Search

We revisit the short-range baryon-baryon potentials in the flavor SU(3) sector, using the constituent quark model. We employ the color Coulomb, linear confining, and color magnetic forces between two constituent quarks, and solve the three-quark Schr\"{o}dinger equation using the Gaussian expansion method to evaluate the wave functions of the octet $( N , \Lambda , \Sigma , \Xi )$ and decuplet $( \Delta , \Sigma ^{\ast} , \Xi ^{\ast} , \Omega )$ baryons. We then solve the six-quark equation using the resonating group method and systematically calculate equivalent local potentials for the $S$-wave two-baryon systems which reproduce the relative wave functions of two baryons in the resonating group method. As a result, we find that the flavor antidecuplet states with total spin $J = 3$, namely, $\Delta \Delta$, $\Delta \Sigma ^{\ast}$, $\Delta \Xi ^{\ast}$-$\Sigma ^{\ast} \Sigma ^{\ast}$, and $\Delta \Omega$-$\Sigma ^{\ast} \Xi ^{\ast}$ systems, have attractive potentials sufficient to generate dibaryon bound states as hadronic molecules. In addition, the $N \Omega$ system with $J = 2$ in coupled channels has a strong attraction and forms a bound state. We also make a comparison with the baryon-baryon potentials from lattice QCD simulations and try to understand the behavior of the potentials from lattice QCD simulations., Comment: Version accepted for publication in Physical Review C. Parameters, especially the constituent quark masses, have been refined. All of the explicit potential values in our model are provided in the ancillary files

The J-PARC Hadron Experimental Facility was constructed with an aim to explore the origin and evolution of matter in the universe through the experiments with intense particle beams. In the past decade, many results on particle and nuclear physics have been obtained at the present facility. To expand the physics programs to unexplored regions never achieved, the extension project of the Hadron Experimental Facility has been extensively discussed. This white paper presents the physics of the extension of the Hadron Experimental Facility for resolving the issues in the fields of the strangeness nuclear physics, hadron physics, and flavor physics., Comment: 261 pages, 186 figures

The meson-baryon molecular components for the $N^{\ast}$ and $\Delta ^{\ast}$ resonances are investigated in terms of the compositeness, which is defined as the norm of the two-body wave function from the meson-baryon scattering amplitudes. The scattering amplitudes are constructed in a $\pi N$-$\eta N$-$\sigma N$-$\rho N$-$\pi \Delta$ coupled-channels problem in a meson exchange model together with several bare $N^{\ast}$ and $\Delta ^{\ast}$ states, and parameters are fitted so as to reproduce the on-shell $\pi N$ partial wave amplitudes up to the center-of-mass energy 1.9 GeV with the orbital angular momentum $L \le 2$. As a result, the Roper resonance $N (1440)$ is found to be dominated by the $\pi N$ and $\sigma N$ molecular components while the bare-state contribution is small. The squared wave functions in coordinate space imply that both in the $\pi N$ and $\sigma N$ channels the separation between the meson and baryon is about more than 1 fm for the $N (1440)$ resonance. On the other hand, dominant meson-baryon molecular components are not observed in any other $N^{\ast}$ and $\Delta ^{\ast}$ resonances in the present model, although they have some fractions of the meson-baryon clouds., Comment: 20 pages, 5 figures, version accepted for publication in PRC, parameters are updated, description of the discussion part is improved

We investigate theoretically the $K^{0} p$ invariant mass spectrum of the $K^{+} d \to K^{0} p p$ reaction and scrutinize how the signal of the "$\Theta ^{+}$" pentaquark, if it exists, emerges in the $K^{0} p$ spectrum. The most prominent advantage of this reaction is that we can clearly judge whether the "$\Theta ^{+}$" exists or not as a direct-formation production without significant backgrounds, in contrast to other reactions such as photoproduction and $\pi$-induced productions. We show that while the impulse or single-step scattering process can cover the "$\Theta ^{+}$" energy region with an initial kaon momentum $k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ in the laboratory frame, the contributions from double-step processes may have a potential possibility to reach the "$\Theta ^{+}$" energy region with a higher kaon momentum $k_{\mathrm{lab}} \sim 1 \, \mathrm{GeV} / c$. Assuming that the full decay width of the "$\Theta ^{+}$" is around $0.5\, \mathrm{MeV}$, we predict that the magnitude of the peak corresponding to the "$\Theta^+$" is around a few hundred $\mu \mathrm{b}$ to $1\, \mathrm{mb}$ with the momentum of the kaon beam $k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ while it is around $\lesssim 1\, \mu \mathrm{b}$ with $k_{\mathrm{lab}} \approx 0.85\, \mathrm{GeV} / c$. Thus, the "$\Theta^+$" peak is more likely to be seen at $k_{\mathrm{lab}} \approx 0.40\, \mathrm{GeV} / c$ than at $k_{\mathrm{lab}} \approx 0.85 \,\mathrm{GeV} / c$., Comment: 14 pages. 11 figures. Three more figures are included and the text was revised

