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Register a new userTwo-body Wave Functions, Compositeness, And The Internal Structure Of Dynamically Generated Resonances
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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.
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The $rhorho$ interaction and the corresponding dynamically generated bound states are revisited. We demonstrate that an improved unitarization method is necessary to study the pole structures of amplitudes outside the near-threshold region. In this work, we extend the study of the covariant $rhorho$ scattering in a unitarized chiral theory to the $S$-wave interactions for the whole vector-meson nonet. We demonstrate that there are unphysical left-hand cuts in the on-shell factorization approach of the Bethe-Salpeter equation. This is in conflict with the correct analytic behavior and makes the so-obtained poles, corresponding to possible bound states or resonances, unreliable. To avoid this difficulty, we employ the first iterated solution of the $N/D$ method and investigate the possible dynamically generated resonances from vector-vector interactions. A comparison with the results from the nonrelativistic calculation is provided as well.
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.
The interactions of $bar{D}Sigma_{c}$-$bar DLambda_c$, $bar{D}^{*}Sigma_{c}$-$bar D^*Lambda_c$, and related strangeness channels, are studied within the framework of the coupled channel unitary approach with the local hidden gauge formalism. A series of meson-baryon dynamically generated relatively narrow $N^*$ and $Lambda^*$ resonances are predicted around 4.3 GeV in the hidden charm sector. We make estimates of production cross sections of these predicted resonances in $bar{p} p $ collisions for PANDA at the forthcoming FAIR facility.
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 $Xi (1690)$.
In this talk I report on the recent developments in the subject of dynamically generated resonances. In particular I discuss the $gamma p to K^0 Sigma^+$ and $gamma n to K^0 Sigma^0$ reactions, with a peculiar behavior around the $K^{*0} Lambda$ threshold, due to a $1/2^-$ resonance around 2035 MeV. Similarly, I discuss a BES experiment, $J/psi to eta K^{*0} bar K^{*0}$ decay, which provides evidence for a new $h_1$ resonance around 1830 MeV that was predicted from the vector-vector interaction. A short discussion is then made about recent advances in the charm and beauty sectors.
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