Genuine quark state versus dynamically generated structure for the Roper resonance
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, πDelta, 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 quasibound 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.