Based on the scenario that a $\bar{K} N N$ bound state is generated and it eventually decays into $\Lambda p$, we calculate the cross section of the $K^{-} {}^{3} \text{He} \to \Lambda p n$ reaction, which was recently measured in the J-PARC E15 experiment. We find that the behavior of the calculated differential cross section $d ^{2} \sigma / d M_{\Lambda p} d q_{\Lambda p}$, where $M_{\Lambda p}$ and $q_{\Lambda p}$ are the $\Lambda p$ invariant mass and momentum transfer in the $(K^{-} , \, n)$ reaction in the laboratory frame, respectively, is consistent with the experiment. Furthermore, we can reproduce almost quantitatively the experimental data of the $\Lambda p$ invariant mass spectrum in the momentum transfer window $350 \text{ MeV} /c < q_{\Lambda p} < 650 \text{ MeV} /c$. These facts strongly suggest that the $\bar{K} N N$ bound state was indeed generated in the J-PARC E15 experiment., Comment: 4 pages, 4 EPS figures, talk given at the 8th International Conference on Quarks and Nuclear Physics (QNP2018), Tsukuba, Japan, 13-17 November, 2018

We predict a new three-body hadronic molecule composed of antikaon $\bar{K}$, anticharm meson $\bar{D}$, and nucleon $N$ with spin/parity $J^{P} = 1/2^{+}$ and isospin $I = 1/2$. This state behaves like an explicit pentaquark state because its minimal quark configuration is $u u d s \bar{c}$ or $u d d s \bar{c}$. Owing to the attraction between every pair of two hadrons, in particular the $\bar{K}\bar{D}$ attraction which dynamically generates $D_{s 0} (2317)^{-}$ and $\bar{K} N$ attraction which dynamically generates $\Lambda (1405)$, the $\bar{K}\bar{D} N$ system is bound, and its eigenenergy is calculated as $3244 - 17 i$ MeV in a nonrelativistic three-body potential model. We discuss properties of this $\bar{K} \bar{D} N$ quasibound state which emerge uniquely in three-body dynamics., Comment: 12 pages, 5 figures

Based on a baryon-baryon interaction model with meson exchanges, we investigate the origin of the strong attraction in the $N \Omega ( {}^{5}S_{2} )$ interaction, which was indicated by recent lattice QCD simulations. The long range part of the potential is constructed by the conventional mechanisms, the exchanges of the $\eta$ meson and of the correlated two mesons in the scalar-isoscalar channel, denoted by "$\sigma$" in the literature. The short range part is represented by the contact interaction. We find that the meson exchanges do not provide sufficient attraction. This means that most of the attraction is attributed to the short range contact interaction. We then evaluate the effect of the coupled channels to the $N \Omega ( {}^{5}S_{2} )$ interaction. We find that, while the $D$-wave mixing of the $N \Omega$ channel is negligible, the inelastic $\Lambda \Xi$, $\Sigma \Xi$, and $\Lambda \Xi (1530)$ channels via the $K$ meson exchange give the attraction of the $N \Omega ( {}^{5}S_{2} )$ interaction to the same level with the elastic meson exchanges. Although the elimination of these channels induces the energy dependence of the single-channel $N \Omega$ interaction, this effect is not significant. With the present model parameters fitted to reproduce the scattering length of the HAL QCD result of the nearly physical quark masses, we obtain the $N \Omega ( {}^{5}S_{2} )$ quasibound state with its eigenenergy $2611.3 - 0.7 i$ MeV, which corresponds to the binding energy $0.1$ MeV and width $1.5$ MeV for the decay to the $\Lambda \Xi$ and $\Sigma \Xi$ channels. From the analysis of the spatial structure and the compositeness, the quasibound state is shown to be the molecular state of $N\Omega$. We also construct an equivalent local potential for the $N \Omega ( {}^{5}S_{2} )$ system which is useful for various applications., Comment: 22 pages, 17 eps figures

