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

TL;DR

This paper demonstrates that two-pole structures naturally emerge in a relativistic Friedrichs-Lee model combined with a quark pair creation model, providing insights into enigmatic meson states and their scattering phase shifts.

Contribution

It introduces a relativistic scheme showing how two-pole structures arise from $q\bar q$ states coupling to open-flavor continua, explaining several mysterious mesons.

Findings

Many enigmatic states are explained as two-pole structures.

Two-pole structures contribute about 180° phase shift in scattering.

The scheme offers insights into non-$q\bar q$ states.

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 $f_0(500)/\sigma$, $K_0^*(700)/\kappa$, $a_0(980)$, $f_0(980)$, $D_0^*(2300)$, $D_{s0}^*(2317)$, 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.