Eur. Phys. J. C (2020) 80: 1191
https://doi.org/10.1140/epjc/s10052-020-08752-8

Regular Article – Theoretical Physics

Relativistic Friedrichs–Lee model and quark-pair creation model

¹ School of Physics, Southeast University, 211189, Nanjing, People’s Republic of China
² NSFC-SFTP Peng Huanwu Center for Fundamental Theory and Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, 230026, Hefei, Anhui, China

^b xiaozg@ustc.edu.cn

Received: 24 October 2020
Accepted: 10 December 2020
Published online: 24 December 2020

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^{\mathit{PC}}=0^{++}$$(u\overline{u}+d\overline{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.