Dynamical study of $πN\to ππN$ reactions revisited

TL;DR

This work uses the ANL-Osaka dynamical coupled-channel framework, fitted to two-body meson-nucleon data, to predict the cross sections and distributions for $πN\to ππN$ across a wide energy range. By decomposing the reaction into quasi-two-body channels $πΔ$, $ρN$, and $σN$ plus a direct term, the study identifies how $N^*$ couplings to these channels shape the observables and demonstrates where current single-meson data leave ambiguities in the high-mass resonance sector. Comparisons with existing data reveal overall qualitative agreement but systematic overestimation above $W\sim1.65$ GeV, pointing to needed refinements of $N^*\toπΔ$, $N^*\to ρN$, and $N^*\to σN$ couplings, especially in the Roper region and higher-mass states in the $S_{31}$, $P_{33}$, $D_{33}$, and $F_{37}$ partial waves. The paper provides a detailed sensitivity analysis that maps which observables and energy ranges are most effective for constraining $N^*$ parameters, offering practical guidance for upcoming J-PARC measurements of $πN\toππN$ and for improving the extraction of high-mass nucleon resonances.

Abstract

Using the Argonne National Laboratory-The University of Osaka (ANL-Osaka) DCC model of meson-nucleon reactions, we extend the study of Phys. Rev. C 79, 025206 (2009) and Phys. Rev. C 88, 045203 (2013) to predict the cross sections of the $πN \to ππN$ reactions. The model was constructed by fitting only the two-body reactions: $πN,γN \to πN, ηN, KΛ, KΣ$. Thus, the results for $πN \to ππN$ presented here are predictions of the ANL-Osaka DCC model, which serve to examine the extent to which the forthcoming data from J-PARC can be described. This study provides information for improving the extraction of nucleon resonances that have large decay widths to $ππN$ states. We present results for the total cross sections, invariant mass distributions, and angular distributions. We also identify the observables and energy regions where the higher mass nucleon resonances in the $S_{31}$, $P_{33}$, $D_{33}$, $F_{37}$, $D_{13}$, $D_{15}$, and $F_{15}$ partial waves can be most effectively investigated.

Figures (28)

• Figure 1: Schematic representation of the $\pi N \to \pi\pi N$ reaction mechanisms. The figure is from Ref. ao13-2.
• Figure 2: Total cross sections of (a) $\pi^+ p \to \pi^+\pi^+ n$, (b) $\pi^+p \to \pi^+\pi^0p$, (c) $\pi^- p \to \pi^+\pi^- n$, (d) $\pi^-p \to \pi^0\pi^0 n$, and (e) $\pi^- p \to \pi^-\pi^0 p$. Solid (red) curves are the full results; dashed (blue) curves are the results of $T^{\pi\Delta}$ process only; dash-dot (green) curves are the results of $T^{\rho N}$ process only; dash-dash-dot (indigo) curves are the results of $T^{\sigma N}$ process only; and dotted (black) curves are the results of $T^\textrm{dir}$ process only. See Refs. manleyao09-1 and references therein for the data.
• Figure 3: Contribution of each partial wave to the $\pi^+ p \to \pi \pi N$ total cross sections: (a) $\pi^+ p \to \pi^+ \pi^+ n$ and (b) $\pi^+ p \to \pi^+ \pi^0 p$. Solid curves are the full results, while dashed curves are contributions of each partial wave to the cross sections. See Refs. manleyao09-1 and references therein for the data.
• Figure 4: Contribution of each partial wave to the $\pi^- p \to \pi \pi N$ total cross sections. Panels (a) and (b) $\pi^- p \to \pi^+ \pi^- n$, (c) and (d) $\pi^- p \to \pi^0 \pi^0 n$, and (e) and (f) $\pi^- p \to \pi^-\pi^0 p$. Panels (a), (c), and (e) [(b), (d), and (f)] present $I=1/2$ [$I=/3/2$] partial waves. Solid curves are the full results, while dashed curves are contributions of each partial wave to the cross sections. See Refs. manleyao09-1 and references therein for the data.
• Figure 5: Comparison with the HADES data hades for the invariant mass distributions at $W=1487$ MeV ($p_{\textrm{in}}=685$ MeV/c with $p_{\textrm{in}}$ being pion beam momenta). Panels (a) and (b) are of $\pi^- p \to \pi^+\pi^- n$, and panels (c) and (d) are of $\pi^- p \to \pi^-\pi^0 p$. The meaning of each curve is the same as in Fig. \ref{['fig:tcrs']}