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

Abstract

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 $q\bar{q}$ state couples to the open-flavor continuum state in the $S$ partial wave. We found that many enigmatic states, such as $f_0(500)/\sigma$, $K_0^{\ast }(700)/\kappa$, $a_0(980)$, $f_0(980)$, $D_0^{\ast }(2300)$, $D_{s0}^{\ast }(2317)$, 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${}^{\circ }$ 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-$q\bar{q}$ state. It is also suggested that such two-pole structure could be a common phenomenon which deserves studying both from theoretical and experimental perspectives.

Comments: 9 pages, 4 figure; Major revisions, figures added, more discussions and references are added; Published version