Related papers: Probabilistic interpretation of compositeness rela…
We present in this talk a series of new results on the nature of a bound state or resonance based on the calculation of the expectation values of the number operators of the free particles in the state of interest. In this way, a new…
In many physical applications, bound states and/or resonances are observed, which raises the question whether these states are elementary or composite. Here we elaborate on several methods for calculating the compositeness $X$ of bound…
We discuss the relation between the "compositeness" of an s-wave bound state, as derived from a related partial wave scattering amplitude, and the corresponding spatial probability densities, for the case of spherically symmetric,…
We discuss the composite nature of hadrons appearing near the s-wave two-hadron threshold. Generalizing the Weinberg's weak-binding relation for stable bound states, we show that the compositeness of near-threshold resonances and…
The near-threshold clustering phenomenon is well understood by the low-energy universality, for shallow bound states below the threshold. Nevertheless, the characteristics of resonances slightly above the threshold still lack thorough…
The ``spatial interpretation of compositeness'', presented and discussed in [1,2] in the context of non-relativistic potential scattering, is extended to higher partial waves. A particular set of basis states is used to arrive at a slightly…
A novel theoretical approach to the problem of the compositeness ($X$) of a resonance or bound state is developed on the basis of the expectation values of the number operators of the free particles in the continuum. This formalism is…
We discuss in general terms pole trajectories of resonances coupling to a continuum channel as some strength parameter is varied. It is demonstrated that, regardless the underlying dynamics, the trajectories of poles that couple to the…
Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in invariant mass distributions, with branching…
In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the…
We develop a theoretical framework to investigate the two-body composite structure of a resonance as well as a bound state from its wave function. For this purpose, we introduce both one-body bare states and two-body scattering states, and…
The compositeness $X$ is defined as the probability to observe the composite structure such as the hadronic molecule component in a bound state. One of the model-independent approaches to calculate $X$ is the weak-binding relation. However,…
Each and every energy dependent partial-wave analysis is parameterizing the pole positions in a procedure defined by the way how the continuous energy dependence is implemented. These pole positions are, henceforth, inherently model…
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…
We present the recent developments in the studies of the structure of hadron resonances, focusing on the compositeness in terms of the hadronic degrees of freedom. We discuss the model dependence of the compositeness, and show that the…
Recently, the Weinberg compositeness condition of a bound state was generalized to account for resonant states and higher partial waves. We apply this extension to the case of the $\Lambda(1520)$ resonance and quantify the weight of the…
We provide probabilistic interpretation of resonant states. This we do by showing that the integral of the modulus square of resonance wave functions (i.e., the conventional norm) over a properly expanding spatial domain is independent of…
Several methods for studying the nature of a resonance are applied to resonances recently discovered in the bottonomium and charmonium sectors. We employ the effective-range expansion, the saturation of the width and compositeness of a…
We quantify the internal structure of near-threshold bound, virtual, and resonance states in systems where Coulomb and short-range interactions coexist by evaluating the compositeness. Using the Coulomb-modified effective range expansion,…
We investigate the internal structure of near-threshold $s$-wave eigenstates in a two-body system with Coulomb plus short-range interactions. Using a nonrelativistic effective field theory, we derive the expression for the compositeness in…