Various Decays of Particles, Universal Decay Formulas and Their Possible Dynamic Basis and Applications

TL;DR

This paper proposes a universal decay formula for particle decays based on associated Legendre functions, linking decay modes to a dynamic basis and applying it to hadron decays with good agreement.

Contribution

It introduces a unified decay formula using associated Legendre functions and a dynamic basis, simplifying the understanding of various particle decay modes.

Findings

Decay formulas match experimental data well

Coupling constants are invariant for similar particles

Application to hadrons demonstrates model effectiveness

Abstract

The decay modes and fractions in particle physics are some quantitative and very complex questions. Various decays of particles and some known decay formulas are discussed. Many important decays of particles and some known decays of resonances can be generally described by the square of some types of the associated Legendre functions. It is combined with the selection rule, then the agreements are very good. The decay formulas of the similar decay modes are the same. For the same types of particles, the coupling constants are kept to be invariant, and only six constants are independent. The simplest dynamical basis is probably that the decay formulas are the square of the solution of free field equation of the decay particles in the momentum coordinate system. Further, we discuss some general decays and their rules. Finally, we apply the decay formulas to some massive hadrons.