Two-pole structures in a relativistic Friedrichs–Lee-QPC scheme

A general appearance of two-pole structures is exhibited in a relativistic Friedrichs–Lee model combined with a relativistic quark pair creation model in a consistent manner. This kind of two-pole structure could be found when a $$q\bar{q}$$ q q ¯ state couples to the open-flavor continuum state in the S partial wave. We found that many enigmatic states, such as $$f_0(500)/\sigma $$ f 0 ( 500 ) / σ , $$K_0^*(700)/\kappa $$ K 0 ∗ ( 700 ) / κ , $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) , $$D_0^*(2300)$$ D 0 ∗ ( 2300 ) , $$D_{s0}^*(2317)$$ D s 0 ∗ ( 2317 ) , and X(3872), together with another higher state for each, all result from this kind of two-pole structures. Furthermore, an interesting observation is that this kind of two-pole structure will contribute roughly a total of $$180^\circ $$ 180 ∘ phase shift for the scattering process in a single channel approximation. This relativistic scheme may provide more insights into the understanding of the properties of non-$$q\bar{q}$$ q q ¯ state. It is also suggested that such two-pole structure could be a common phenomenon which deserves studying both from theoretical and experimental perspectives.