Related papers: Remarks on the origin of Castillejo-Dalitz-Dyson p…
We discuss the relation between the analytic structure of the scattering amplitude and the origin of an eigenstate represented by a pole of the amplitude.If the eigenstate is not dynamically generated by the interaction in the channel of…
In quantum scattering theory, there exists a relationship between the difference in the scattering phase shifts at threshold and infinity and the number of bound states, which is established by the Levinson theorem. The presence of…
We study the origin of the resonances associated with pole singularities of the scattering amplitude in the chiral unitary approach. We propose a "natural renormalization" scheme using the low-energy interaction and the general principle of…
We introduce two basic concepts: the compositeness for resonance and the Castillejo-Dalitz-Dyson (CDD) pole. Applying them to hadron states $X(3872)$, $Z_b(10610)$ and $Z_b(10650)$, and $T_{cc}$, we obtain their compositeness values and…
This article provides a pedagogical exploration of coupled-channel scattering in hadronic physics, focusing on theoretical methodologies, and practical applications. It covers key concepts such as the $N/D$ method, Castillejo-Dalitz-Dyson…
In 2021, LHCb collaboration reported a very narrow state in the $D^0D^0\pi^+$ mass spectrum just below the $D^{*+}D^0$ mass threshold. We consider the influence of the Castillejo-Dalitz-Dyson (CDD) pole in the scattering amplitude to derive…
Charmonium-like resonances and bound states with isospin zero and $J^{PC}=0^{++},~1^{--},~2^{++},~3^{--}$ are extracted on the lattice. Coupled $D\bar D$ and $D_s\bar D_s$ scattering suggests three charmonium-like states with…
Compound states manifest themselves as bound states, resonances, or primitives, and their character is determined by their interaction with the continuum. If the interaction experiences a perturbation, a compound state can change its…
We present the first lattice investigation of coupled-channel $D\bar D$ and $D_s\bar D_s$ scattering in the $J^{PC}=0^{++}$ and $2^{++}$ channels. The scattering matrix for partial waves $l=0,2$ and isospin zero is determined using multiple…
We solve the dispersion relation for the P-wave pi pi amplitude.We discuss the role of the left hand cut vs Castillejo-Dalitz-Dyson (CDD), pole contribution and compare the solution with a generic quark model description. We review the the…
In this paper it is proposed that the charged charmonium-like state $Z_c(3900)$ is a resonance above the threshold from the $D\bar{D}^*$ interaction. The $D\bar{D}^*$ interaction is described by the one-boson exchange model with light meson…
We make use of a unitarized coupled-channel model to analyze the mass distribution data of final states in production processes of $X(4260)$. By analyzing the analytical structures of the decay amplitudes, we find that the line shape of…
Relationships between partial-wave amplitude parametrizations, in particular the Chew-Mandelstam approach, and dynamical coupled-channel models are established and investigated. A bare pole corresponding to the Delta(1232) resonance, found…
The dynamical mechanism of channel coupling with the decay channels is applied to the case of coupled charmonium - $DD^*$ states with $J^{PC}=1^{++}$. A pole analysis is done and the $DD^*$ production cross section is calculated in…
In this work, we construct the $S$-wave, $P$-wave, and $D$-wave $D^{(*)}\bar{D}^{*}_{(s)}$/$B^{(*)}\bar{B}^{*}_{(s)}$ interactions by considering the lowest order contributions from the leading order (LO), next-to-leading order (NLO), and…
Soliton equations are derived which characterize the boundary CFT a la Callan et al. Soliton fields of classical soliton equations are shown to appear as a neutral bound state of a pair of soliton fields of BCFT. One soliton amplitude under…
We study the quark mass dependence of the H-dibaryon in the strangeness $S=-2$ baryon-baryon scattering. A low-energy effective field theory is used to describe the coupled-channel scattering, in which the quark mass dependence is…
This report presents an investigation of the pion-nucleon elastic scattering in low energy region using a production representation of the partial wave $S$ matrix. The phase shifts are separated into contributions from poles and branch…
We consider the 1D Dirac operator on the half-line with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties…
Using Hollowood's conjecture for the S-matrix for elementary solitons in complex $a_n^{(1)}$ affine Toda field theories we examine the interactions of bound states of solitons in $a_2^{(1)}$ theory. The elementary solitons can form two…