Mass spectra and wave functions of toponia

TL;DR

This paper solves the Bethe-Salpeter equation for toponium using Cornell and Coulomb potentials, revealing negligible mass splitting due to the top quark's heaviness and providing nonrelativistic wave functions for various states.

Contribution

It presents a detailed nonrelativistic analysis of toponium mass spectrum and wave functions, incorporating solutions to the Bethe-Salpeter equation with specific potentials.

Findings

Negligible mass splitting between singlet and triplet toponium states.

Nonrelativistic wave functions for S, P, D-wave toponia are provided.

Decay modes of toponium states are studied.

Abstract

In this article, {we solve the instantaneous Bethe-Salpeter equation with Cornell potential and Coulomb potential} and conduct a meticulous study of the mass spectrum and wave function of toponium. Our investigation reveals that, owing to the exceedingly heavy mass of the top quark, the mass splitting between singlet and triplet states, as well as within the triplet states, is negligible. Consequently, relativistic corrections can be safely disregarded in the study of toponium. As such, we present the nonrelativistic wave functions for $S$-wave, $P$-wave, and $D$-wave toponia and study the decays $\eta_t\to \gamma\gamma$, $\eta_t\to gg$, and $\Theta\to \ell^+\ell^-$.