Degenerate two-body and three-body coupled-channels systems: Renormalized effective Alt-Grassberger-Sandhas equations and near-threshold resonances
作者： Atsunari Konishi , Osamu Morimatsu , Shigehiro Yasui
DOI: 10.1103/PHYSREVC.97.064001
关键词: Hadron 、 Eigenvalues and eigenvectors 、 Gravitational singularity 、 Energy (signal processing) 、 Physics 、 Singularity 、 Exotic hadron 、 Quantum mechanics 、 Renormalization 、 Degenerate energy levels
摘要: Motivated by the existence of candidates for exotic hadrons whose masses are close to both two-body and three-body hadronic thresholds lying each other, we study degenerate coupled-channel systems. We first formulate scattering problem non-degenerate coupled-channels as an effective problem, i.e.\ Alt-Grassberger-Sandhas (AGS) equations. next investigate behavior $S$-matrix poles near threshold when degenerate. solve eigenvalue equations kernel AGS instead themselves obtain pole energy. then face a unphysical singularity: though physical transition amplitudes have singularities only, singularities. show, however, that these can be removed appropriate reorganization mass renormalization. The is found universal in sense complex energy, $E$, determined real parameter, $c$, $c - E \log{\left( \right)} = 0$, or equivalently, ${\rm Im} \pi {\rm Re} / \log{\mid \mid}$. This different from either system characteristic system. expect this new class might play key role understanding hadrons.
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