29 March 2025 AD, Saturday

St. Gundleus (5^th Century AD)

 

Is it possible to obtain somehow the boson mixing angles from existing data such as the quark and neutrino mixing/oscillation angles? I claim that it is possible, provided we have at least one boson mixing angle, multiplication factor for that particular boson, and the angle from the main equation.

Yes, we have all of those:

• Weinberg angle ('running' of the weak mixing angle)

• Six multiplication factors of quarks and neutrinos

• Three boson angles from the main equation

Now, we need a simple formula to put all of this together.

In my opinion, the neutrinos and quarks are determining the values of some other properties of the bosons (and the gravitons for that matter), and bosons and gravitons will determine the properties of time and space, etc. So, the properties of the bosons will be obtained through the mixing angles of quarks and neutrinos and angles of the bosons, which are known from the main equation.

 

Let us start with multiplication factors of quarks and neutrinos.

 

Multiplication factors for neutrino are (PDG 2024):

Nθ₁₃ = (1 / (2*FIB^1/3)) = 0.425901198485

Nθ₂₃ = (2*FIB) / 11 = 0.294185143583

Nθ₁₂ = (9*FIB) / 10 = 1.45621646074

 

Where

 

FIB = (7/5)(π/e) = 1.61801828971

 

Multiplication factors for quark are (PDG2022):

Qθ₁₃ = (11/20π) = 0.175070437401

Qθ₂₃ = e/3π = 0.288418659811

Qθ₁₂ = (1/(C0* C5)) = 1.0 / (0.986976350384 * 2.035090375149) = 0.497862657894

 

Weinberg angle: ‘ In 2005 results were published from a study of parity violation in Møller scattering in which a value of sin² θ_w = 0.2397±0.0013 was obtained at ∆q = 0.16 GeV/c, establishing experimentally the so-called 'running' of the weak mixing angle. These values correspond to a Weinberg angle varying between 28.7° and 29.3° ≈ 30°’

 

Weinberg angle experimental result:

 

Best measurements:

 

Sin² θ_w = 0.2397±0.0013 radians

Θ_w = 0.511621393213 ±0.036063329356 radians = 29.3137465397⁰ ±2.06627656729⁰

And

Sin² θ_w = 0.23142 radians

Θ_w = 0.501864921629 radians = 28.754741895⁰

 

CODATA 2022 gives different value of Weinberg angle:

Sin² θ_w = 0.22305(23) radians

And

Θ_w = 0.491877565734 radians = 28.1825085537⁰

 

More here:

https://en.wikipedia.org/wiki/Weinberg_angle

 

Boson ‘raw’ angles from the main equation:

 

ALFA C_3 INVISIBLE  ( A + Bi) and ALFA C_3 VISIBLE  ( C + Di):

SUM   ( A + Bi ) + ( C + Di )

   -0.15002182541659514925D+02   -0.62211775082955496075D+01

 MAGNITUDE & THETA IN RADIANS

    0.16240952268971049932D+02   -0.27484913873336704881D+01

 MAGNITUDE & THETA IN DEGREES

    0.16240952268971049932D+02   -0.15747695652227574215D+03

 

This is boson theta13 ‘raw’ angle.

Bθ₁₃ raw = -157. 47695652227574215⁰

 

ALFA C_4 INVISIBLE  ( A + Bi) and ALFA C_4 VISIBLE  ( C + Di):

SUM   ( A + Bi ) + ( C + Di )

   -0.22870922013068116030D+03    0.66931037067238946747D+02

 MAGNITUDE & THETA IN RADIANS

    0.23830163888584669962D+03    0.28568954285731971154D+01

 MAGNITUDE & THETA IN DEGREES

    0.23830163888584669962D+03    0.16368805056746273863D+03

 

This is boson theta23 ‘raw’ angle.

Bθ₂₃ raw = 163.68805056746273863⁰

 

ALFA C_5 INVISIBLE  ( A + Bi) and ALFA C_5 VISIBLE  ( C + Di):

SUM   ( A + Bi ) + ( C + Di )

    0.10002511580723258667D+07    0.99330459428622107953D+06

 MAGNITUDE & THETA IN RADIANS

    0.14096653490297417156D+07    0.78191366808625295537D+00

 MAGNITUDE & THETA IN DEGREES

    0.14096653490297417156D+07    0.44800353124935384130D+02

 

This is boson theta12 ‘raw’ angle.

Bθ₁₂ raw = 44.800353124935384130⁰

 

How to obtain boson mixing angles?

