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Leptons

Here are some quark models of leptons. All leptons are built-up around the heart of familial seeds shown on the left. Particles with a different angular momentum or charge are modeled by including various quarks around this common kernel. Then excited states are obtained by adding even more quarks. The leptons may share more quarks in addition to the familial pattern. But this nugget is the minimum necessary to distinguish the leptons from other  particle families.  Nuclear particles are classified on this basis. EthnoPhysics analyzes the mechanics of leptons using chains of events  noted by \Psi = ( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\Omega}_{3} \; \ldots \; ) where each repeated cycle \mathsf{\Omega} is composed of the following quarks.

The foregoing quark models completely specify the quantum numbers of leptons. The charge, angular momentum, baryon-number, lepton-number and strangeness are all correct. These models also produce accurate calculated values for the lifetime, width and mass. Results that fall outside of experimental uncertainty are noted with an X in all tables. There are just a handful of these errors from among hundreds of models.

Particle Cores

Some highly excited states contain so many quarks that may be difficult to see how the models work. So to view the underlying pattern, we remove most of the quark/anti-quark pairs. These \mathsf{q \overline{q}} pairs are needed for stability. But the field of \mathsf{q \overline{q}} pairs obscures the minimum number of quarks required to identify a particle and account for its mass. These minima are called core coefficients. They show more clearly how excited leptons are built-up over blocks of the same baryonic quarks. The mass depends on  \Delta n not  n, so  m is unchanged by any variation in the field of \mathsf{q \overline{q}} pairs. A particle’s rest mass is completely determined by its core quarks.

Experimentally observed values are taken from this reference .

Sample Calculations

Here is a spreadsheet that shows a step-by-step calculation for a specific lepton. For more detail about cell contents and formulae, you can see a read-only, on-line version by clicking on the icon in the black bar at the bottom of the sheet. You can also get a copy of the spreadsheet by clicking on the download link at the bottom of this page. Then you may enter other quark-coefficients in the yellow field to assess other particles.

The Electron

EthnoPhysics describes the electron by starting with an a chain of events written as

\Psi \! \left( \mathsf{e^{-}} \right) = \left( \mathsf{\Omega}_{1}, \, \mathsf{\Omega}_{2}, \, \mathsf{\Omega}_{3} \; \ldots \; \right)

The electron is represented by this collage of 40 seed icons.

where each repeated cycle  \mathsf{\Omega} is a bundle of 40 Anaxagorean sensations. The chain of events  \Psi is generically called a history of the electron. To be exact, the sensations are eight right-side and twelve left-side somatic feelings; two burning, two freezing, two warm and two cool thermal perceptions; four yellow, four blue and four white visual sensations. Each of these Anaxagorean sensations may be objectified to define a seed. And so to make a seed-aggregate model of the electron we express  \mathsf{\Omega} as a bundle of seeds

\mathsf{\Omega} \!    \left( \mathsf{e^{-}} \right) \leftrightarrow \mathrm{4} \mathsf{U} + \mathrm{2} \mathsf{B} + \mathrm{2} \mathsf{T} + \mathrm{2} \mathsf{S} + \mathrm{2} \mathsf{C} + \mathrm{4} \mathsf{G} + \mathrm{4} \mathsf{E} + \mathrm{8} \mathsf{O} + \mathrm{12} \overline{\mathsf{O}}

A Quark Model of the Electron

Quarks are defined by pairs of seeds. So the seed-aggregate model of the electron is further developed by associating seeds in pairs to form the following quarks

+

+

+

+

+

+

+

Thus an electron is represented by a bundle of twenty quarks. Here is a mathematical way of expressing the arrangement, along with an iconic image for the model.

  \mathsf{\Omega} \! \left( \mathsf{e^{-}} \right) \leftrightarrow \mathrm{4}\overline{\mathsf{u}} + \mathrm{2}\overline{\mathsf{b}} + \mathrm{2}\mathsf{t} + \mathrm{2} \overline{\mathsf{s}} + \mathrm{2}\mathsf{c} + \mathrm{4} \overline{\mathsf{g}} + \mathrm{4}\mathsf{e}

The electron is represented by this image of twenty quark icons.

