken (20) $$ \xi_{rw} = \left( \begin{array}{ccc} \xi_{\mathrm{ud}} & \xi_{\mathrm{us}} & \xi_{\mathrm{ub}} \\\xi_{\mathrm{cd}} & \xi_{\mathrm{cs}} & \xi_{\mathrm{cb}} \\\xi_{\mathrm{td}} & \xi_{\mathrm{ts}} & \xi_{\mathrm{tb}} \end{array} \right) = \left( \begin{array}{ccc} +0.200\updownarrow & -1.792 & -0.032 \\-1.0753 & +0.1248 & -0.2016 \\-0.03086 & -0.140571 & +0.003429 \end{array} \right) \tag{19} $$ $$ I _ {3} \left(\xi_ {r w}\right) _ {\mathrm {C K M}} = \left( \begin{array}{c c c c} I _ {3} (\vec {\mathrm {d}} _ {\mathrm {u}}) \updownarrow & I _ {3} (\vec {\mathrm {s}} _ {\mathrm {u}}) & I _ {3} (\vec {\mathrm {b}} _ {\mathrm {u}}) \\I _ {3} (\vec {\mathrm {d}} _ {\mathrm {c}}) & I _ {3} (\vec {\mathrm {s}} _ {\mathrm {c}}) & I _ {3} (\vec {\mathrm {b}} _ {\mathrm {c}}) \\I _ {3} (\vec {\mathrm {d}} _ {\mathrm {t}}) & I _ {3} (\vec {\mathrm {s}} _ {\mathrm {t}}) & I _ {3} (\vec {\mathrm {b}} _ {\mathrm {t}}) \end{array} \right) = \left( \begin{array}{c c c c} \frac {- 1}{2} \cdot (\mathbf {d}) & \frac {- 3}{2} \cdot (\mathbf {s}) & \frac {- 5}{2} \cdot (\mathbf {b}) \\\frac {- 1}{2} \cdot (1. 0 1 1) \updownarrow & \frac {- 3}{2} \cdot (0. 9 6 6 8) & \frac {- 5}{2} \cdot (0. 9 9 9 6) \\\frac {- 1}{2} \cdot (0. 9 4 0 3) & \frac {- 3}{2} \cdot (1. 0 0 2 3) & \frac {- 5}{2} \cdot (0. 9 9 7 8) \\\frac {- 1}{2} \cdot (0. 9 9 8 3) & \frac {- 3}{2} \cdot (0. 9 9 7 4) & \frac {- 5}{2} \cdot (1. 0 0 0 3 8) \end{array} \right) \tag {20} $$ - Mindful of the deviated values of the third isospin components above: for diagonal terms $I_{3}(\vec{\mathsf{d}}_{\mathsf{u}}), I_{3}(\vec{\mathsf{s}}_{\mathsf{c}}), I_{3}(\vec{\mathsf{b}}_{\mathsf{t}}) > 1$ and for off-diagonal terms $I_{3}(\xi_{rw}) < 1$ - Formula (16) be filled in (21). After the fullness of the eight other elements in CKM Matrix, ultimately we complete the processes of CKM Matrix colorization below $$ \text{Matrix} (3) \star \quad \mathrm{V} ^ {\mathrm{C K M}} \left(q _ {\mathrm{R G B}}, \Phi , \xi\right) = \left( \begin{array}{c c c c} & \Downarrow & \Downarrow & \Downarrow \\& \vec{u ^ {\prime}} \cdot \vec{\mathrm{d}} _ {\mathrm{u}} \updownarrow & \vec{u ^ {\prime}} \cdot \vec{\mathrm{s}} _ {\mathrm{u}} & \vec{u ^ {\prime}} \cdot \vec{\mathrm{b}} _ {\mathrm{u}} \\& \vec{c ^ {\prime}} \cdot \vec{\mathrm{d}} _ {\mathrm{c}} & \vec{c ^ {\prime}} \cdot \vec{\mathrm{s}} _ {\mathrm{c}} & \vec{c ^ {\prime}} \cdot \vec{\mathrm{b}} _ {\mathrm{c}} \\& \vec{t ^ {\prime}} \cdot \vec{\mathrm{d}} _ {\mathrm{t}} & \vec{t ^ {\prime}} \cdot \vec{\mathrm{s}} _ {\mathrm{t}} & \vec{t ^ {\prime}} \cdot \vec{\mathrm{b}} _ {\mathrm{t}} \end{array} \right) = \left( \begin{array}{c c c c} & \Downarrow & \Downarrow & \Downarrow \\& 0.9 7 5 \updownarrow & 0.2 2 4 & 0.0 0 4 \\& 0.2 2 4 & 0.9 7 4 & 0.0 4 2 \\& 0.0 0 9 & 0.0 4 1 & 0.9 9 9 \\& & & \end{array} \right) \tag{21} $$ ## IV. CONCLUSIONS In interaction【3】region, isospin $I_{3} = I_{3}(\xi_{rw})_{\mathsf{CKM}}$, is not conserved, which lead to charge-deviated of quarks $\mathcal{Q}_{\mathbf{dsb}}^{\mathsf{CKM}}(\xi_{rw})$ (Ref. (E)) $$ Q _ {\mathsf {d} _ {\mathsf {U}}} = I _ {3} (\mathsf {d} _ {\mathsf {U}}) + \frac {+ 1}{6} = \frac {- 1}{2} (1. 0 1 1) + \frac {+ 1}{6} = \frac {- 1}{3} (1. 0 1 1) e $$ $$ Q_{\mathrm{d}_{\mathrm{c}}} = I_{3}(\mathrm{d}_{\mathrm{c}}) + \frac{+1}{6} = \frac{-1}{2} (0.9403) + \frac{+1}{6} = \frac{-1}{3} (0.91045)e $$ $$ Q_{d_{t}} = I_{3}(d_{t}) + \frac{+1}{6} = \frac{-1}{2} (0.9983) + \frac{+1}{6} = \frac{-1}{3} (0.99745)e $$ $$ Q_{\mathbf{s}_{\mathsf{U}}} = I_{3}(\mathbf{s}_{\mathsf{U}}) + \frac{+7}{6} = \frac{-3}{2} (0.9668) + \frac{+7}{6} = \frac{-1}{3} (0.8506) e $$ $$ Q_{\mathfrak{S}_{\mathbb{C}}} = I_{3}(\mathfrak{S}_{\mathbb{C}}) + \frac{+7}{6} = \frac{-3}{2} (1.0023) + \frac{+7}{6} = \frac{-1}{3} (1.01035) e $$ $$ Q_{\mathbf{S}_{\mathrm{t}}} = I_{3}(\mathbf{S}_{\mathrm{t}}) + \frac{+7}{6} = \frac{-3}{2} (0.9974) + \frac{+7}{6} = \frac{-1}{3} (0.9883) e $$ $$ Q_{b u} = I_{3}(b u) + \frac{+13}{6} = \frac{-5}{2} (0.9996) + \frac{+13}{6} = \frac{-1}{3} (0.997) e $$ $$ Q _ {\mathsf {b c}} = I _ {3} (\mathsf {b c}) + \frac {+ 1 3}{6} = \frac {- 5}{2} (0. 9 9 7 8) + \frac {+ 1 3}{6} = \frac {- 1}{3} (0. 9 8 3 5) e $$ $$ Q_{b_t} = I_3(b_t) + \frac{+13}{6} = \frac{-5}{2}(1.00038) + \frac{+13}{6} = \frac{-1}{3}(1.00285)e $$ OR $$ Q _ {\mathrm{d s b}} ^ {\mathrm{C K M}} (\xi _ {r w}) = \left( \begin{array}{c c c c} & Q _ {\mathrm{d} _ {\mathrm{U}}} & Q _ {\mathrm{s} _ {\mathrm{U}}} & Q _ {\mathrm{b} _ {\mathrm{U}}} \\& Q _ {\mathrm{d} _ {\mathrm{C}}} & Q _ {\mathrm{s} _ {\mathrm{C}}} & Q _ {\mathrm{b} _ {\mathrm{C}}} \\& Q _ {\mathrm{d} _ {\mathrm{t}}} & Q _ {\mathrm{s} _ {\mathrm{t}}} & Q _ {\mathrm{b} _ {\mathrm{t}}} \end{array} \right) = \left( \begin{array}{c c c c} & \frac{- 1}{3} \cdot (1.0 1 1) e & \frac{- 1}{3} \cdot (0.8 5 0 6) e & \frac{- 1}{3} \cdot (0.9 9 7) e \\& \frac{- 