Bethe-Salpeter study of radially excited vector quarkonia

TL;DR

This paper solves the Bethe-Salpeter equation for heavy quarkonia using a confining potential and gluon exchange, successfully reproducing known radial excitations and analyzing the spectrum above the quark-antiquark threshold.

Contribution

It introduces a method to solve the full four-dimensional Bethe-Salpeter equation for excited quarkonium states, including above-threshold states, with a detailed analysis of the confining potential scale.

Findings

Successfully reproduces all known radial excitations of vector charmonia.

Finds that J/ψ is the only state below the quark-antiquark threshold.

Determines the Bethe-Salpeter string breaking scale to be around 350 MeV.

Abstract

We solve the Bethe-Salpeter equation (BSE) for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found 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. We develop a method which is enable to provide solution of full four dimensional BSE for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale $\mu\simeq 350MeV$ appears to be relatively larger then the one defined in various potential models $\mu\simeq 150MeV$.