Using these quarks, the mass of the electron is calculated to be 0.5109989280 (MeV/c2). This is exactly the same as the experimentally observed value because adjustable parameters like quark energies have been carefully chosen1The mass of the electron  m can be written in terms of the work, enthalpy and quark coefficients. The resulting quadratic equation can be solved to find  U^{\mathsf{U}} the internal-energy of up-quarks as


 U^{\mathsf{U}} = \dfrac{ m^{2} c^{4} - \beta^{2} + 16k_{ee} \left( U^{\mathsf{E}} + U^{\mathsf{G}} \right)^{2} }{ 8\beta -32k_{ez} \left( U^{\mathsf{E}} + U^{\mathsf{G}} \right) }


where


 \beta = -4U^{\mathsf{E}} + 4U^{\mathsf{G}} - 2U^{\mathsf{T}} + 2U^{\mathsf{B}} + 2U^{\mathsf{S}} - 2U^{\mathsf{C}}


This relationship is then used to constrain the selection of other adjustable parameters.
to get this result. For more detail, please see the Nuclear Particles spreadsheet.

A Ground-State Electron Model

In the foregoing model, quark coefficients are all integer multiples of two, and so the image is drawn with the back row of quarks the same as the front row. But we cannot have two identical quarks in the same bundle and still satisfy Pauli’s exclusion principle. So the quark model is developed further with an additional requirement that the quarks in the front and back rows are out of phase with each other. That is, they are distinguished by the helicity of their reference frames as noted by   \mathsf{F}_{\mdsmwhtcircle} or   \mathsf{F}_{\mdsmblkcircle}. This satisfies the definition for being in a ground-state and so the new arrangement is called a ground-state model of the electron. It is expressed mathematically as

\mathsf{\Omega} \!     \left( \mathsf{e^{-}} \right) = \left\{ \rule{0px}{14px} \left\{ \left\{ \mathsf{e},  \mathsf{t},  \overline{\mathsf{s}},  \overline{\mathsf{g}},  \overline{\mathsf{u}} \right\}, \,  \mathsf{e}, \, \mathsf{c}, \, \overline{\mathsf{b}}, \, \overline{\mathsf{g}}, \,  \overline{\mathsf{u}}, \,  \mathsf{F}_{\mdsmwhtcircle} \right\}, \left\{ \left\{ \mathsf{e},  \mathsf{t},  \overline{\mathsf{s}},  \overline{\mathsf{g}},  \overline{\mathsf{u}} \right\}, \,  \mathsf{e}, \, \mathsf{c}, \, \overline{\mathsf{b}}, \, \overline{\mathsf{g}}, \, \overline{\mathsf{u}}, \, \mathsf{F}_{\mdsmblkcircle}  \right\}   \right\}

To illustrate this model, we show quarks with a background that is dark or bright depending on their phase. Then the image above can be made into a short movie that uses shadows, horizons and background brightness to suggest a quark’s relationship with the frame-of-reference.

References
1The mass of the electron  m can be written in terms of the work, enthalpy and quark coefficients. The resulting quadratic equation can be solved to find  U^{\mathsf{U}} the internal-energy of up-quarks as

 U^{\mathsf{U}} = \dfrac{ m^{2} c^{4} - \beta^{2} + 16k_{ee} \left( U^{\mathsf{E}} + U^{\mathsf{G}} \right)^{2} }{ 8\beta -32k_{ez} \left( U^{\mathsf{E}} + U^{\mathsf{G}} \right) }

where

 \beta = -4U^{\mathsf{E}} + 4U^{\mathsf{G}} - 2U^{\mathsf{T}} + 2U^{\mathsf{B}} + 2U^{\mathsf{S}} - 2U^{\mathsf{C}}

This relationship is then used to constrain the selection of other adjustable parameters.