Establishment theoretical framework as the standard theory of electroweak interactions: Higgs searches, quark mixing, neutrino oscillations.
{% include list.liquid all=true %}
Gauge invariance is a powerful tool to determine the dynamical forces. Particle content, structure and symmetries of Lagrangian are discussed.
***The Higgs and the electromagnetic field have no effect on each other***, at the level of the fundamental forces ("tree level"), while any other combination of the hypercharge and the weak isospin must interact with the Higgs. ***This causes an apparent separation between the weak force, which interacts with the Higgs, and electromagnetism, which does not***. _([Wikipedia](https://en.wikipedia.org/wiki/Electroweak_interaction#Formulation))_
Experiments have verified that the weak and electromagnetic force become identical at very small distances and provide the GUT description of the carrier particles for the forces.
Fermion | spinors | charged | neutrinos | quark | components | parameter
Field | (s) | (c) | (n) | (q=s.c.n) | Σ(c+n+q | (complex)
===========+=========+=========+===========+===========+============+===========
boson-1 | .. | .. | .. | .. | 5 | i5
-----------+---------+---------+-----------+-----------+------------+-----------
boson-2 | .. | .. | .. | .. | 7 | i7
-----------+---------+---------+-----------+-----------+------------+-----------
boson-3 | .. | .. | .. | .. | 11 | i11
-----------+---------+---------+-----------+-----------+------------+-----------
boson-4 | .. | .. | .. | .. | 13 | i13
-----------+---------+---------+-----------+-----------+------------+-----------
boson-5 | .. | .. | .. | .. | 17 | i17
===========+=========+=========+===========+===========+============+===========
SubTotal | .. | .. | .. | .. | 53 | i53
===========+=========+=========+===========+===========+============+===========
bispinor-1 | 2 | 3 | 3 | 18 | 24 | 19
-----------+---------+---------+-----------+-----------+------------+-- 17
bispinor-2 | 2 | 3 | 3 | 18 | 24 | i12
===========+=========+=========+===========+===========+============+===========
bispinor-3 | 2 | 3 | 3 | 18 | 24 | 11
-----------+---------+---------+-----------+-----------+------------+-- 19
bispinor-4 | 2 | 3 | 3 | 18 | 24 | i18
===========+=========+=========+===========+===========+============+===========
SubTotal | 8 | 12 | 12 | 72 | 96 | 66+i30
===========+=========+=========+===========+===========+============+===========
majorana-1 | 2x2 | - | 18 | - | 18 | 18
-----------+---------+---------+-----------+-----------+------------+-----------
majorana-2 | 2x2 | - | 12 | - | 12 | 12
-----------+---------+---------+-----------+-----------+------------+-----------
majorana-3 | 2x2 | - | 13 | - | 13 | i13
===========+=========+=========+===========+===========+============+===========
SubTotal | 12 | - | 43 | - | 43 | 30+i13
===========+=========+=========+===========+===========+============+===========
Total | 20 | 12 | 55 | 72 | 192 | 96+i96 ✔️The pattern of [weak isospin](https://en.wikipedia.org/wiki/Weak_isospin), T3, and [weak hypercharge](https://en.wikipedia.org/wiki/Weak_hypercharge), YW, of the known elementary particles, showing electric charge along the [weak mixing angle](https://en.wikipedia.org/wiki/Weinberg_angle). The four components of the Higgs field (squares) break the electroweak symmetry and interact with other particles to give them mass, with three components becoming part of the massive W and Z bosons. Allowed decays of the neutral Higgs boson, H, (circled) satisfy electroweak charge conservation. _([Wikipedia](https://en.wikipedia.org/wiki/Electroweak_interaction))_
The Lagrangian for the electroweak interactions is divided into four parts before electroweak symmetry breaking becomes manifest,
$True Prime Pairs:
(5,7$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-----+ ---
17¨ | {5¨}| {3¨}| 2¨ | 7¨ | 4¤ -----> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| 6¨ | 6¨ | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | 3¨ | {3¨}| {5¨}| 3¤ ---> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | 4¨ | 4¨ | ❓ | ❓ | 4¤ ✔️ ---> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ Unlike the strong and electromagnetic forces, the intermediary particles of the weak interaction, the W+, the W-, and the Z0 have rather large masses.
A key aspect of the theory is the explanation of why three out of four of the intermediary particles of the electroweak force are massive. Illustration of two weak reactions.
- The left panel shows beta decay while the middle panel shows how electron antineutrinos can be detected by conversion to a positron.
