Impact of $\pi N\to \pi \pi N$ data on determining high-mass nucleon resonances

Motivated by an experimental proposal for the measurement of the $\pi N\to \pi \pi N$ reactions at J-PARC, we examine the potential impact of the $\pi N\to \pi \pi N$ cross section data on the determination of the resonance parameters of the high-mass $N^{*}$ states. For this purpose, we make use of the ANL-Osaka dynamical coupled-channels model, which has been developed recently through a combined analysis of the unpolarized cross section as well as polarized observables from pion- and photon-induced $\pi N$, $\eta N$, $K\Lambda$, and $K\Sigma$ production reactions off a proton target. We present predictions for the $\pi N\to \pi \pi N$ total cross sections and invariant mass distributions, and demonstrate that the $\pi N\to \pi \pi N$ differential cross section data can indeed be a crucial source of information for understanding $N^{*}\to \pi \Delta ,\rho N,\sigma N\to \pi \pi N$ decay of the high-mass $N^{*}$ states.

Figure 1

Graphical representation of Eq. (1).

Figure 2

The $\pi N\to \pi \pi N$ total cross sections predicted with the ANL-Osaka DCC models. The red solid curves are from our new model recently developed in Ref. [8], while the green dotted curves are from our early model [2]. The reaction channels are for (a) ${\pi }^{+}p\to {\pi }^{+}{\pi }^{+}n$, (b) ${\pi }^{+}p\to {\pi }^{+}{\pi }^{0}p$, (c) ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$, (d) ${\pi }^{-}p\to {\pi }^0{\pi }^{0}n$, and (e) ${\pi }^{-}p\to {\pi }^{-}{\pi }^{0}p$. See Refs. [1, 2] 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) ${\pi }^{+}p\to {\pi }^{+}{\pi }^{0}p$. The total cross section and the individual partial wave contributions are shown as thick-solid and dashed curves, respectively. See Refs. [1, 2] and references therein for the data.

Figure 4

Contribution of each partial wave to the ${\pi }^{-}p\to \pi \pi N$ total cross sections. (a) and (b) ${\pi }^{-}p\to {\pi }^{+}{\pi }^{-}n$; (c) and (d) ${\pi }^{-}p\to {\pi }^0{\pi }^{0}n$; (e) and (f) ${\pi }^{-}p\to {\pi }^{-}{\pi }^{0}p$. (a), (c), and (e) [(b), (d), and (f)] present $I=1/2$ [$I=3/2$] partial waves for each reaction. The total cross section and the individual partial wave contributions are shown as thick-solid and dashed curves, respectively. See Refs. [1, 2] and references therein for the data.

Figure 5

$F_{37}$ $\pi N$ partial wave amplitude. Solid (red) curves are from the original DCC model [8]; dashed (blue) curves show the refitted DCC model. The data points are from the SAID energy-independent solution [17].

Figure 6

Comparison of the ${\pi }^{+}p\to {\pi }^{+}{\pi }^{+}n$ cross sections: (a) total cross section; the invariant mass distributions of (b) ${\pi }^{+}{\pi }^{+}$ and (c) ${\pi }^{+}n$ at $W=1.87$ GeV. Solid (red) curves are the original DCC; dashed (blue) curves are the refitted DCC. See Refs. [1, 2] and references therein for the total cross section data.

Figure 7

Comparison of the ${\pi }^{+}p\to {\pi }^{+}{\pi }^{0}p$ cross sections: (a) total cross section; the invariant mass distributions of (b) ${\pi }^{+}{\pi }^0$, (c) ${\pi }^{0}p$, and (d) ${\pi }^{+}p$ at $W=1.87$ GeV. Solid (red) curves are the original DCC; dashed (blue) curves are the refitted DCC. See Refs. [1, 2] and references therein for the total cross section data.