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 $$q\bar{q}$$ 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.

Scrutinizing $ππ$ scattering in light of recent lattice phase shifts

“…The situation for the σ at the physical pion mass seems a bit different, since it is found that the broad σ resonance could be easily generated by only including the nonperturbative two-pion interactions. Recall that in the Friedrichs-Lee model, which devotes to the explanation of all the low-lying scalar nonet below 1.0 GeV and the scalar nonet higher than 1.0 GeV, the dynamically generated σ poles on the complex s-plane will move towards the real axis and become two different virtual state poles, and then become a bound state pole and a virtual state pole as the coupling strength increases [19,40]. The bound-virtual states scenario also happens when the quark mass become large.…”

“…[15] that a bare scalar q q seed when coupled to the two-meson channels with the same quantum numbers, could generate an additional set of dynamical states, corresponding to the light scalar nonet below 1 GeV, apart from the seed states, corresponding to the ones above 1 GeV [16,17]. Such a mechanism could be better understood in a relativistic Friedrichs-Lee model since there are light u and d quarks involved, and the scheme could be also extended to study the states with heavy c or b quarks [18,19]. Another method to study the σ resonance is to unitarize the χPT amplitudes with some unitarization scheme and extract the poles of the scattering amplitude [20,21].…”

Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules

“…The only allowed strong decay channels are the D ( * ) s π which break the isospin symmetry and their decay widths are therefore extremely narrow. Since the discoveries, these two states inspired strong interests in the charm-strange mesons due to the following puzzles: (i) the masses of the D * In order to unveil the mysteries of the D * s0 (2317) and D s1 (2460), there exist a lot of investigations in literature, including the quenched and unquenched c s quark model [27,28,29,30,31,32,33,34,35,36], the hadronic molecules [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58], the compact tetraquark states [59,60,61,62,63], and the mixing of the c s state and tetraquark state [64,65,66,32]. The readers may consult the reviews [7,67,11,68,…”

The investigations of the P-wave Bs states combining quark model and lattice QCD in the coupled channel framework

“…These two states have been widely investigated by both theoretical and experimental sides, see reviews [5][6][7][8] for more details. Various proposals regarding their nature are proposed, including the quenched and unquenched cs quark models [4, [9][10][11][12][13][14][15][16][17][18], the molecule model , the tetraquark model [43][44][45][46][47], and the cs plus tetraquark model [12,[48][49][50][51].…”