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Orion1

Higgs boson mass...

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My calculation for the Higgs boson mass for the Standard Model.

 

The Higgs boson mass is equal to one-half the Higgs vacuum expectation value.

 

Higgs boson mass:

[math]m_H = \frac{v_h}{2} = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}} = 123.111 \; \frac{\text{Gev}}{\text{c}^2}[/math]

 

[math]\boxed{m_H = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}}[/math]

 

CERN Higgs boson mass:

[math]m_H = 125.3 \pm 0.6 \; \frac{\text{Gev}}{\text{c}^2}[/math]

 

Which implies that the Higgs boson achieves mass from the Higgs field vacuum via the Higgs mechanism.

Reference:

Physical constants - Wikipedia

Higgs boson - Wikipedia

Higgs mechanism - Wikipedia

Higgs vacuum expectation value - Wikipedia

Vector Boson Decay - ATLAS

Edited by Orion1

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Interesting. But I am not sure if I understand the implication correctly... Are you suggesting that the difference between your calculation and the measurement is caused by the Higgs field itself? Then, can you calculate this difference the other way around (I mean starting from the expectation)?

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My calculation for the Higgs boson mass for the Standard Model.

 

The Higgs boson mass is equal to one-half the Higgs vacuum expectation value.

 

Higgs boson mass:

[math]m_H = \frac{v_h}{2} = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}} = 123.111 \; \frac{\text{Gev}}{\text{c}^2}[/math]

 

[math]\boxed{m_H = \frac{1}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}}[/math]

 

CERN Higgs boson mass:

[math]m_H = 125.3 \pm 0.6 \; \frac{\text{Gev}}{\text{c}^2}[/math]

 

Which implies that the Higgs boson achieves mass from the Higgs field vacuum via the Higgs mechanism.

Reference:

Physical constants - Wikipedia

Higgs boson - Wikipedia

Higgs mechanism - Wikipedia

Higgs vacuum expectation value - Wikipedia

Vector Boson Decay - ATLAS

[latex]m_{H}=(parameter)\upsilon _{h}[/latex]

 

Why the parameter value is 1/2?

Do you have any reason? Empirical coefficient from the yesterday announcement?

Edited by alpha2cen

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Are you suggesting that the difference between your calculation and the measurement is caused by the Higgs field itself?[/Quote]

No' date=' [/color']the Higgs boson achieves mass from the Higgs field vacuum via the Higgs mechanism. The difference between my calculation and the measurement is due to the mathematical limitations in the model presented. Mathematical models constructed by scientists do not always agree absolutely exactly with experimental observations, there are often variances.

Can you calculate this difference the other way around (I mean starting from the expectation)?[/Quote]

The most accurate expectation value I have read to date' date=' places the Higgs boson mass at around 115 Gev.

Why the parameter value is 1/2? Do you have any reason? Empirical coefficient from the yesterday announcement?[/Quote]

The parameter value of 1/2 is an empirical coefficient due to integration and the quantum properties of the Higgs boson, a spin-0 particle for example.

Reference:

Has the Higgs boson been discovered? - Nature

Edited by Orion1

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Orion1 Higgs boson mass:

[math]m_H = 123.111 \; \frac{\text{Gev}}{\text{c}^2}[/math]

 

CERN Higgs boson mass:

[math]m_H = 125.3 \pm 0.6 \; \frac{\text{Gev}}{\text{c}^2} \; \; \; \; \; \; 4.9 \; \sigma[/math]

 

ATLAS Higgs boson mass:

[math]m_H = 126.5 \; \frac{\text{Gev}}{\text{c}^2} \; \; \; \; \; \; 5 \; \sigma[/math]

 

According to reference 3, pg. 4, the Higgs vacuum expectation value for the Standard Model is defined as:

[math]v_h = \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math]

According to reference 3, pg. 4, the mass of the Higgs boson for the Standard Model is defined as:

[math]m_H = \sqrt{\frac{\lambda_h}{2}} v_h = \sqrt{\frac{\lambda_h (\hbar c)^3}{2 \sqrt{2} G_F}}[/math]

 

[math]\boxed{m_H = \sqrt{\frac{\lambda_h (\hbar c)^3}{2 \sqrt{2} G_F}}}[/math]

