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arXiv · 1908.11750

Dynamical generation of resonances in the P33 partial wave

B. Golli·H. Osmanović·S. Širca
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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 $πN$ and $πΔ$ component, respectively. The added genuine resonant state in the $(1s)^3$ quark configuration mixes with the lower dynamically generated resonance forming the physical $Δ(1232)$ resonance, and pushes the second dynamical resonance to around 1500 MeV, which allows it to be identified with the $Δ(1600)$ 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 $Δ(1600)$ resonance.

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B. Golli, H. Osmanović, S. Širca. 2019-08-30. Dynamical generation of resonances in the P33 partial wave. https://doi.org/10.1103/physrevc.100.035204

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