We theoretically analyze the $K^{-} {}^{3} \text{He} \to \Lambda p n$ reaction for the $\bar{K} N N$ bound-state search in the J-PARC E15 experiment. We find that, by detecting a fast and forward neutron in the final state, an almost on-shell $\bar{K}$ is guaranteed, which is essential to make a bound state with two nucleons from ${}^{3} \text{He}$. Then, this almost on-shell $\bar{K}$ can bring a signal of the $\bar{K} N N$ bound state in the $\Lambda p$ invariant-mass spectrum, although it inevitably brings a kinematic peak above the $\bar{K} N N$ threshold as well. As a consequence, we predict two peaks across the $\bar{K} N N$ threshold in the spectrum: the lower peak coming from the $\bar{K} N N$ bound state, and the higher one originating from the kinematics., Comment: 4 pages, 4 EPS figures, talk given at XVII International Conference on Hadron Spectroscopy and Structure (Hadron2017), Salamanca, Spain, 25-29 September, 2017

We theoretically investigate a possibility of an $\eta ^{\prime} d$ bound state and its formation in the $\gamma d \to \eta d$ reaction. First, in the fixed center approximation to the Faddeev equations we obtain an $\eta ^{\prime} d$ bound state with a binding energy of 25 MeV and width of 19 MeV, where we take the $\eta ^{\prime} N$ interaction with a coupling to the $\eta N$ channel from the linear $\sigma$ model. Then, in order to investigate the feasibility from an experimental point of view, we calculate the cross section of the $\gamma d \to \eta d$ reaction at the photon energy in the laboratory frame around 1.2 GeV. As a result, we find a clear peak structure with the strength $\sim$ 0.2 nb/sr, corresponding to a signal of the $\eta ^{\prime} d$ bound state in case of backward $\eta$ emission. This structure will be prominent because a background contribution coming from single-step $\eta$ emission off a bound nucleon is highly suppressed. In addition, the signal can be seen even in case of forward $\eta$ emission as a bump or dip, depending on the relative phase between the bound-state formation and the single-step background., Comment: 9 pages, 13 eps figures, version accepted for publication in PRC, description of the discussion part is improved

Recently a peak structure was observed near the $K^{-} p p$ threshold in the in-flight ${}^{3} {\rm He} (K^{-} , \, \Lambda p) n$ reaction of the E15 experiment at J-PARC, which could be a signal of a $\bar{K} N N$ bound state. In order to investigate what is the origin of this peak, we calculate the cross section of this reaction, in particular based on the scenario that the $\bar{K} N N$ bound state is indeed generated and decays into $\Lambda p$. We find that the numerical result of the $\Lambda p$ invariant-mass spectrum in the $\bar{K} N N$ bound scenario is consistent with the J-PARC E15 data., Comment: 6 pages, 6 EPS figures, talk given at the 2nd Jagiellonian Symposium on Fundamental and Applied Subatomic Physics, Krakow, Poland, 4-9 June, 2017

Recently, the compositeness, defined as the norm of a two-body wave function for bound and resonance states, has been investigated to discuss the internal structure of hadrons in terms of hadronic molecular components. From the studies of the compositeness, it has been clarified that the two-body wave function of a bound state can be extracted from the residue of the scattering amplitude at the bound state pole. Of special interest is that the two-body wave function from the scattering amplitude is automatically normalized. In particular, while the compositeness is unity for energy-independent interactions, it deviates from unity for energy-dependent interactions, which can be interpreted as a missing-channel contribution. In this manuscript, we show the formulation of the two-body wave function from the scattering amplitude, evaluate the compositeness for several dynamically generated resonances such as $f_{0} (980)$, $\Lambda (1405)$, and $\Xi (1690)$, and investigate their internal structure in terms of the hadronic molecular components., Comment: 8 pages, 2 eps figures, talk given at the International Nuclear Physics Conference 2016 (INPC2016), Adelaide, Australia, 11-16 Sep. 2016

