0. INTRODUCTION

• In particle physics, six leptons and six antileptons are labelled by a group of unified three symbols ${\mathsf{L}}_e$, ${\mathsf{L}}_{\mu }$, ${\mathsf{L}}_{\tau }$ (00.1), which are their identity quantum numbers in particle community.

The values of ${\mathsf{L}}_e,{\mathsf{L}}_{\mu },$ and ${\mathsf{L}}_{\tau }$ are illustrated in Table1 below, in which there are all together 36 positions filled with integers $+1,-1$ and zero.

Experimental scientists discover: ${\mathsf{L}}_e,{\mathsf{L}}_{\mu }$, and ${\mathsf{L}}_{\tau }$ are conserved separately in weak interactions for leptons and their antileptons. especially the sum $\mathsf{L}={\mathsf{L}}_e+{\mathsf{L}}_{\mu }+{\mathsf{L}}_{\tau }$ are conserved too, which are along with the horizontal direction in Table1 [1]

Theoretical scientists wonder: Is there an unified math approach which could explain Where The values, integers $+1$, $-1$ and zero, of ${\mathsf{L}}_e,{\mathsf{L}}_{\mu },{\mathsf{L}}_{\tau }$ of leptons and of antileptons, that appear in Table1, come from?

• The experimental searchers for neutrino oscillations, they obtain Pontecorvo-Maki-Nakagawa-Sakata Matrix, PMNS $(V_L^e{)}^{†}{V}_L^v$ [2], which is the extremely perfect achievement from their spirits of awe and adventure. long time persistent effor in analysing the data collected from weak interaction. There are many profound digits appear in the nine elements of PMNS that given in Matrix(1) and Matrix(2) below.

Theoretical searchers wonder: the origin of these mysterious digits, that occupy the elements of these matrices, where the odd digit arrangements come from?

Matrix(1)

" The UPMNS looks very different from that of CKM, which is very diagonal. The leptonic sector is characterized by a very lare degree of mixing. As of today, the origin of this pattern remains an unsolved and profound puzzle!". André Rubbia [3] And

Matrix(2) As of today, assuming the unitary of the matrix and three active neutrinos, the absolute values of the elements of the matrix are estimated from a global fit of all measurements, which gives (Esteban et al., 2020) " PASCAL PAGANINI [4]

And

Matrix(3)

Matrix(0)

The magnitudes of the element digits of PMNS in Matrix(1) and Matrix(2) could be graphical approached by the circle areas in Matrix(3) qualitatively above [5]. Andzel J. Buras:

" The explanation of these patterns and in particular why they differ from each other remains an important goal of the theorists. " and " Why the mixing angles of CKM matrix so small and those of PMNS matrix rather large? "

1. COLOR OF FLAVOR OF LEPTONS

This paper attempts to explore and answer the above two "come from? " questions. So two concepts of • Color Similarity and • lepton color are introduced following

Current particle physics shows an amazing Flavor Similarity between three generations of quark and those of leptons below

Since six quarks and six antiquarks have been unified by means of " fundamental color representation of six flavor $t,c,u,d,s,b$ of quarks and their six antiquarks [6,7,8,9,10], And in this idea, why not continues to have a try to do the six flavor ${\upsilon }_{\tau },{\upsilon }_{\mu },{\upsilon }_e,e^{-},{\mu }^{-},{\tau }^{-}$ of leptons and the six antileptons? That is, besides Flovor Similarity (0.00), there may be

Base on (0.00), This paper postulates an ansatz, If the six fermion leptons & their antileptons (0.00) also are attributed to color degree of freedom as six fermion quarks & their antiquarks were done in Stand Model historically, and then the third component $I_3(l)$ isospin of a lepton $l$ could be written by • lepton color $l_{\text{RGB}}$, $(l_{\text{R}},l_{\text{G}},l_{\text{B}})$ as below

Or details

Further we, very naturally, could obtain a universal color representation of leptons and antileptons below, which is the analogous to that of quarks [7]. And isospin $I_3(l_{\mathrm{RGB}})$ (0.0) is an underlying classifications of three generation of leptons.

• Remark: we see the color values $l_{\mathrm{R}},l_{\mathrm{G}},l_{\mathrm{B}}$ of each lepton in Table2 are selected from the third components ${\pi }_3(l)$ of one-half spin $\overrightarrow{\pi }(l)$ below

Comparability between color freedom of quarks [1] and that of leptons above:

Quark are closed-color, color confinement, quark color $q_{\alpha }=q_{\mathrm{RGB}}\subseteq$ one-sixth series [7]

Lepton are opened-color, color freer, lepton color $l_{\alpha }=l_{\mathrm{RGB}}\subseteq$ one-half series (0.7).

Both quark ${\pi }_3(q)$ and lepton ${\pi }_3(l)$ are the third components of Non-Hermitian spin angular momentum $\overrightarrow{\pi }$ in Spin Topological Space STS.[11]. ${\pi }_3(q)$ and ${\pi }_3(l)$ are Hermitian operators in STS.

This paper are particular about neutrino lepton numbers, further Table1 is down to Table3 below

2. COLOR SCALAR PRODUCTS $\mathsf{L}({\upsilon }^{†}{\upsilon }^{\prime })$ OF NEUTRINO LEPTON NUMBER

Inspire with the idea of quarkcolor scalar product [10] and base on ansatz, Color Similarity mentioned previously, further an amusing leptoncolor scalar product is introduced to essential of lepton numbers ${\mathsf{L}}_e,{\mathsf{L}}_{\mu },{\mathsf{L}}_{\tau }$ of six leptons and six antileptons in Table1. This paper lays emphases on neutral leptons, neutrinos, then the leptoncolor scalar product representations of Table 3 are given on details following (0)

Matrix(4)

Matrix(5)

Matrix(5) is the digit graph of lepton number conservation (Table1).

From now on, we discuss the case of the left handed neutrino family $\upsilon ={\upsilon }_L$

Example $V_{11}$ of ${\overrightarrow{v_e}}^{†}\cdot {\overrightarrow{v_e}}^{\prime }=+1.000\downarrow$ in expression (0) with Table3 below (left handed neutrino ${\nu }_L$ ) is given explicitly following