1. We have to start with running weak mixing angle (about 29 degrees).

2. If the calculated value of a weak mixing angle matches, then remaining two mixing angles should be correct.

3. Since the quark and neutrino are ‘the foundation’ of all other particles, the boson multiplication factor should consist of neutrino and quark multiplication factors.

4. I will explain later why boson and graviton are one step higher above quark and neutrino, instead of time and space or internal and external membrane.

5. From many calculations, it can be concluded that each boson multiplication factor consists of two neutrino multiplication factors and one quark multiplication factor.

6. These values multiplied by a respective boson ‘raw’ angle (angle from the main equation) will give the boson weak mixing angles, starting with Weinberg angle or rather running weak mixing angle (which may be the same or not).

 

The formula for a weak mixing angle is the following:

(Boson ‘raw’ mixing angle) x (two neutrinos multiplication factors) x (quark multiplication factor). This is equal to the respective boson's weak mixing angle.

 

The candidates:

 

Boson theta13:

(Boson theta13 raw angle) x (neutrino theta12 multiplication factor) x (neutrino theta23 multiplication factor) x (quark theta13 multiplication factor) = boson theta 13 mixing angle.

 

i.e.,

 

(Bθ₁₃ raw = -157. 47695652227574215⁰) * (Nθ₁₂ = (9*FIB) / 10 = 1.45621646074) *

*(Nθ₂₃ = (2*FIB) / 11 = 0.294185143583) * (Qθ₁₃ = (11/20π) = 0.175070437401) =

= (Bθ₁₃ ‘raw’= -157. 47695652227574215⁰) * (0.0749996936921) = -11.8107235027⁰

 

The boson theta13 weak mixing angle is equal to:

Bθ₁₃ = -11.8107235027⁰

The result is not running weak mixing angle, but it is correct as you will see in a moment.

 

Boson theta12:

(Boson theta12 raw angle) x (neutrino theta13 multiplication factor) x (neutrino theta23 multiplication factor) x (quark theta12 multiplication factor) = boson theta 12 mixing angle.

 

i.e.,

 

(Bθ₁₂ raw = 44.800353124935384130⁰) * (Nθ₁₃ = (1 / (2*FIB^1/3)) = 0.425901198485) *

*(Nθ₂₃ = (2*FIB) / 11 = 0.294185143583) *

*(Qθ₁₂ = (1/(C0* C5)) = 1.0 / (0.986976350384 * 2.035090375149) = 0.497862657894) =

= (Bθ₁₂ raw = 44.800353124935384130⁰) * (0.0623791068888) = 2.79460601624⁰

 

Bθ₁₂  = 2.79460601624⁰

The result is not running weak mixing angle, but it is correct as you will see in a moment.

 

Boson theta23:

(Boson theta23 raw angle) x (neutrino theta13 multiplication factor) x (neutrino theta12 multiplication factor) x (quark theta23 multiplication factor) = boson theta 23 mixing angle.

 

i.e.,

 

(Bθ₂₃ raw = 163.68805056746273863⁰) * (Nθ₁₃ = (1 / (2*FIB^1/3)) = 0.425901198485) *

*(Nθ₁₂ = (9*FIB) / 10 = 1.45621646074) *

*(Qθ₂₃ = e/3π = 0.288418659811) =

= (Bθ₂₃ raw = 163.68805056746273863⁰) * (0.178878503364) = 29.2802735042⁰

 

Boson theta23 mixing angle (running weak mixing angle):

Bθ₂₃ = 29.2802735042⁰

 

And this is the running weak mixing angle versus 29.3137465397⁰ with ‘relative error’

ԑ = 0.114%

 

And finally, here are the results:

 

Multiplication factors for boson are:

 

Bθ₁₃ Mul Fact = 0.0749996936921

Bθ₂₃ Mul Fact = 0.178878503364

Bθ₁₂ Mul Fact = 0.0623791068888

 

And the weak mixing angles for bosons:

 

Bθ₁₃ = -11.8107235027⁰

Bθ₂₃ = 29.2802735042⁰

Bθ₁₂ = 2.79460601624⁰

 

Boson raw angles from the main equation:

 

Bθ₁₃  raw = -157.476956522⁰

Bθ₂₃  raw = 163.688050568⁰

Bθ₁₂  raw = 44.800353125⁰

 

 

Next article – graviton mixing angles and delta charge-parity vilolating phase angles for quark, neutrino and boson.

 

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