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 define the
compositeness as a fraction of the contribution of the two-body wave function to the normalization of the total wave function. Writing down explicitly the wave function for a resonance state obtained with a general separable interaction, we formulate the compositeness in terms of the position of the resonance pole, the residue of the scattering amplitude at the pole and the derivative of the Green function of the free two-body scattering system. At the same time, our formulation provides the elementariness expressed with the resonance properties and the two-body effective interaction, and confirms the sum rule showing that the summation of the compositeness and elementariness gives unity. In this formulation the Weinbergs relation for the scattering length and effective range can be derived in the weak binding limit. The extension to the resonance states is performed with the Gamow vector, and a relativistic formulation is also established. As its applications, we study the compositeness of the $Lambda (1405)$ resonance and the light scalar and vector mesons described with refined amplitudes in coupled-channel models with interactions up to the next to leading order in chiral perturbation theory. We find that $Lambda (1405)$ and $f_{0}(980)$ are dominated by the $bar{K} N$ and $K bar{K}$ composite states, respectively, while the vector mesons $rho (770)$ and $K^{ast} (892)$ are elementary. We also briefly discuss the compositeness of $N (1535)$ and $Lambda (1670)$ obtained in a leading-order chiral unitary approach.
The structures of the hyperon resonance $Lambda (1405)$ and the scalar mesons $sigma$, $f_{0}(980)$, and $a_{0}(980)$ are investigated based on the coupled-channels chiral dynamics with finite volume effect. The finite volume effect is utilized to ex
tract the coupling constant, compositeness, and mean squared distance between two constituents of a Feshbach resonance state as well as a stable bound state. In this framework, the real-valued size of the resonance can be defined from the downward shift of the resonance pole according to the decreasing finite box size $L$ on a given closed channel. As a result, we observe that, when putting the $bar{K}N$ and $Kbar{K}$ channels into a finite box while other channels being unchanged, the poles of the higher $Lambda (1405)$ and $f_{0}(980)$ move to lower energies while other poles do not show downward mass shift, which implies large $bar{K}N$ and $Kbar{K}$ components inside higher $Lambda (1405)$ and $f_{0}(980)$, respectively. Extracting structures of $Lambda (1405)$ and $f_{0}(980)$ in our method, we find that the compositeness of $bar{K}N$ ($Kbar{K}$) inside $Lambda (1405)$ [$f_{0}(980)$] is 0.82-1.03 (0.73-0.97) and the mean distance between two constituents is evaluated as 1.7-1.9 fm (2.6-3.0 fm).
The internal structure of the resonant Lambda(1405) state is investigated based on meson-baryon coupled-channels chiral dynamics. We evaluate Lambda(1405) form factors which are extracted from current-coupled scattering amplitudes in meson-baryon deg
rees of freedom. Using several probe currents and channel decomposition, we find that the resonant Lambda(1405) state is dominantly composed of widely spread Kbar around N, with escaping pi Sigma component.
We investigate the possibilities of using measurements in present and future experiments on heavy ion collisions to answer some longstanding problems in hadronic physics, namely identifying hadronic molecular states and exotic hadrons with multiquark
components. The yields of a selected set of exotic hadron candidates in relativistic heavy ion collisions are discussed in the coalescence model in comparison with the statistical model. We find that the yield of a hadron is typically an order of magnitude smaller when it is a compact multiquark state, compared to that of an excited hadronic state with normal quark numbers. We also find that some loosely bound hadronic molecules are formed more abundantly than the statistical model prediction by a factor of two or more. Moreover, due to the significant numbers of charm and bottom quarks produced at RHIC and even larger numbers expected at LHC, some of the proposed heavy exotic hadrons could be produced with sufficient abundance for detection, making it possible to study these new exotic hadrons in heavy ion collisions.
The scattering length and effective range of the piSigma channel are studied in order to characterize the strangeness S=-1 meson-baryon scattering and the Lambda(1405) resonance. We examine various off-shell dependence of the amplitude in dynamical c
hiral models to evaluate the threshold quantities with the constraint at the KbarN threshold. We find that the piSigma threshold parameters are important to the structure of the Lambda(1405) resonance and provide further constraints on the subthreshold extrapolation of the KbarN interaction.
Identifying hadronic molecular states and/or hadrons with multi-quark components either with or without exotic quantum numbers is a long standing challenge in hadronic physics. We suggest that studying the production of these hadrons in relativistic
heavy ion collisions offer a promising resolution to this problem as yields of exotic hadrons are expected to be strongly affected by their structures. Using the coalescence model for hadron production, we find that compared to the case of a non-exotic hadron with normal quark numbers, the yield of an exotic hadron is typically an order of magnitude smaller when it is a compact multi-quark state and a factor of two or more larger when it is a loosely bound hadronic molecule. We further find that due to the appreciable numbers of charm and bottom quarks produced in heavy ion collisions at RHIC and even larger numbers expected at LHC, some of the newly proposed heavy exotic states could be produced and realistically measured in these experiments.
We derive a single-channel effective Kbar N interaction from chiral SU(3) coupled-channel dynamics, emphasizing the important role of the pi Sigma channel and the structure of the Lambda(1405) resonance. The chiral low energy theorem requires strongl
y attractive interaction not only in the Kbar N channel but also in the pi Sigma channel. As a consequence of the strong pi Sigma dynamics, the equivalent potential in single Kbar N channel turns out to be less attractive than the one used in a purely phenomenological approach.
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 the scatter
ing theory. We develop a method to distinguish dynamically generated resonances from genuine quark states [Castillejo-Dalitz-Dyson (CDD) poles] using the natural renormalization scheme and phenomenological fitting. Analyzing physical meson-baryon scatterings, we find that the Lambda(1405) resonance is largely dominated by the meson-baryon molecule component. In contrast, the N(1535) resonance requires a sizable CDD pole contribution, while the effect of the meson-baryon dynamics is also important.
We study the behavior with the number of colors (Nc) of the two poles associated to the Lambda(1405) resonance obtained dynamically within the chiral unitary approach. The leading order chiral meson-baryon interaction manifests a nontrivial Nc depend
ence for SU(3) baryons, which gives a finite attractive interaction in some channels in the large Nc limit. As a consequence, the SU(3) singlet (Kbar N) component of the Lambda(1405) survives in the large Nc limit as a bound state, while the other components dissolve into the continuum. The Nc dependence of the decay widths shows different behavior from the general counting rule for a qqq state, indicating the dynamical origin of the two poles for the Lambda(1405) resonance.
The structure of N(1535) is discussed in dynamical and symmetry aspects based on chiral symmetry. We find that the N(1535) in chiral unitary model has implicitly some components other than meson-baryon one. We also discuss the N(1535) in the chiral doublet picture.
