Decays of $N^*$ and $Δ^*$ resonances into $Nρ$, $Δπ$, and $Nσ$

TL;DR

The paper tackles the problem of mapping the decay patterns of $N^*$ and $\Delta^*$ resonances into $N\rho$, $\Delta\pi$, and $Nf_0(500)$ final states using a comprehensive coupled-channel analysis of pion- and photo-induced two-pion production data. It adopts the Bonn-Gatchina PWA framework with a covariant $D$-matrix and a $P$-vector treatment for photoproduction, integrating two-body and quasi-three-body channels and a detailed three-body phase-space treatment. The analysis yields resonance pole positions, Breit-Wigner parameters, helicity amplitudes, and branching ratios for 36 resonances, revealing substantial decays into the three intermediate states and highlighting several high-mass BRs that differ from PDG expectations. Uncertainty assessments are performed by varying data weights, model space, and external amplitudes, demonstrating robustness while acknowledging ambiguities in the high-mass region. Overall, the work advances light-quark baryon spectroscopy by constraining decay dynamics of $N^*$ and $\Delta^*$ and showcasing the power of large-scale, polarization-enabled coupled-channel analyses.

Abstract

The decays of $N^*$ and $Δ^*$ resonances into $Nρ$, $Δπ$ and $Nσ$ final states are studied in a coupled-channel analysis of data on pion- and photo-induced reactions. Improvements in the fit were observed when new resonance contributions were introduced. Frequencies for the intermediate isobars $Δ(1232)π$, $Nρ$, $Nσ$ are reported.

Figures (2)

• Figure 1: The number of 3* and 4* $N^*$ and $\Delta^*$ resonances in ParticleDataGroup:2024cfk above the ground states in 50 MeV bins. The arrows mark the mass range for the Dalitz plots shown below. The second, third, fourth, and fifth resonance regions are covered.
• Figure 2: (top) CBELSA/TAPS data CBELSATAPS:2015kka on $\gamma p\to \pi^0\pi^0 p$ for different ranges of $\sqrt s$. (second row) CLAS data CLAS:2024iir on $\gamma p\to \pi^+\pi^- p$. (third and fourth row, left) BNL data CrystalBall:2004qln on $\pi^- p\to \pi^0\pi^0 n$, (middle) HADES data HADES:2020kce on $\pi^- p\to \pi^+\pi^- n$, (right) HADES data HADES:2020kce on $\pi^- n\to \pi^0\pi^- n$. BNL has reported data for six mass ranges, HADES for four ranges, the lowest and highest mass ranges are shown. The data are shown without acceptance correction and flux normalization.