Can We Measure the Weak Nuclear Fine Structure Constant via Beta Decay?

[Orion1]

Penning trap upper limit for the electron particle radius:
r_e \leq 10^{-22} \; \text{m}

QED Compton wavelength electron radius:
\boxed{r_e = \alpha_e \overline{\lambda}_c}

QED Compton electron radius:
\boxed{r_e = \frac{\hbar \alpha_e}{m_e c}}

QED electron fine structure constant:
\alpha_e = \frac{r_e}{\overline{\lambda}}_c = \frac{m_e c r_e}{\hbar}

\boxed{\alpha_e = \frac{m_e c r_e}{\hbar}}

Weak nuclear fine structure constant:
\alpha_w = \sqrt{ \frac{T_{\Delta}}{T_{\Sigma}}} = 2.738 \cdot 10^{-7}
T - Delta and Sigma particle lifetimes

\boxed{\alpha_e = 2.589 \cdot 10^{-10}}
\boxed{\alpha_w = 2.738 \cdot 10^{-7}}

The QED electron fine structure constant magnitude corresponds with the weak nuclear fine structure constant.

How is \alpha_w measured via weak \beta decay?

Are these equations correct?
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Reference:
http://en.wikipedia.org/wiki/Electron#Fundamental_properties"
http://en.wikipedia.org/wiki/Weak_nuclear_force"
http://hyperphysics.phy-astr.gsu.edu/HBASE/forces/couple.html#c4"
http://hyperphysics.phy-astr.gsu.edu/HBASE/particles/weastr.html#c1"

 

[malawi_glenn]

what do you want?

 

[Vanadium 50]

Weak nuclear fine structure constant:
\alpha_w = \sqrt{ \frac{T_{\Delta}}{T_{\Sigma}}} = 2.738 \cdot 10^{-7}

No, it's not. It's \alpha/\sin^2\theta_w.

According to QED, the electron is defined by the Weak nuclear force.

No, it's not. That doesn't even make any sense, as QED doesn't know anything about the weak nuclear force.

 

[Orion1]

It's \alpha/\sin^2\theta_w.

Vanadium, that is an element, not an equation.

Is this the equation that you attempted to define?

Weak nuclear fine structure constant:
\alpha_w = \frac{\alpha}{\sin^2 \theta_w}
\theta_w - Weinberg angle (weak mixing angle)

Please state the numerical value for that solution and cite a reference.

Have you examined my references in post #1?

Why is the university level hyperphysics weak nuclear fine structure constant equation incorrect?
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Reference:
http://en.wikipedia.org/wiki/Weinberg_angle"

 

[malawi_glenn]

Vanadium, please state the numerical value for that solution and cite a reference.
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Look in mandl's textbook in Quantum Field theory for instance. Or any book that contains the gauge theory of the electroweak unification.

Also, what is the purpose of your original post? Are you asking something?

 

[Orion1]

Also, what is the purpose of your original post? Are you asking something?

Have you examined my references in post #1?

Are my equations listed in post #1 correct?

Anyone have mandl's textbook in Quantum Field Theory?
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[malawi_glenn]

Are my equations listed in post#1 correct?
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as Vanadium pointed out, no.

The QED fine structure constant is 1/137

why are you doing all this?

A good, easy, reference on this, I consider particle physics by Martin

And yes, Manls textbook on QFT is quite common to have... your Library should definitely have one copy. Otherwise, there should be millions of tutorials on www, try search for "Antonio Pich" on ArXiV

Your references in post 1 is wikipedia and hyperphysics, what should I say?... they are not rigour

 

[Orion1]

as Vanadium pointed out, no.

Vanadium only stated one equation as incorrect. You are now stating all the equations are incorrect? Including the university level hyperphysics equations?

The QED fine structure constant is 1/137

Negative, that value for \alpha is not 'rigorous'.

malawi_glenn, you are unable to state a numerical value for Mandl and Martin's \alpha_w.

rig·or·ous:
. precise
. severely accurate

malawi_glenn, based upon the 'incorrect' equations in post #1, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?