- The right panel shows how W- emission works according to the quark model, ***resulting in the conversion of a down quark to an up quark and the resulting transformation of a neutron into a proton***.
The real reason for the apparent weakness of the weak force is the large mass of the intermediary particles. As we have seen, large mass translates into short range for a virtual particle at low momentum transfers. This short range is what causes the weak force to appear weak for momentum transfers much less than the masses of the W and Z particles. _([libre texts.org](https://phys.libretexts.org/Bookshelves/University_Physics/Radically_Modern_Introductory_Physics_Text_II_(Raymond)/20%3A_The_Standard_Model/20.03%3A_The_Electroweak_Theory))_
$True Prime Pairs:
(5,7$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-----+ ---
17¨ | {5¨}| {3¨}| 2¨ | 7¨ | 4¤ -----> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| 6¨ | 6¨ | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | 3¨ | {3¨}| {5¨}| 3¤ ---> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+----+-----+ |
19¨ | 4¨ | 4¨ | 5¨ | 6¨ | 4¤ ✔️ ---> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ Consider the following contradiction in the electroweak theory of the Standard Model.
The electroweak theory of neutrino interaction uses factors like in order to account for a complete parity violation. This factor implies a massless neutrino [1]: “Nature had the choice of an aesthetically satisfying, but a left-right, symmetry violating theory, with a neutrino which travels exactly with the same velocity of light; or alternatively a theory where left-right symmetry is preserved, but the neutrino has a tiny mass – some ten thousand times smaller than the mass of the electron.”
The neutrino masslessness is also stated by other authors. A review article on neutrino properties states that “two-components left-handed massless neutrino fields play a crucial role in the determination of the charged current structure of the Standard Model” (see the Abstract of [2]). Similarly, a Quantum Field Theory textbook states: “Thus, massless neutrinos are a prediction of the Standard Model” (see [4], p. 555). Indeed, a massless neutrino is the basis for the two-component Weyl neutrino, which shows parity violation (see e.g. section 2.2 of [2]). The same argument appears on p. 139 of [3].
On the other hand, a recent review article negates the foregoing ides and states that it is now admitted “that neutrinos can no longer be considered as massless particles” (see [5], p. 1307). This statement is adopted by the Particle Data Group [6], which is the authorized organization for the definition of reliable particle data. The recognition of this fact by the community was demonstrated by the 2015 Nobel Prize, awarded to the persons who have discovered this property [7].
It follows that the experimentally confirmed massive neutrino undermines the basis of the Standard Model electroweak theory, since the massless neutrino is a crucial element in this theory.
Research topic: Can the validity of the electroweak theory be restored?
Remark: Further contradictions are discussed in [8]. _([Research Topics](https://oprassn.org/a-problem-in-the-electroweak-theory/))_
The True Prime Pairs
(5,7), (11,13), (17,19)
Tabulate Prime by Power of 10
loop(10) = π(10)-π(1) = 4-0 = 4
loop(100) = π(100)-π(10)-1th = 25-4-2 = 19
loop(1000) = π(1000) - π(100) - 10th = 168-25-29 = 114
--------------------------+----+----+----+----+----+----+----+----+----+-----
True Prime Pairs → Δ→π | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Sum
==========================+====+====+====+====+====+====+====+====+====+=====
19 → π(∆10) → π(10) | 2 | 3 | 5 | 7 | - | - | - | - | - | 4th 4 x Root
--------------------------+----+----+----+----+----+----+----+----+----+-----
17 → π(10+∆9) → π(19) | 11 | 13 | 17 | 19 | - | - | - | - | - | 8th 4 x Twin
==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
13 → π(19+∆10) → π(29) | 23 | 29 | - | - | - | - | - | - | - |10th
--------------------------+----+----+----+----+----+----+----+----+----+-----
11 → π(29+∆12) → π(41) | 31 | 37 | 41 | - | - | - | - | - | - |13th
==========================+====+====+====+====+====+====+====+====+====+===== 1st Twin
7 → π(41+∆18) → π(59) | 43 | 47 | 53 | 59 | - | - | - | - | - |17th
--------------------------+----+----+----+----+----+----+----+----+----+----- 3rd Twin
5 → π(59+∆13) → π(72) | 61 | 67 | 71 | - | - | - | - | - | - |20th
==========================+====+====+====+====+====+====+====+====+====+===== 4th Twin
3,2 → 18+13+12 → 43 | 73 | 79 | 83 | 89 | 97 | 101| 103| 107| 109|29th
==========================+====+====+====+====+====+====+====+====+====+=====
Δ Δ
12+13+(18+18)+13+12 ← 36th-Δ1=151-1=150=100+2x(13+12) ← 30th = 113 = 114-How do you resolve Maxwell equations as euler-lagrange equation without electromagnetic electromagnetism, lagrangian formalism, field theory, Maxwell equations, variational principle potential.