 

Higgs self-coupling parameter definition for lambda:

[math]\lambda_h = 2 \left( \frac{m_H}{v_h} \right)^2[/math]

 

Orion1 lambda:

[math]\lambda_h = 2 \left( \frac{123.111}{246.221} \right)^2 = 0.5[/math]

 

CERN lambda:

[math]\lambda_h = 2 \left( \frac{125.3}{246.221} \right)^2 = 0.517943[/math]

 

ATLAS lambda:

[math]\lambda_h = 2 \left( \frac{126.5}{246.221} \right)^2 = 0.527911[/math]

Reference:

Higgs boson - Wikipedia

Higgs vacuum expectation value - Wikipedia

Higgs Bosons: Theory And Searches - Fermi National Accelerator Laboratory

Edited by Orion1

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The biggest problem I can see with your prediction, is that you pulled it out of your ass.

 

Where did you get [math] v_h = \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math] from?

 

Perhaps you were meaning to write [math] M_W = \frac{g}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math]? The difference between this and your "prediction" is that this is derived from the theory.

 

Admittedly, it is mildly interesting that [math]M_W \approx g M_H[/math] but it is most likely coincidence.

Edited by Severian

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The biggest problem I can see with your prediction, is that you pulled it out of your ass.

 

Where did you get [math] v_h = \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math] from?

 

Perhaps you were meaning to write [math] M_W = \frac{g}{2} \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math]? The difference between this and your "prediction" is that this is derived from the theory.

 

Admittedly, it is mildly interesting that [math]M_W \approx g M_H[/math] but it is most likely coincidence.

Glad to have you posting with us again, Severian. Have you been busy at CERN this whole time?

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Glad to have you posting with us again, Severian. Have you been busy at CERN this whole time?

 

That Higgs boson wasn't going to find itself!

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Higgs vacuum expectation value for the Standard Model: (ref. 1, pg. 4)

[math]v_h = \sqrt{\frac{(\hbar c)^3}{\sqrt{2} G_F}}[/math]

 

Higgs boson mass for the Standard Model: (ref. 1, pg. 4)

[math]m_H = \sqrt{\frac{\lambda_h}{2}} v_h = \sqrt{\frac{\lambda_h (\hbar c)^3}{2 \sqrt{2} G_F}}[/math]

 

Fermi coupling constant: (ref. 1, pg. 4),(ref. 2)

[math]\frac{G_F}{(\hbar c)^3} = \frac{\sqrt{2}}{8} \frac{g_w^2}{m_W^2} = \frac{1}{\sqrt{2} v_h^2}[/math]

 

Higgs vacuum expectation value:

[math]\boxed{v_h = \frac{2 m_W}{g_w}}[/math]

 

Integration via substitution:

[math]m_H = \sqrt{\frac{\lambda_h}{2}} v_h = \sqrt{\frac{\lambda_h}{2}} \left( \frac{2 m_W}{g_w} \right) = \frac{\sqrt{2 \lambda_h} m_W}{g_w}[/math]

 

Higgs boson mass:

[math]\boxed{m_H = \frac{\sqrt{2 \lambda_h} m_W}{g_w}}[/math]

 

Reference:

Higgs Bosons: Theory And Searches - Fermi National Accelerator Laboratory

Fermi coupling constant - Wikipedia

Higgs boson - Wikipedia

Higgs vacuum expectation value - Wikipedia

W and Z bosons - Wikipedia

Vector Boson Decay - ATLAS

Edited by Orion1

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That's better, but it is not what you wrote before. Now you correctly have the [math]\lambda[/math] in the Higgs mass, and since you don't know [math]\lambda[/math] you no longer have a Higgs mass prediction.

Edited by Severian

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Higgs boson mass for the Standard Model: (ref. 1, pg. 4)

[math]m_H = \sqrt{\frac{\lambda_h}{2}} v_h[/math]

 

Higgs boson mass for the Standard Model: (ref. 2, pg. 14)

[math]m_H = \sqrt{2 \lambda_h} v_h[/math]

 

Which definition is correct?

Reference:

Higgs Bosons: Theory And Searches - Fermi National Accelerator Laboratory

The Standard Model Higgs - University of Chicago

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