And why exactly do all these equations fail dimensional examination?
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[malawi_glenn]

why would anyone use "electron radius" since it is not a 'real' concept, just a unit?

ok, the fine structure constant is 1/137.03599907 which is a numerical value of 2.39934 e-4If you want to define a constant which has the units of length by introducing <br /> r_e = \alpha \lambda_r<br /> you are free to do it, it is just a unit, nothing 'physical'

The relation between 'the classical electron radius' and the electron comptonwavelngth is: r_e{\text{ }}_{class} = {\alpha \lambda_e \over 2\pi} = \alpha^2 a_0

where a_0 is the bohr radius.

The weak 'fine structure' constant is \alpha _W \approx 0.58\alpha (martin)

in QED, the electron is a point-particle, so don't call it "QED electron radius"..

 

[Orion1]

as Vanadium pointed out, no.

And why exactly do all these equations fail dimensional examination?

in QED, the electron is a point-particle.

The Penning trap experiment that determined the electron radius upper limit considers the electron as a QED point-particle.

malawi_glenn, then by your own supposition:
\alpha_w = \frac{\alpha}{\sin^2 \theta_w} = 0.58 \cdot \alpha = 4.232 \cdot 10^{-3}

A rigorously determined value: (Martin)
\alpha_w = 4.232 \cdot 10^{-3}

Is this equation correct?

malawi_glenn, based upon the 'incorrect' equations in post #1 and post #9, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?
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Reference:
http://en.wikipedia.org/wiki/Penning_trap"

 

[malawi_glenn]

because physics is more advanced then this...

e.g. the bohr radius is just a unit, it is not an orbital radius of the electron in hydrogen (as we know, the radial distance in hydrogen is a probabilistic quantity)

the number 1/137 is more rigour than your <br /> \boxed{\alpha_e = 2.589 \cdot 10^{-10}}<br /> ... rigour in that sense that it is close to the experimental measured value.

I mean, what is the physical (first principle reason) for someone to suggest that the electron radius is alpha time electron Compton wavelength? What is the underlying idea?

 

[Orion1]

I mean, what is the physical (first principle reason) for someone to suggest that the electron radius is alpha time electron Compton wavelength? What is the underlying idea?

malawi_glenn, based upon the 'incorrect' equations in post #1 and post #9, what is the numerical value for the electron radius if the QED fine structure constant for electromagnetism is used?

And why exactly do all these equations fail dimensional examination?
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[malawi_glenn]

you don't have a calculator or what?

and "what" electron radius? There are many kinds of electron radii units, you mean your suggestion <br /> \boxed{r_e = \alpha_e \overline{\lambda}_c}<br />? Which you call "QED compton wavelength radius"?

 

[Orion1]

Which you call "QED Compton wavelength electron radius"?

\boxed{r_e = \alpha_e \overline{\lambda}_c}

Affirmative.

malawi_glenn, you still have not stated why exactly do all these equations fail dimensional examination?

The QED fine structure constant is 1/137

Negative, that value for \alpha is numerology and not 'rigorous' at all.

the fine structure constant is . . . a numerical value of 2.39934 e-4. Rigour in that sense that it is close to the experimental measured value.

Negative, that numerical value is incorrect, and certainly not even close to rigorous.

malawi_glenn, what are the physical (first principle reasons) for these equations?

Classical electron radius:
r_e =\frac{\alpha \lambda_e}{2 \pi}

Rigorous classical electron radius:
r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2} = 2.8179402894(58) \cdot 10^{-15} \; \text{m}

Your references in post 1 is wikipedia and hyperphysics, what should I say?... they are not rigour

Negative, the numerical value for the classical electron radius from Wikipedia is excellent, they are both extremely rigorous.

1/137, 2.39934 e-4, you don't have a calculator or what?

Negative, I do not believe that I am the one that requires a calculator at the moment.

Reference:
http://en.wikipedia.org/wiki/Classical_electron_radius"
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[malawi_glenn]

Affirmative.
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roger copral

 

[Vanadium 50]

Negative, that value for \alpha is numerology and not 'rigorous' at all.

Negative, that numerical value is incorrect, and certainly not even close to rigorous.

What in blazes are you talking about?

 

[malawi_glenn]

What in blazes are you talking about?

Only God knows... he usally does this kind of approach =/

1/137 is not rigour, it is just "numerology" LOL

 

[Orion1]

What in blazes are you talking about?

the fine structure constant is . . . a numerical value of 2.39934 e-4

malawi_glenn's numerical value for the electromagnetic fine structure constant is incorrect.

malawi_glenn, you still have not stated a correct numerical value for the electromagnetic fine structure constant.