Heavy ion collisions (HIC) at high energies are excellent ways for producing heavy hadrons and composite particles. With upgraded detectors at RHIC and LHC, it has become possible to measure hadrons beyond their ground states. Therefore, HIC provide a new method for studying exotic hadrons that are either hadronic molecular states or compact multiquark systems. Because their structures are related to the fundamental properties of QCD, studying exotic hadrons is currently one of the most active areas of research in hadron physics. Experiments carried out at various accelerator facilities have indicated that some exotic hadrons may have already been produced. The present review is a summary of the current understanding of a selected set of exotic particle candidates that can be potentially measured in HIC. It also includes discussions on the production of exotic hadrons in HIC based on the coalescence and statistical models. A more detailed discussion leads to the conclusion that the yield of a hadron is typically an order of magnitude smaller when it is a compact multiquark state than that of an excited hadronic state with normal quark numbers and/or a molecular configuration. Attention is also given to some of the proposed heavy exotic hadrons that could be produced with sufficient abundance in HIC because of the significant numbers of charm and bottom quarks produced at RHIC and LHC, making it possible to study them in these experiments. Further included in the discussion are the general formalism for the coalescence model that involves resonance particles and its implication on the present estimated yield for resonance production. Finally, a review is given on recent studies to constrain the hadron-hadron interaction through correlation measurements in HIC and their implications on the interpretation and the possible existence of exotic states in hadronic interactions., Comment: 74 pages, 13 figures

We theoretically investigate the origin of the peak structure around the $K^{-} p p$ threshold observed in the in-flight ${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ reaction in the recent E15 experiment at J-PARC. For this purpose, we consider two scenarios to produce the peak. One is that the $\Lambda (1405)$ is generated but it does not correlate with $p$, and the uncorrelated $\Lambda (1405) p$ system subsequently decays into $\Lambda p$. The other one is that the $\bar{K} N N$ bound state is indeed generated and decays into $\Lambda p$. As a result, the experimental signal is qualitatively well reproduced in the $\bar{K} N N$ bound scenario, definitely discarding the uncorrelated $\Lambda (1405) p$ one., Comment: 5 pages, 9 EPS figures, talk given at the 14th International Conference on Meson-Nucleon Physics and the Structure of the Nucleon (MENU2016), Kyoto, Japan, 25-30 July. 2016

For a general two-body bound state in quantum mechanics, both in the stable and decaying cases, we establish a way to extract its two-body wave function in momentum space from the scattering amplitude of the constituent two particles. For this purpose, we first show that the two-body wave function of the bound state corresponds to the residue of the off-shell scattering amplitude at the bound state pole. Then, we examine our scheme to extract the two-body wave function from the scattering amplitude in several schematic models. As a result, the two-body wave functions from the Lippmann--Schwinger equation coincides with that from the Schr\"{o}dinger equation for an energy-independent interaction. Of special interest is that the two-body wave function from the scattering amplitude is automatically scaled; the norm of the two-body wave function, to which we refer as the compositeness, is unity for an energy-independent interaction, while the compositeness deviates from unity for an energy-dependent interaction, which can be interpreted to implement missing channel contributions. We also discuss general properties of the two-body wave function and compositeness for bound states in the schematic models., Comment: 18 pages, 14 eps files; version accepted for publication in PRC; Section IID is added to discuss the model dependence of the compositeness

We show that the $\Xi (1690)$ resonance can be dynamically generated in the $s$-wave $\bar{K} \Sigma$-$\bar{K} \Lambda$-$\pi \Xi$-$\eta \Xi$ coupled-channels chiral unitary approach. In our model, the $\Xi (1690)$ resonance appears near the $\bar{K} \Sigma$ threshold as a $\bar{K} \Sigma$ molecular state and the experimental data are reproduced well. We discuss properties of the dynamically generated $\Xi (1690)$., Comment: 4 pages, 4 EPS figures, talk given at the 12th International Conference on Hypernuclear and Strange Particle Physics (HYP2015), Tohoku, Japan, 7-12 Sep. 2015

A theoretical investigation is done to clarify the origin of the peak structure observed near the $K^{-} p p$ threshold in the in-flight ${}^{3}\text{He} ( K^{-}, \, \Lambda p ) n$ reaction of the J-PARC E15 experiment, which could be a signal of the lightest kaonic nuclei, that is, the $\bar{K} N N (I=1/2)$ state. For the investigation, we evaluate the $\Lambda p$ invariant mass spectrum assuming two possible scenarios to interpret the experimental peak. One assumes that the $\Lambda (1405)$ resonance is generated after the emission of an energetic neutron from the absorption of the initial $K^-$, not forming a bound state with the remaining proton. This uncorrelated $\Lambda (1405) p$ system subsequently decays into the final $\Lambda p$. The other scenario implies that, after the emission of the energetic neutron, a $\bar{K} N N$ bound state is formed, decaying eventually into a $\Lambda p$ pair. Our results show that the experimental signal observed in the in-flight ${}^{3}\text{He} ( K^{-} , \, \Lambda p ) n$ reaction at J-PARC is qualitatively well reproduced by the assumption that a $\bar{K} N N$ bound state is generated in the reaction, definitely discarding the interpretation in terms of an uncorrelated $\Lambda (1405) p$ state., Comment: 27 pages, 18 EPS figures, version accepted for publication in PTEP, discussions on numerical results improved