1}{3} \cdot (0.9 1 0 4 5) e & \frac{- 1}{3} \cdot (1.0 1 0 3 5) e & \frac{- 1}{3} \cdot (0.9 8 3 5) e \\& \frac{- 1}{3} \cdot (0.9 9 7 4 5) e & \frac{- 1}{3} \cdot (0.9 8 8 3) e & \frac{- 1}{3} \cdot (1.0 0 2 8 5) e \end{array} \right) \tag{22} $$ - Mindful of the deviated values in (22): diagonal terms $Q_{\mathrm{du}}, Q_{\mathrm{sc}}, Q_{\mathrm{bt}} > 1$; off-diagonal terms $Q_{\mathrm{dc}}, Q_{\mathrm{dt}}, Q_{\mathrm{su}}, Q_{\mathrm{st}}, Q_{\mathrm{bu}}, Q_{\mathrm{bc}} < 1$ (22). In weak interaction, charges $Q_{\mathrm{dsb}}^{\mathrm{CKM}}(\xi_{rw})$ of down-type quark will be a slight deviated from $\frac{-1}{3} e$ (SM theoretical value), due to isospin broken $I_3(\xi_{rw})_{\mathrm{CKM}}$ of CKM Matrix colorized. ## EPILOGUE - The charge $Q_{q}$ of all known six quarks can be expressed by the sum (E) of isospin $I_{3}$ (0.0) and quark color $q_{\mathrm{RGB}}$ (00.1) below $$ Q_{q} = I_{3}(q) + q_{\mathrm{RGB}} $$ $$ q _ {\mathrm {R G B}} = \left(\frac {1}{6} + n\right), \quad n = 0, \pm 1, \pm 2. \dots \tag {E1} $$ For up-type quark, $n = 0, -1, -2$. (E2) $$ Q _ {t} = I _ {3} (t) + \frac {- 1 1}{6} = \frac {+ 5}{2} + \frac {- 1 1}{6} = \frac {+ 1 5}{6} + \frac {- 1 1}{6} = \frac {+ 4}{6} = \frac {+ 2}{3} e \tag {E.5} $$ $$ Q _ {C} = I _ {3} (c) + \frac{- 5}{6} = \frac{+ 3}{2} + \frac{- 5}{6} = \frac{+ 9}{6} + \frac{- 5}{6} = \frac{+ 4}{6} = \frac{+ 2}{3} e \tag{E.3} $$ $$ Q _ {U} = I _ {3} (u) + \frac{+ 1}{6} = \frac{+ 1}{2} + \frac{+ 1}{6} = \frac{+ 3}{6} + \frac{+ 1}{6} = \frac{+ 4}{6} = \frac{+ 2}{3} e \tag{E.1} $$ For down-type quark, $n = 0, +1, +2$. (E3) $$ Q _ {\mathrm {d}} = I _ {3} (d) + \frac {+ 1}{6} = \frac {- 1}{2} + \frac {+ 1}{6} = \frac {- 3}{6} + \frac {+ 1}{6} = \frac {- 2}{6} = \frac {- 1}{3} e \tag {E.2} $$ $$ Q _ {\mathbf{s}} = I _ {3} (s) + \frac{+ 7}{6} = \frac{- 3}{2} + \frac{+ 7}{6} = \frac{- 9}{6} + \frac{+ 7}{6} = \frac{- 2}{6} = \frac{- 1}{3} e $$ $$ Q _ {b} = I _ {3} (b) + \frac {+ 1 3}{6} = \frac {- 5}{2} + \frac {+ 1 3}{6} = \frac {- 1 5}{6} + \frac {+ 1 3}{6} = \frac {- 2}{6} = \frac {- 1}{3} e \tag {E.6} $$ Compairing (E) with Gell-Mann-Nishijiama relation (E4) [13],[14], then obtain (E5) below $$ Q = I _ {3} + Y / 2 \tag {E4} $$ $$ Y = 2 q_{\mathrm{RGB}} $$ Where, hypercharge $Y = B + S$. $B$ baryon number and $S$ strange number of quark $q$. We see Gell-Mann-Nishijiama relation (E4) is a special situation of (E), The latter (E), math-mysterious, is the