Relativistic Friedrichs-Lee model and quark-pair creation model

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.

v3, figure 3 added, some discussions added, published version

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Cited by in corpus (5)

• A Review on Partial-wave Dynamics with Chiral Effective Field Theory and Dispersion Relation
• A simple alternative to the Breit-Wigner distribution
• Two-pole structures in a relativistic Friedrichs-Lee-QPC scheme
• Scrutinizing $\pi \pi$ scattering in light of recent lattice phase shifts
• Inverse scattering problem with a bare state