Dynamical coupled-channels effects on pion photoproduction

The electromagnetic pion production reactions are investigated within the dynamical coupled-channels model developed by Matsuyama, Sato, and Lee [Phys. Rep. 439, 193 (2007)]. The meson-baryon channels included in this study are $\gamma N,\pi N,\eta N$, and the $\pi \Delta ,\rho N$, and $\sigma N$ resonant components of the $\pi \pi N$ channel. With the hadronic parameters of the model determined in a recent study of $\pi N$ scattering, we show that the pion photoproduction data up to the second resonance region can be described to a very large extent by only adjusting the bare $\gamma N\to N^{*}$ helicity amplitudes, while the nonresonant electromagnetic couplings are taken from previous works. It is found that the coupled-channels effects can contribute about 30–40 % of the production cross sections in the Δ (1232) resonance region, and can drastically change the magnitude and shape of the cross sections in the second resonance region. The importance of the loop-integrations in a dynamical approach is also demonstrated. The meson cloud effects as well as the coupled-channels contributions to the $\gamma N\to N^{*}$ form factors are found to be mainly in the low $Q^2$ region. Necessary improvements to the model and future developments are discussed.

Figure 1

The nonresonant electromagnetic meson production interaction $v_{\mathit{MB},\gamma N}$, where $\mathit{MB}=\pi N,\eta N,\pi \Delta ,\rho N,\sigma N$. The details are given in Ref. [3].

Figure 2

Graphical illustration of the contribution to the $\pi N$ intermediate state to the dressed $\gamma N\to N^{*}$ vertex defined by Eq. (8).

Figure 3

Differential cross section for $\gamma p\to {\pi }^{0}p$ compared to experimental data obtained from Ref. [28].

Figure 4

Differential cross section for $\gamma p\to {\pi }^{+}n$ compared to experimental data obtained from Ref. [28].

Figure 5

Photon asymmetry, ${\Sigma }_{\gamma }$, for $\gamma p\to {\pi }^{0}p$ compared to experimental data obtained from Ref. [28].

Figure 6

Photon asymmetry, ${\Sigma }_{\gamma }$, for $\gamma p\to {\pi }^{+}n$ compared to experimental data obtained from Ref. [28].

Figure 7

Total cross sections. The dashed curves are obtained from turning off all $\mathit{MB}$ channels except the $\pi N$ channel in the the loop integrations in the nonresonant amplitude defined by Eq. (5) and the dressed $\gamma N\to N^{*}$ vertex defined by Eq. (8). The dotted curve is obtained by neglecting the loop-integrations in the $\pi N$ only calculation. Experimental data obtained using Ref. [28]. The diamonds correspond to the SAID solution [20].

Figure 8

Coupled-channels effects on $d\sigma /d\Omega$ at $\mathrm{W}=1.23$, 1.30, 1.54 GeV. The dashed curves are obtained from turning off all $\mathit{MB}$ channels except the $\pi N$ channel in the the loop integrations in the nonresonant amplitude defined by Eq. (5) and the dressed $\gamma N\to N^{*}$ vertex defined by Eq. (8). The dotted curve is obtained by neglecting the loop integrations in the $\pi N$ only calculation. Right-hand side: $\gamma p\to {\pi }^{0}p$, left-hand side: $\gamma p\to {\pi }^{+}n$. The lowest right panel at $W=1544$ MeV includes two additional curves: (a) dot-dashed curve is from including $\pi N$ and $\rho N$ channels, (b) dot-dot-dashed curve is from including $\pi N,\rho N$, and $\pi \Delta$ channels.

Figure 9

The predicted $Q^2$-dependence of meson cloud contributions to the magnetic $M1$ form factor $G_M^{*}$ defined in Ref. [11] and $G_D(Q^2)=1/[1+Q^2/(0.71\hspace{1em}(\mathrm{GeV}/c){}^2)]{}^2$. The dashed curve is the predicted full meson cloud contribution. The dotted curve is obtained after turning off the coupled-channels effects due to $\pi \Delta$ and $\rho N$ channels in the loop integrations of Eq. (8). The solid circle at $Q^2=0$ is the bare value in the fit. The data are compiled in Ref. [19]. The solid curve along the data is mainly to guide the eyes.

Figure 10

The predicted $Q^2$-dependence of meson cloud contributions to the helicity amplitudes ${\overline{A}}_{\lambda }^J$. The dotted curves are from keeping only the π-loop in Eq. (8). The black dot corresponds to the absolute value of the bare helicities listed in Table .