The Roper resonance: a genuine quark state or a dynamically generated structure?

摘要

In view of the recent results of lattice QCD simulation in the P11 partialwave that has found no clear signal for the three-quark Roper state weinvestigate a different mechanism for the formation of the Roper resonance in acoupled channel approach including the $\pi N$, $\pi\Delta$ and $\sigma N$channels. We fix the pion-baryon vertices in the underlying quark model whilethe s-wave sigma-baryon interaction is introduced phenomenologically with thecoupling strength, the mass and the width of the $\sigma$ meson as freeparameters.The Laurent-Pietarinen expansion is used to extract the informationabout the $S$-matrix pole. The Lippmann-Schwinger equation for the $K$ matrixwith a separable kernel is solved to all orders. For sufficiently strong$\sigma NN$ coupling the kernel becomes singular and a quasi-bound stateemerges at around 1.4 GeV, dominated by the $\sigma N$ component and reflectingitself 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 thedynamically generated state and the three-quark resonant state is studied. Itturns out that for the mass of the three-quark resonant state above 1.6 GeV themass of the resonance is determined solely by the dynamically generated state,nonetheless, the inclusion of the three-quark resonant state is imperative toreproduce the experimental width and the modulus of the resonance pole.