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Recently, many efforts are being put in studying three-hadron systems made of mesons and baryons and interesting results are being found. In this talk, I summarize the main features of the formalism used to study such three hadron systems with strangeness $S=-1,0$ within a framework built on the basis of unitary chiral theories and solution of the Faddeev equations. In particular, I present the results obtained for the $pibar{K}N$, $Kbar{K}N$ and $KKbar{K}$ systems and their respective coupled channels. In the first case, we find four $Sigma$s and two $Lambda$s with spin-parity $J^P=1/2^+$, in the 1500-1800 MeV region, as two meson-one baryon s-wave resonances. In the second case, a $1/2^+$ $N^*$ around 1900 MeV is found. For the last one a kaon close to 1420 MeV is formed, which can be identified with K(1460).
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We review the status as regards the existence of three- and four-body bound states made of neutrons and $Lambda$ hyperons. For interesting cases, the coupling to neutral baryonic systems made of charged particles of different strangeness has been addressed. There are strong arguments showing that the $Lambda nn$ system has no bound states. $LambdaLambda nn$ strong stable states are not favored by our current knowledge of the strangeness $-1$ and $-2$ baryon-baryon interactions. However, a possible $Xi^- t$ quasibound state decaying to $LambdaLambda nn$ might exist in nature. Similarly, there is a broad agreement about the nonexistence of $LambdaLambda n$ bound states. However, the coupling to $Xi NN$ states opens the door to a resonance above the $LambdaLambda n$ threshold.
Hadronic composite states are introduced as few-body systems in hadron physics. The $Lambda(1405)$ resonance is a good example of the hadronic few-body systems. It has turned out that $Lambda(1405)$ can be described by hadronic dynamics in a modern technology which incorporates coupled channel unitarity framework and chiral dynamics. The idea of the hadronic $bar KN$ composite state of $Lambda(1405)$ is extended to kaonic few-body states. It is concluded that, due to the fact that $K$ and $N$ have similar interaction nature in s-wave $bar K$ couplings, there are few-body quasibound states with kaons systematically just below the break-up thresholds, like $bar KNN$, $bar KKN$ and $bar KKK$, as well as $Lambda(1405)$ as a $bar KN$ quasibound state and $f_{0}(980)$ and $a_{0}(980)$ as $bar KK$.
We show that the contributions of three-quasiparticle interactions to normal Fermi systems at low energies and temperatures are suppressed by n_q/n compared to two-body interactions, where n_q is the density of excited or added quasiparticles and n is the ground-state density. For finite Fermi systems, three-quasiparticle contributions are suppressed by the corresponding ratio of particle numbers N_q/N. This is illustrated for polarons in strongly interacting spin-polarized Fermi gases and for valence neutrons in neutron-rich calcium isotopes.
In this talk we show recent developments on few body systems involving mesons. We report on an approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two body off shell amplitude with three body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on shell two body amplitudes need to be used. Within this approach, systems of two mesons and one baryon are studied, reproducing properties of the low lying $1/2^+$ states. On the other hand we also report on multirho and $K^*$ multirho states which can be associated to known meson resonances of high spin.
We evaluate the mass polarization term of the kinetic-energy operator for different three-body nuclear $AAB$ systems by employing the method of Faddeev equations in configuration space. For a three-boson system this term is determined by the difference of the doubled binding energy of the $AB$ subsystem $2E_{2}$ and the three-body binding energy $E_{3}(V_{AA}=0)$ when the interaction between the identical particles is omitted. In this case: $leftvert E_{3}(V_{AA}=0)rightvert >2leftvert E_{2}rightvert$. In the case of a system complicated by isospins(spins), such as the kaonic clusters $ K^{-}K^{-}p$ and $ppK^{-}$, the similar evaluation impossible. For these systems it is found that $leftvert E_{3}(V_{AA}=0)rightvert <2leftvert E_{2}rightvert$. A model with an $AB$ potential averaged over spin(isospin) variables transforms the later case to the first one. The mass polarization effect calculated within this model is essential for the kaonic clusters. Besides we have obtained the relation $|E_3|le |2E_2|$ for the binding energy of the kaonic clusters.
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