Dynamical generation of resonances in the P33 partial wave

Abstract

We investigate the formation of resonances in the P33 partial wave with the emphasis on possible emergence of dynamically generated quasi-bound states as a consequence of a strong $p$-wave pion attractive interaction in this partial wave, as well as their possible interaction with the genuine quark excited states. By using the Laurent-Pietarinen expansion we follow the evolution of the $S$-matrix poles in the complex energy plane as a function of the interaction strength. Already without introducing a genuine quark resonant state, two physically interesting resonances emerge with pole masses around 1200 MeV and 1400 MeV, with the dominant $\pi N$ and $\pi \Delta$ component, respectively. The added genuine resonant state in the $(1s{)}^3$ quark configuration mixes with the lower dynamically generated resonance forming the physical $\Delta (1232)$ resonance, and pushes the second dynamical resonance to around 1500 MeV, which allows it to be identified with the $\Delta (1600)$ resonance. Adding a second resonant state with one quark promoted to the $2s$ orbit generates another pole whose evolution remains well separated from the lower two poles. We calculate the helicity amplitudes at the pole and suggest that their $Q^2$ dependence could be a decisive test to discriminate between different models of the $\Delta (1600)$ resonance.

10 pages, 10 figures, to be published in Phys. Rev. C

References in corpus (8)

• Unitary Isobar Model - MAID2007
• Extended Partial-Wave Analysis of piN Scattering Data
• Pion-nucleon scattering in the Roper channel from lattice QCD
• Transition form factors: ${\gamma }^{\ast }+p\to \Delta (1232)$, $\Delta (1600)$
• Pole positions and residues from pion photoproduction using the Laurent+Pietarinen expansion method
• Roper resonances in chiral quark models
• Pole structure from energy-dependent and single-energy fits to $\pi N$ elastic scattering data
• The Roper resonance: a genuine quark state or a dynamically generated structure?

Cited by in corpus (3)

• Electromagnetic Transition Form Factors of Baryon Resonances
• Two-body wave functions and compositeness from scattering amplitudes: II. Application to the physical $N^{\ast }$ and ${\Delta }^{\ast }$ resonances
• The $\Lambda (1405)$ resonance as a genuine three-quark or molecular state