Axial (e-e rES repulsions blue aggregating to black axial outward, vs weak axial inward) to generate the Bose “cylinder surface” proof of statistical mechanics.
- Axial View of one hemisphere set of one subshell (N,1,many,-1/2) quantum number example below:
- That gives the path from Planck strength to the Maxwell strengths. Those are not independent, but all based upon h (or h-hat*c version in this case).
- Yes, I used Euler to get there! The weakness of the Lagrangian is that introduces errors in (a0/re)N scaling ^2 vs ^3 (extra 1/r wrongly called angular momentum by Bohr) that introduces an error correction. Hence, circling back to QED methods of error-correction (loops, re-normalization).
So, in the end, you do need. But the path can get similar when you move off arbitration x,y,z or X1,X2,X3 frame-of-reference to the quantitized hemispherical coordinates of the quantum numbers understood as (r#,theta#,phi#,z#).
1729 = 7 x 13 x 19
1729 / 7 = 13 x 19 = 247
1729 = 7 x 13 x 19
7 + 13 = 20 = d(2)
└── 2 x 19 = 38
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| {1}| 2 | 3 | 4 | 5 | {6}| {7}| 8 | 9 | 10 | 11 | 12 | 13 | 14 |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| {3}| {4}| 3 | 4 | 5 | 2 | 3 | 2 | 2 | 1 | 2 | 5 | 1 | 1 |{38}
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+---- } 285
| 3 | 8 | 9 | 16 | 25 |{12}|{21}| 16 | 18 | 10 | 22 | 60 |{13}|{14}|{247}
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
|-- 38 ---| |-- 33 ---| |-- {27}--|$True Prime Pairs:
(5,7$True Prime Pairs:
(5,7$True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 |
-----+-----+-----+-----+-----+ ---
19¨ | 3¨ | 4¨ | 6¨ | 6¨ | 4¤ -----> assigned to "id:30" 19¨
-----+-----+-----+-----+-----+ ---
17¨ | {5¨}| {3¨}| 2¨ | 7¨ | 4¤ -----> assigned to "id:31" |
+-----+-----+-----+-----+ |
{12¨}| 6¨ | 6¨ | 2¤ (M & F) -----> assigned to "id:32" |
+-----+-----+-----+ |
11¨ | 3¨ | {3¨}| {5¨}| 3¤ ---> Np(33) assigned to "id:33" -----> 👉 77¨
-----+-----+-----+-----+-----+ |
19¨ | 4¨ | 4¨ | 5¨ | 6¨ | 4¤ ✔️ ---> assigned to "id:34" |
+-----+-----+-----+-----+ |
{18¨}| .. | .. | .. | 3¤ -----> assigned to "id:35" |
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
43¨ | .. | .. | .. | .. | .. | .. | .. | .. | .. | 9¤ (C1 & C2) 43¨
-----+-----+-----+-----+-----+-----+-----+-----+-----+-----+ ---
139¨ | 1 2 3 | 4 5 6 | 7 8 9 |
Δ Δ Δ 
True Prime Pairs:
(5,7), (11,13), (17,19)
| 168 | 618 | ✔️
-----+-----+-----+-----+-----+ -----------------------------------------------
{786}| 1,2 | 2 | 2,3 | 3,4 | {19} |
-----+-----+-----+-----+-----+ |
{86}| 4 | 4,5 | 5,6 |{6,7}| 17 Base Zone
+-----+-----+-----+-----+ |
{78}|{7,8}| 8,9 | 12 (M dan F) ----> Δ |
+-----+-----+-----+ -----------
{67}| 9,11|11,12|12,14| 11 <----------- Mid Zone |
----+-----+-----+-----+-----+ |
{6}|15,16|17,18|18,20|21,22| 19 Mirror Zone
+-----+-----+-----+-----+ |
{8}|23,25|25,27|27,29| 18 |
+-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------
{7}|29,33|33,36|36,39|39,41|41,45|46,51|51,57|58,66|{67,77}| 43 (C1 dan C2)<---Δ
-----+-----+-----+-----+-----+-----+-----+-----+-----+-------+ -----------