Possibilities of observing a signal of an $\eta ^{\prime} n$ bound state are investigated by considering photoproductions of the $\eta$ and $\eta ^{\prime}$ mesons on a deuteron target with forward proton emission. For this purpose, we take the $\eta ^{\prime} n$ interaction from the linear sigma model with a coupling to $\eta n$, in which an $s$-wave $\eta ^{\prime} n$ bound state can be dynamically generated, and we fix the $\gamma p \to \eta p$ and $\eta ^{\prime} p$ scattering amplitudes so as to reproduce the experimental cross sections with forward proton emission. By using these $\gamma p \to \eta ^{( \prime )} p$ and $\eta ^{( \prime )} n \to \eta ^{( \prime )} n$ amplitudes, we calculate cross sections of the $\gamma d \to \eta n p$ and $\eta ^{\prime} n p$ reactions with forward proton emission in single and $\eta ^{(\prime )}$-exchange double scattering processes. As a result, we find that the signal of the $\eta ^{\prime} n$ bound state can be seen below the $\eta ^{\prime} n$ threshold in the $\eta n$ invariant mass spectrum of the $\gamma d \to \eta n p$ reaction and is comparable with the contribution from the quasifree $\eta ^{\prime}$ production above the $\eta ^{\prime} n$ threshold. We also discuss the behavior of the signal of the $\eta ^{\prime} n$ bound state in several experimental conditions and model parameters., Comment: 11 pages, 15 EPS figures, version accepted for publication in PRC, a numerical error in Fig. 10 corrected, discussion on the eta^prime N amplitude improved

In this review we give a perspective of the theoretical work done recently on the interpretation of results from $B$, $D$, $\Lambda_b$, $\Lambda_c$ weak decays into final states that contain interacting hadrons, and how it is possible to obtain additional valuable information that is increasing our understanding of hadron interactions and the nature of many hadronic resonances. The novelty of these processes is that one begins with a clean picture at the quark level which allows one to select the basic mechanisms by means of which the process proceeds. Finally, one has a final state described in terms of quarks. To make contact with the experiments, where mesons and baryons are observed, one must hadronize, creating pairs of $q \bar q$ and writing the new states in terms of mesons and baryons. This concludes the primary hadron production in these processes. After that, the interaction of these hadrons takes place, offering a rich spectrum of resonances and special features from where it is possible to learn much about the interaction of these hadrons and the nature of many resonances in terms of the components of their wave functions., Comment: Review paper comissioned for International Journal of Modern Physics E

We analyze the CLAS data on the photoproduction of hyperon resonances, as well as the available data for the ground state $\Lambda$ and $\Sigma ^{0}$ of the CLAS and SLAC-E84 collaborations, by considering constituent-counting rule suggested by perturbative QCD. The counting rule emerges as a scaling behavior of cross sections in hard exclusive reactions with large scattering angles, and it enables us to determine the number of elementary constituents inside hadrons. Therefore, it could be used as a new method for identifying internal constituents of exotic-hadron candidates. From the analyses of the $\gamma \, p \to K^{+} \Lambda$ and $K^{+} \Sigma ^{0}$ reactions, we find that the number of the elementary constituents is consistent with $n_{\gamma} = 1$, $n_{p} = 3$, $n_{K^{+}} = 2$, and $n_{\Lambda} = n_{\Sigma ^{0}} = 3$. Then, the analysis is made for the photoproductions of the hyperon resonances $\Lambda (1405)$, $\Sigma (1385)^{0}$, and $\Lambda (1520)$, where $\Lambda (1405)$ is considered to be a $\bar K N$ molecule and hence its constituent number could be five. However, we find that the current data are not enough to conclude the numbers of their constituent. It is necessary to investigate the higher-energy region at $\sqrt{s} > 2.8$ GeV experimentally beyond the energy of the available CLAS data for counting the number of constituents clearly. We also mention that our results indicate energy dependence in the constituent number, especially for $\Lambda (1405)$. If an excited hyperon is a mixture of three-quark and five-quark states, the energy dependence of the scaling behavior could be valuable for finding its composition and mixture., Comment: 7 pages, 9 eps figures, version accepted for publication in PRD, discussions improved

