AbstractIn 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 $$J^{PC}=0^{++}$$
J
PC
=
0
+
+
$$(u\bar{u}+d\bar{d})/\sqrt{2}$$
(
u
u
¯
+
d
d
¯
)
/
2
bound state in the potential model is coupled to the $$\pi \pi $$
π
π
continuum, two resonance poles could be found from the scattering amplitude for the continuum states. One of them could correspond to the $$f_0(500)/\sigma $$
f
0
(
500
)
/
σ
and the other probably $$f_0(1370)$$
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.