Vanadium_50, why is the university level hyperphysics weak nuclear fine structure constant equation incorrect?

Vanadium_50, and why exactly do all these equations fail dimensional examination?

Vanadium_50, is the equation and numerical values correct in post #10?
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Reference:
https://www.physicsforums.com/showpost.php?p=2123562&postcount=10"

 

[malawi_glenn]

orion, in post #9 I gave you a better (closer to experimental) value of alpha (1/137 is a VERY good number for alpha, orion you are a pain in our *** with your style..

the figure 2.39934 e-4 is of course wrong, i made that on purpose LOL, why can't you just take 1/137.03599907 in your own calculator??

This is an open forum, I can answer to anything I want to.

Why do you want to calculate all this crap anyway?

The value hyperphysics gives you for the weak finestructure is just an approximation, the hadrons are composite objects etc, you have to go to elementary particle level to examine the couplings of interactions. If you want the latest values, go to particle data group, not wikipedia or hyperphysics.

You are the one who proposed that a unit called "QED electron radius" should be invented, you have to motivate "why". I am not the guy who should say on what first principles it relies on.

The classical electron radius is something which you evaluate from classical electrodynamics, when you evaluate Thomson scattering etc. It should be done in great detail in e.g. Jackson.

I now invent a thing called "Glenn electron radius"

r_e^{\text{Glenn}} = \alpha_e^3 \frac{1}{4\pi\epsilon_0}\frac{e^2}{m_e c^2}

And what does it mean? I have no idea, it is just a unit.

You see my point why all your 'effort' is pointless?

 

[Orion1]

I now invent a thing called "Glenn electron radius"
r_e^{\text{Glenn}} = \alpha_e^3 \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2}

Negative, that equation is dimensionally incorrect.

hyperphysics gives you for the weak fine structure is just an approximation.

An accurately measured approximation is not a failure in dimensional examination.

malawi_glenn, instead of deliberately introducing known unbalanced and non-formulated dimensionally incorrect equations on this forum without any referencing at all, why not state exactly why do all these equations fail dimensional examination?

malawi_glenn, you have not stated what 'first principle' the classical electron radius is based upon.

Classical electron radius:
r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2}

\boxed{\frac{e^2}{4 \pi \epsilon_0} = \hbar c \alpha}

r_e = \frac{1}{4 \pi \epsilon_0} \frac{e^2}{m_e c^2} = \frac{\hbar \alpha}{m_e c} = \alpha \overline{\lambda}_c

Electromagnetic fine structure constant:
\boxed{\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}} = 7.2973525705 \cdot 10^{-3}

\boxed{\alpha = 7.2973525705 \cdot 10^{-3}}

QED Compton wavelength electron radius:
\boxed{r_e = \alpha \overline{\lambda}_c}
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Reference:
http://en.wikipedia.org/wiki/Fine-structure_constant"
http://en.wikipedia.org/wiki/Classical_electron_radius"

 

[malawi_glenn]

that is because I am using "Glenn units" on the electric charge so that r_e^{\text{Glenn}} get the unit of length.

I did not name it after myself... the name is from Glenn Strömberg, a great soccer player.

The reason for why just some dimensional analysis and puzzling is pointless is the amount of arbitrariness.

You consider the thing called "QED compton wavelength radius"
<br /> \boxed{r_e = \alpha \overline{\lambda}_c}<br />

Now WHAT do you want to achieve/describe with that? It is just a unit, with dimensions of length.

I can invent infinite number of those, by just multiplying a quantity without dimensions

Questions:

1) What do you want to achieve with this? What is the physical meaning of "QED Compton wavelength electron radius"? Why do you call it QED.. when it has nothing to do with QED at all? You "cooked" the unit you have by multiplying the electron compton wavelength with the fine structure constant, why?

2) Do you know where the units "electron compton wavelength" and "Classical electron radius" come from and aware of what they mean and have the names which they have?

The first principle physics behind the unit "classic electron radius" can, as I said, be found in references like Jackson or just google it. I don't have to give you a clash course in classic electrodynamics here.

 

[Doc Al]

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