extension of the former (E4), empirical. - The algebra symmetry of $q_{\mathsf{RGB}}$ of color representation of flavor Table 1 [3] could permute many possible arrangements. Further a series of magic figures, those are multiples of $1/3$, are constructed, that may illuminate the hypothesis about possible existence of higher-charges of quark $q$. Two examples of quark charge formula (E) with $q_{\mathrm{RGB}} = \frac{+1}{6}$, and with the fourth general quark are given below For $I_{3} = \frac{+1}{2}, \frac{-1}{2}$ $$ I _ {3} + \frac {+ 1}{6} = \frac {+ 1}{2} + \frac {+ 1}{6} = \frac {+ 3}{6} + \frac {+ 1}{6} = \frac {+ 4}{6} = \frac {+ 2}{3} e $$ $$ I_{3} + \frac{+1}{6} = \frac{-1}{2} + \frac{+1}{6} = \frac{-3}{6} + \frac{+1}{6} = \frac{-2}{6} = \frac{-1}{3} e $$ For $I_{3} = \frac{+3}{2}, \frac{-3}{2}$ $$ I _ {3} + \frac {+ 1}{6} = \frac {+ 3}{2} + \frac {+ 1}{6} = \frac {+ 9}{6} + \frac {+ 1}{6} = \frac {+ 1 0}{6} = \frac {+ 5}{3} e $$ $$ I _ {3} + \frac {+ 1}{6} = \frac {- 3}{2} + \frac {+ 1}{6} = \frac {- 9}{6} + \frac {+ 1}{6} = \frac {- 8}{6} = \frac {- 4}{3} e $$ For $I_{3} = \frac{+5}{2},\frac{-5}{2}$ $$ I _ {3} + \frac {+ 1}{6} = \frac {+ 5}{2} + \frac {+ 1}{6} = \frac {+ 1 5}{6} + \frac {+ 1}{6} = \frac {+ 1 6}{6} = \frac {+ 8}{3} e $$ $$ I _ {3} + \frac {+ 1}{6} = \frac {- 5}{2} + \frac {+ 1}{6} = \frac {- 1 5}{6} + \frac {+ 1}{6} = \frac {- 1 4}{6} = \frac {- 7}{3} e $$ For $I_{3} = \frac{+7}{2},\frac{-7}{2}$ $$ I _ {3} + \frac {+ 1}{6} = \frac {+ 7}{2} + \frac {+ 1}{6} = \frac {+ 2 1}{6} + \frac {+ 1}{6} = \frac {+ 2 2}{6} = \frac {+ 1 1}{3} e $$ $$ I _ {3} + \frac {+ 1}{6} = \frac {- 7}{2} + \frac {+ 1}{6} = \frac {- 2 1}{6} + \frac {+ 1}{6} = \frac {- 2 0}{6} = \frac {- 1 0}{3} e $$ Charges of the fourth general quark $I_{3} = \frac{+7}{2}, \frac{-7}{2}$ <table><tr><td>I3</td><td>||</td><td>+7/2</td><td>-7/2</td><td>+7/2</td><td>-7/2</td><td>+7/2</td><td>-7/2</td><td>+7/2</td><td>-7/2</td><td>+7/2</td><td>-7/2</td><td>+7/2</td><td>-7/2</td></tr><tr><td>qRGB</td><td>||</td><td>+19/6</td><td>+19/6</td><td>+13/6</td><td>+13/6</td><td>+7/6</td><td>+7/6</td><td>+1/6</td><td>+1/6</td><td>-5/6</td><td>-5/6</td><td>-11/6</td><td>-11/6</td></tr><tr><td>Q</td><td>||</td><td>+20/3</td><td>-1/3</td><td>+17/3</td><td>-4/3</td><td>+14/3</td><td>-7/3</td><td>+11/3</td><td>-10/3</td><td>+8/3</td><td>-13/3</td><td>+5/3</td><td>-16/3</td></tr></table>

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