A Theoretical Explanation on Gell-Mann-Nishijima Formula with Singular Number and the Establishment of Lepton Quantum Number Constrained Equation

Abstract

In this paper, two fundamental problems of particle physics are studied theoretically. The first one is: to solve the problem of establishing general quantum number constrained equation, the symmetry transformation mechanism of charge eigenstates for elementary particles is adopted, and the general quantum number constrained equations are established, which are applicable to physical particles. For hadrons, an equation is completely consistent with Gell-Mann-Nishijima formula. For leptons, the lepton quantum numbers are exactly the solutions of an equation, which is just the lepton quantum number constrained equation. The second problem is: to solve the problem of understanding singularity and calculating singular numbers, a hypothesis that a composite particle may has virtual structure is proposed. According to this hypothesis, the singular particles must be composite particles, and have virtual structures. In a virtual structure, the particles and antiparticles of component particles can form particle-antiparticle pairs, which have great influence such as improving mass and changing life of composite particles. Therefore, the composite particle with particle-antiparticle pairs in its virtual structure is singular particle, and the singular number is the number of particle-antiparticle pairs. These two theoretical results are in good agreement with the already achieved experimental results of particle physics, can explain the related phenomena of physical particles from a deeper physical mechanism, and theoretically predict the existence of singular leptons and several new singular hadrons.

Summing up the Feynman diagrams: Toward quantum gluonodynamics

“…Nishijima and Gell-Mann independently proposed that these strange behaviors could be understood if they had a quantum number known as "strangeness." This explanation led to the emergence of the Gell-Mann-Nishijima formula, which came to form an integral part of particle physics 10,11 .…”

“…(1) Equation 11,12 Today, physicists describe the Standard Model mathematically using the notation of group theory. Given that 𝑆𝑈(3)=gauge group of strong interactions and 𝑆𝑈(2) × 𝑈(1)=gauge group of electroweak interactions, the group theory notation becomes:…”