We present a formulation of the compositeness for baryonic resonances in order to discuss the meson-baryon molecular structure inside the resonances. For this purpose, we derive a relation between the residue of the scattering amplitude at the resonance pole position and the two-body wave function of the resonance in a sophisticated way, and we define the compositeness as the norm of the two-body wave functions. As applications, we investigate the compositeness of the $\Delta (1232)$, $N (1535)$, and $N (1650)$ resonances from precise $\pi N$ scattering amplitudes in a unitarized chiral framework with the interaction up to the next-to-leading order in chiral perturbation theory. The $\pi N$ compositeness for the $\Delta (1232)$ resonance is evaluated in the $\pi N$ single-channel scattering, and we find that the $\pi N$ component inside $\Delta (1232)$ in the present framework is nonnegligible, which supports the previous work. On the other hand, the compositeness for the $N (1535)$ and $N (1650)$ resonances is evaluated in a coupled-channels approach, resulting that the $\pi N$, $\eta N$, $K \Lambda$ and $K \Sigma$ components are negligible for these resonances., Comment: 23 pages, 7 eps figures, version accepted for publication in PRC, discussions improved

We evaluate the $\pi N$ compositeness of the $\Delta (1232)$ resonance so as to clarify the internal structure of $\Delta (1232)$ in terms of the $\pi N$ component. Here the compositeness is defined as contributions from two-body wave functions to the normalization of the total wave function and is extracted from the $\pi N$ scattering amplitude. In this study we employ the chiral unitary approach with the interaction up to the next-to-leading order plus a bare $\Delta$ term in chiral perturbation theory and describe $\Delta (1232)$ in an elastic $\pi N$ scattering. Fitting the $\pi N$ scattering amplitude to the solution of the partial wave analysis, we obtain a large real part of the $\pi N$ compositeness for $\Delta (1232)$ comparable to unity and non-negligible imaginary part as well, with which we reconfirm the result in the previous study on the $\pi N$ compositeness for $\Delta (1232)$., Comment: 4 pages, 1 eps figure, talk given at the 10th International Workshop on the Physics of Excited Nucleons (NSTAR2015), Osaka, Japan, 25-28 May 2015

We study the semileptonic decays of $D_{s}^{+}$, $D^{+}$, and $D^{0}$ mesons into the light scalar mesons [$f_{0} (500)$, $K_{0}^{\ast} (800)$, $f_{0} (980)$, and $a_{0}(980)$] and the light vector mesons [$\rho (770)$, $\omega (782)$, $K^{\ast} (892)$, and $\phi (1020)$]. With the help of a chiral unitarity approach in coupled channels, we compute the branching fractions for scalar meson processes of the semileptonic $D$ decays in a simple way. Using current known values of the branching fractions, we make predictions for the branching fractions of the semileptonic decay modes with other scalar and vector mesons. Furthermore, we calculate the $\pi ^{+} \pi ^{-}$, $\pi \eta$, $\pi K$, and $K^{+} K^{-}$ invariant mass distributions in the semileptonic decays of $D$ mesons, which will help us clarify the nature of the light scalar mesons., Comment: 17 pages, 11 eps figures, version accepted for publication in PRD, several references added

We show that a $\Xi ^{\ast}$ pole can be dynamically generated near the $\bar{K} \Sigma$ threshold as an $s$-wave $\bar{K} \Sigma$ molecular state in a coupled-channels unitary approach with the leading-order chiral interaction. This $\Xi ^{\ast}$ state can be identified with the $\Xi (1690)$ resonance with $J^{P} = 1/2^{-}$. We find that the experimental $\bar{K}^{0} \Lambda$ and $K^{-} \Sigma ^{+}$ mass spectra are qualitatively reproduced with the $\Xi ^{\ast}$ state. Moreover we theoretically investigate properties of the dynamically generated $\Xi ^{\ast}$ state., Comment: 10 pages, 3 eps files, version accepted for publication in PTEP

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 Weinberg's 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., Comment: 34 pages, 1 figure, version accepted for publication in PTEP