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

Abstract

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 $\pi N$, $\pi \Delta$ and $\sigma N$ 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 $\sigma$ 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 $\sigma NN$ coupling the kernel becomes singular and a quasi-bound state emerges at around 1.4~GeV, dominated by the $\sigma N$ component and reflecting itself in a pole of the $S$-matrix. The alternative mechanism involving a $(1s{)}^{2}2s$ 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.

11 pages, 11 figures; two figures added with some minor modifications of the text. To be published in Phys. Rev. C

References in corpus (10)

• Extended Partial-Wave Analysis of piN Scattering Data
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Electroexcitation of the Roper resonance in the relativistic quark models
• Hamiltonian effective field theory study of the ${\mathbf{N}}^{\ast }(1440)$ resonance in lattice QCD
• Empirical transverse charge densities in the nucleon-to-P11(1440) transition
• Electroproduction of the Roper resonance on the proton: the role of the three-quark core and the molecular N-sigma component
• Pole positions and residues from pion photoproduction using the Laurent+Pietarinen expansion method
• Chiral corrections to the Roper mass
• Roper resonances in chiral quark models
• Wilson coefficients and four-quark condensates in QCD sum rules for medium modifications of $D$ mesons

Cited by in corpus (9)

• Nucleon-to-Roper electromagnetic transition form factors at large-$Q^2$
• Electromagnetic Transition Form Factors of Baryon Resonances
• Transition form factors: ${\gamma }^{\ast }+p\to \Delta (1232)$, $\Delta (1600)$
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• The Roper Resonance in a finite volume
• A lattice QCD study of pion-nucleon scattering in the Roper channel
• Dynamical generation of resonances in the P33 partial wave
• Nucleon-to-Resonance Form Factors at Large Photon Virtualities
• The $\Lambda (1405)$ resonance as a genuine three-quark or molecular state