| 1 2 3 | 4 5 6 | 7 8 9 |
|------ 29' ------|--------------- 139' ----------------|
|------ 618¨ -----|--------------- 168¨ ----------------|Scheme 13:9
===========
(1){1}-7: 7'
(1){8}-13: 6‘
(1)14-{19}: 6‘
------------- 6+6 -------
(2)20-24: 5' |
(2)25-{29}: 5' |
------------ 5+5 -------
(3)30-36: 7:{70,30,10²}|
------------ |
(4)37-48: 12• --- |
(5)49-59: 11° | |
--}30° 30• |
(6)60-78: 19° | |
(7)79-96: 18• --- |
-------------- |
(8)97-109: 13 |
(9)110-139:{30}=5x6 <--x-
--
{43}The True Prime Pairs:
(5,7), (11,13), (17,19)
|-------------------------------- 2x96 -------------------------------|
|--------------- 7¤ ---------------|------------ 7¤ ------------------|
|-------------- {89} --------------|{12}|-- {30} -|-- {36} -|-- {25} -|
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
| 5 | 7 | 11 |{13}| 17 | 19 | 17 |{12}| 11 | 19 | 18 | 18 | 12 | 13 |
+----+----+----+----+----+----+----+----+----+----+----+----+----+----+
|--------- {53} ---------|---- {48} ----|---- {48} ----|---- {43} ----|
|---------- 5¤ ----------|------------ {96} -----------|----- 3¤ -----|
|-------- Bosons --------|---------- Fermions ---------|-- Gravitons--|
13 variations 48 variations 11 variations 
The Prime Recycling ζ(s):
(2,3), (29,89), (36,68), (72,42), (100,50), (2,3), (29,89), ...**infinity**
----------------------+-----+-----+-----+ ---
7 --------- 1,2:1| 1 | 30 | 40 | 71 (2,3) ‹-------------@---- |
| +-----+-----+-----+-----+ | |
| 8 ‹------ 3:2| 1 | 30 | 40 | 90 | 161 (7) ‹--- | 5¨ encapsulation
| | +-----+-----+-----+-----+ | | |
| | 6 ‹-- 4,6:3| 1 | 30 | 200 | 231 (10,11,12) ‹--|--- | |
| | | +-----+-----+-----+-----+ | | | ---
--|--|-----» 7:4| 1 | 30 | 40 | 200 | 271 (13) --› | {5®} | |
| | +-----+-----+-----+-----+ | | |
--|---› 8,9:5| 1 | 30 | 200 | 231 (14,15) ---------› | 7¨ abstraction
289 | +-----+-----+-----+-----+-----+ | |
| ----› 10:6| 20 | 5 | 10 | 70 | 90 | 195 (19) --› Φ | {6®} |
--------------------+-----+-----+-----+-----+-----+ | ---
67 --------› 11:7| 5 | 9 | 14 (20) --------› ¤ | |
| +-----+-----+-----+ | |
| 78 ‹----- 12:8| 9 | 60 | 40 | 109 (26) «------------ | 11¨ polymorphism
| | +-----+-----+-----+ | | |
| | 86‹--- 13:9| 9 | 60 | 69 (27) «-- 3xΔ9 (2xMEC30) | {2®} | |
| | | +-----+-----+-----+ | | ---
| | ---› 14:10| 9 | 60 | 40 | 109 (28) ------------- | |
| | +-----+-----+-----+ | |
| ---› 15,18:11| 1 | 30 | 40 | 71 (29,30,31,32) ---------- 13¨ inheritance
329 | +-----+-----+-----+ |
| ‹--------- 19:12| 10 | 60 | {70} (36) ‹--------------------- Φ |
-------------------+-----+-----+ ---
786 ‹------- 20:13| 90 | 90 (38) ‹-------------- ¤ |
| +-----+-----+ |
| 618 ‹- 21,22:14| 8 | 40 | 48 (40,41) ‹---------------------- 17¨ class
| | +-----+-----+-----+-----+-----+ | |
| | 594 ‹- 23:15| 8 | 40 | 70 | 60 | 100 | 278 (42) «-- |{6'®} |
| | | +-----+-----+-----+-----+-----+ | | ---
--|--|-»24,27:16| 8 | 40 | 48 (43,44,45,46) ------------|---- |
| | +-----+-----+ | |
--|---› 28:17| 100 | {100} (50) ------------------------» 19¨ object
168 | +-----+ |
| 102 -› 29:18| 50 | 50(68) ---------> ∆27-∆9=Δ18 |
----------------------+-----+ ---