Higgs Boson From The Quantized Superfluid Proton

Summary: Proton Radius, Mass, and Higgs Boson Energy

This summary outlines the key equations, relationships, and results discussed concerning the proton's radius, mass, and its potential connection to the Higgs boson's mass-energy.

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Proton Radius and the Trinhammer-Bohr Equation

• Equation: The core formula is derived from or related to the Trinhammer-Bohr equation, which connects the proton's charge radius ($r_p$) to its Compton wavelength ($\lambda_{c,p}$).

• Relationship: $r_p = \frac{2 \lambda_{c,p}}{\pi}$. This establishes a direct proportionality between the proton's radius and its Compton wavelength.

• Compton Wavelength: The proton's Compton wavelength is defined as $\lambda_{c,p} = \frac{h}{m_p c}$, where $h$ is Planck's constant, $m_p$ is the proton mass, and $c$ is the speed of light.

• Combining Equations: Substituting the expression for $\lambda_{c,p}$ into the Trinhammer-Bohr equation yields $r_p = \frac{2}{\pi} \times \frac{h}{m_p c} = \frac{2h}{\pi m_p c}$.

• Relating to the Formula: The formula $\ell = \frac{nh}{2\pi c m_p}$ is conceptually similar, especially when considering the relationship $h = 2\pi\hbar$ (where $\hbar$ is the reduced Planck constant).

• Result (n=4): Calculating $4 \times \frac{h}{2\pi m_p c}$ (equivalent to $\frac{2h}{\pi m_p c}$) produces a value of approximately 0.8412 fm. This figure closely aligns with the proton radius obtained from muonic hydrogen experiments, which is around 0.84 fm. The quantum number $n=4$ in the formulas is consequently linked to this calculation of the proton radius based on its Compton wavelength.

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Higgs Boson Mass-Energy and the $\frac{533}{4}$ Factor

• Relationship: The energy equivalent of $\frac{533.0}{4.0} \times m_p$ was determined to be approximately 125085 MeV.

• Higgs Boson Mass: The experimentally measured mass-energy of the Higgs boson is approximately 125 GeV, which is equivalent to 125,000 MeV.

• Comparison: The calculated value (125085 MeV) exhibits a strong correspondence with the Higgs boson's energy (125,000 MeV).

• Interpretation of $\frac{533}{4}$: The factor $\frac{533}{4}$ (or $133.25$) is likely a parameter within a specific theoretical model. This model appears to relate the proton's mass to the Higgs boson's mass, potentially suggesting an exploration of connections between the proton's internal structure and the Higgs mechanism.

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The Role of the Higgs Boson

• The Higgs boson is associated with the Higgs field, which is responsible for giving mass to elementary particles such as quarks and electrons.

• It's important to note that the majority of the proton's mass originates from the strong nuclear force that binds the quarks, not directly from the Higgs mechanism.

• The notable numerical agreement between $\frac{533}{4} \times m_p$ and the Higgs boson's mass-energy points towards a theoretical framework that utilizes the given equations to explore this connection, despite the Higgs mechanism not being the primary source of the proton's mass.

Proton as Quantized Superfluid Vortex - Detailed Summary

Overview

This summary examines the quantized superfluid vortex model of the proton, where energy levels are given by \(E_n = 234.5 \times n\) MeV. The proton mass (938 MeV) corresponds to \(n=4\). Transitions from \(n=4\) to \(n=5\) and \(n=4\) to \(n=6\) are analyzed, with their energies added to the proton mass and compared to proton resonances like \(\Delta(1232)\) and \(N(1440)\).

Energy Levels and Correlated States

Key energy levels and their potential correlations to known particles or resonances:

Quantum Number (n)	Energy (MeV)	Correlated State	Actual Mass (MeV)	Discrepancy (MeV)
4	938	Proton	938	0
5	1172.5	\(\Delta(1232)\)	1232	59.5
6	1407	\(N(1440)\)	1440	33

Quantum Transitions and Resonances

Transitions from the proton state (\(n=4\)) with energies added to the proton mass (938 MeV):

Transition	\(\Delta E\) (MeV)	Total Energy (MeV)	Correlated Resonance	Actual Resonance Mass (MeV)	Discrepancy (MeV)
\(n=4\) to \(n=5\)	234.5	1172.5	\(\Delta(1232)\)	1232	59.5
\(n=4\) to \(n=6\)	469	1407	\(N(1440)\)	1440	33

Note: Total Energy = \(\Delta E + 938\) MeV (proton mass). Discrepancies indicate approximate matches, suggesting a loose correlation rather than an exact fit.

Conclusion

The transitions from \(n=4\) to \(n=5\) and \(n=4\) to \(n=6\) yield total energies of 1172.5 MeV and 1407 MeV, respectively, when added to the proton mass. These values approximately match the \(\Delta(1232)\) (1232 MeV) and \(N(1440)\) (1440 MeV) resonances, with discrepancies of ~60 MeV and ~33 MeV. This loose correlation suggests the model captures some aspects of proton resonances but lacks precision, highlighting its theoretical nature and the need for further validation.