Excited charmonium states from Bethe-Salpeter equation

TL;DR

This paper solves the Bethe-Salpeter equation for heavy quark-antiquark pairs with a screened confining potential, improving the description of excited charmonium states by considering spin degrees of freedom.

Contribution

It demonstrates the necessity of including spin effects in Bethe-Salpeter calculations for accurate charmonium spectra, and discusses threshold effects with free quark propagators.

Findings

Reproduces known radial excitations of vector charmonium

Identifies $J/$ as the only state below the quark-antiquark threshold

Highlights the importance of spin degrees of freedom in quarkonium modeling

Abstract

We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a screened linear confining potential. First we show the spinless QFT model is inadequate and fail to describe even gross feature of the quarkonia spectrum. In order to get reliable description the spine degrees of freedom has to be considered. Within the approximation employed we reasonably reproduce known radial excitation of vector charmonium. The BSE favors relatively large string breaking scale $\mu\simeq 350MeV$ . Using free charm quark propagators we observe that $J/\Psi$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. Within the numerical method we overcome obstacles related with threshold singularity and discuss the consequences of the use of free propagators for calculation of excited states above the threshold.