The Roper resonance: a genuine quark state or a dynamically generated structure?
英文摘要：
In view of the recent results of lattice QCD simulation in the P11 partial wave that has found no clear signal for the three-quark Roper state we investigate a different mechanism for the formation of the Roper resonance in a coupled channel approach including the $πN$, $πΔ$ and $σN$ channels. We fix the pion-baryon vertices in the underlying quark model while the $s$-wave sigma-baryon interaction is introduced phenomenologically with the coupling strength, the mass and the width of the $σ$ meson as free parameters. The Laurent-Pietarinen expansion is used to extract the information about the $S$-matrix pole. The Lippmann-Schwinger equation for the $K$ matrix with a separable kernel is solved to all orders. For sufficiently strong $σNN$ coupling the kernel becomes singular and a quasi-bound state emerges at around 1.4~GeV, dominated by the $σN$ component and reflecting itself in a pole of the $S$-matrix. The alternative mechanism involving a $(1s)^22s$ quark resonant state is added to the model and the interplay of the dynamically generated state and the three-quark resonant state is studied. It turns out that for the mass of the three-quark resonant state above 1.6~GeV the mass of the resonance is determined solely by the dynamically generated state, nonetheless, the inclusion of the three-quark resonant state is imperative to reproduce the experimental width and the modulus of the resonance pole.
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