Prediction of Toponium Levels Using a Logarithmic Potential Modeel

TL;DR

This paper predicts the energy levels of toponium resonant states using a logarithmic potential model based on empirical laws observed in hadron resonance states, providing specific mass formulas and collider energy requirements.

Contribution

It introduces a novel logarithmic potential model for toponium energy levels, extending empirical resonance laws to top quark systems.

Findings

Mass of n-th toponium state: 0.81ln(n) + 347 GeV

Resonance production cross-section: 3×10^{-9} mb

Collider energy needed: 270 GeV × 270 GeV

Abstract

In this paper, the energy levels of the resonant states of toponium, composed of top quark and anti-top quark, are given on the basis of an empirical law. We predict that the mass of the n-th resonant state of toponium is given by Mass(n)=0.81ln}(n) + 347GeV from the empirical law on the resonance level of the bottomonium. The cross-section produced by electron-positron collisions is 3X10^{-9}mb and an electron-positron collider would need an energy of 270GeV X 270 GeV to find out the resonance state of toponium. This prediction is based on the empirical law that the energy levels of hadron resonance states are expressed in logarithms. An interpretation of the appearance of quark resonance states in logarithmic intervals is also given in the paper. An application of this model, we present that the Okubo-Zwig-lizuka law can be viewed as a creation 11and annihilation problem of the two-dimensional resonance planes.