Hadronic few-body systems in chiral dynamics, -- Few-body systems in hadron physics --

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 $\bar KK$.Comment: 8 pages, 2 figures, contribution to 20th International IUPAP Conference on Few-Body Problems in Physics (FB20), 20-25 August 2011, Fukuoka, Japa

QCD Sum Rules and 1/NcN_c expansion

The 1/$N_c$ arguments are developed to classify the hadronic states in the correlators. Arguments applied to the $\sigma$ meson correlator enable to separate the instanton, glueball, and, in particular, the $\pi\pi$ scattering states by $1/N_c$ from both 2q and 4q correlators. The bare resonance pole with no mixing effects are analyzed with the QCD sum rules (QSR). The results suggest the existence of nontrivial correlation for the mass reduction of 4q system.Comment: Presented at at YITP International Symposium Fundamental Problems in Hot and / or Dense QCD, Kyoto, Japan, 3-6 Mar 200

Pion properties at finite nuclear density based on in-medium chiral perturbation theory

The in-medium pion properties, {\it i.e.} the temporal pion decay constant $f_t$, the pion mass $m_\pi^*$ and the wave function renormalization, in symmetric nuclear matter are calculated in an in-medium chiral perturbation theory up to the next-to-leading order of the density expansion $O(k_F^4)$. The chiral Lagrangian for the pion-nucleon interaction is determined in vacuum, and the low energy constants are fixed by the experimental observables. We carefully define the in-medium state of the pion and find that the pion wave function plays an essential role for the in-medium pion properties. We show that the linear density correction is dominated and the next-leading corrections is not so large at the saturation density, while their contributions can be significant in higher densities. The main contribution of the next-leading order comes from the double scattering term. We also discuss whether the low energy theorems, the Gell-Mann--Oakes--Renner relation and the Glashow--Weinberg relation, are satisfied in nuclear medium beyond the linear density approximation. We find also that the wave function renormalization is enhanced as largely as $50\%$ at the saturation density including the next-leading contribution and the wave function renormalization could be measured in the in-medium $\pi^0\to \gamma\gamma$ decay.Comment: 26 pages, 5 figure