9. Borros Arneth, Pythagorean numbers and the calculation ....

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Volume 34: Pages 323-331, 2021

Pythagorean numbers and the calculation of the masses of the elementary particles

Borros Arnetha)

Justus Liebig University Giessen, Feulgenstr. 12, 35392 Giessen, Germany


We attempt here to calculate the particle masses for all known elementary particles starting from the Rydberg equation and from the Sommerfeld fine structure constant. Remarkably, this is possible. Next, we try to explain why this is possible and what the meaning of the approach seems to be. Thereby, we find some interesting connections. In addition, we realize that there are two different kinds of mass-charge binding energies in an elementary particle: The internal mass-charge binding energy and the external mass-charge binding energy. These two kinds of mass-charge binding energies can explain the higher masses of the highly charged brother particles in some of the heavier particle triplets (such as the charmed sigma particles).


Nous essayons ici de calculer les masses de toutes les particules élémentaires connues, à commencer par l’équation de Rydberg et la constante des structures fines de Sommerfeld. Une telle possibilité est remarquable. Ensuite, nous essayons d’expliquer les raisons de cette possibilité ainsi que la signification apparente de cette approche. En procédant de la sorte, nous rencontrons certaines connexions intéressantes. Nous constatons par ailleurs qu’il existe deux formes différentes d’énergies de liaison masse/charge dans une particule élémentaire : l’énergie de liaison masse/charge interne et l’énergie de liaison masse/charge externe. Ces deux catégories d’énergies de liaison masse/charge peuvent expliquer les masses plus élevées des particules apparentées fortement chargées dans certains triplets de particules assez lourds (telles que les particules sigma charmées).


Key words: Pythagorean Numbers; Charmed Sigma Particles; Rydberg Equation; Sommerfeld Fine Structure Constant; Mass-Charge Binding Energies.

Received: August 4, 2020; Accepted: June 10, 2021; Published Online: July 16, 2021

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