Relativistic Friedrichs-Lee model and quark-pair creation model

TL;DR

This paper extends the Friedrichs-Lee model to a relativistic framework and combines it with a relativistic quark pair creation model to better understand meson spectra and the emergence of additional hadron states.

Contribution

It introduces a relativistic extension of the Friedrichs-Lee model combined with a quark pair creation model for studying unquenched meson spectra.

Findings

Identified two resonance poles corresponding to known mesons.

Demonstrated the scheme's ability to explain extra states in hadron spectra.

Abstract

In this paper, we present how the Friedrichs-Lee model could be extended to the relativistic scenario and be combined with the relativistic quark pair creation model in a consistent way. This scheme could be applied to study the "unquenched" effect of the meson spectra. As an example, if the lowest $J^{PC}=0^{++}$ $(u\bar u+d\bar d)/\sqrt{2}$ bound state in the potential model is coupled to the $\pi\pi$ continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the $f_0(500)/\sigma$ and the other probably $f_0(1370)$. This scheme might shed more light on why extra states could appear in the hadron spectrum other than the prediction of the quark potential model.