Neutral pion photoproduction on the nucleon in a chiral quark model

A chiral quark-model approach is adopted to study the $\gamma p\to {\pi }^{0}p$ and $\gamma n\to {\pi }^{0}n$ reactions. Good descriptions of the total and differential cross sections and single-polarization observables are obtained from the pion production threshold up to the second resonance region. It is found that (i) the $n=0$ shell resonance $\mathrm{\Delta }\left(1232\right)P_{33}$, the $n=1$ shell resonances $N\left(1535\right)S_{11}$ and $N\left(1520\right)D_{13}$, and the $n=2$ shell resonance $N\left(1720\right)P_{13}$ play crucial roles in these two processes. They are responsible for the first, second, and third bump structures in the cross sections, respectively. (ii) Furthermore, obvious evidence of $N\left(1650\right)S_{11}$ and $\mathrm{\Delta }\left(1620\right)S_{31}$ is also found in the reactions. They notably affect the cross sections and the polarization observables from the second resonance region to the third resonance region. (iii) The $u$-channel background plays a crucial role in the reactions. It has strong interferences with the $s$-channel resonances. (iv) The $t$-channel background seems to be needed in the reactions. Including the $t$-channel vector-meson exchange contribution, the descriptions in the energy region $E_{\gamma }=600–900$ MeV are improved significantly. The helicity amplitudes of the main resonances, $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}, N\left(1720\right)P_{13}, N\left(1650\right)S_{11}$, and $\mathrm{\Delta }\left(1620\right)S_{31}$, are extracted and compared with the results from other groups.

Figure 1

Differential cross section of the $\gamma p\to {\pi }^{0}p$ reaction as a function of scattering angle. Data are taken from [4] (solid circles), [5] (solid squares), [75] (solid triangles), and [9] (open triangles). The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass (c.m.) energy $W$ (MeV), respectively.

Figure 2

Total cross section as a function of c.m. energy $W$ for the $\gamma p\to {\pi }^{0}p$ reaction. Data are taken from [9] (open circles), [76] (solid circles), and [72] (triangles). The results for switching off the contributions from $N\left(1650\right)S_{11}, \mathrm{\Delta }\left(1620\right)S_{31}$, and $t$ channel and the partial cross sections for $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}, N\left(1720\right)P_{13}$, and the $u$ channel are indicated explicitly by different legends in the figure.

Figure 3

Photon energy dependent differential cross section of the $\gamma p\to {\pi }^{0}p$ reaction. Data are taken from [5] (left triangles), [77] (open squares), [78] (solid stars), [79] (open triangles), [80] (open circles), [81] (solid squares), [82] (solid circles), [9] (down triangles), [11] (up triangles), and [12] (diamonds). The partial cross sections for $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}$, and $N\left(1720\right)P_{13}$ are indicated explicitly by different legends in the figure.

Figure 4

Effects of $N\left(1650\right)S_{11}, \mathrm{\Delta }\left(1620\right)S_{31}$, and $t$ channel on the differential cross sections of the $\gamma p\to {\pi }^{0}p$ process. Data are taken from [9] (open squares) and [11] (solid squares). The results by switching off the contributions from $N\left(1650\right)S_{11}, \mathrm{\Delta }\left(1620\right)S_{31}$, and $t$ channel are indicated explicitly by different legends in the figure. The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 5

Beam asymmetry of the $\gamma p\to {\pi }^{0}p$ process as a function of scattering angle. The data are taken from [5] (solid left triangles), [83] (open squares), [84] (open up triangles), [85] (solid circles), [11] (solid squares), [13] (diamonds), [86] (solid down triangles), and [14] (stars). The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 6

Photon energy dependent beam asymmetry of the $\gamma p\to {\pi }^{0}p$ reaction. The data are taken from [84] (right triangles), [83] (open up triangles), [85] (open diamonds), [11] (solid diamonds), [13] (down triangles), [86] (open circles), [14] (solid squares), [87] (solid circles), and [88] (open squares). The results by switching off the contributions from various partial waves are indicated explicitly by different legends in the figure.

Figure 7

Polarization of recoil protons $P$ of the $\gamma p\to {\pi }^{0}p$ reaction as a function of scattering angle. Data are taken from [85] (circles), [89] (triangles), and [10] (squares). The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 8

Photon energy dependent polarization of recoil protons for the $\gamma p\to {\pi }^{0}p$ reaction. Data are taken from [90] (open circles), [91](solid circles), [92] (diamonds), [93] (solid down triangles), [94] (solid stars), [95] (open stars), [96] (solid squares), [85] (solid up triangles), [97] (solid left triangles), [98] (open down triangles), and [99] (solid right triangles). The results by switching off the contributions from various partial waves are indicated explicitly by different legends in the figure.

Figure 9

Target asymmetry of the $\gamma p\to {\pi }^{0}p$ reaction as a function of scattering angle. The data are taken from [85] (solid circles), [100] (solid triangles), [101] (open circles), and [10] (solid squares). The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 10

Photon energy dependent target asymmetry of the $\gamma p\to {\pi }^{0}p$ reaction. The data are taken from [100] (solid squares), [101] (open squares), [102] (solid circles), and [85] (open triangles). The results by switching off the contributions from various partial waves are indicated explicitly by different legends in the figure.

Figure 11

Differential cross sections of the $\gamma n\to {\pi }^{0}n$ reaction as a function of scattering angle. Data are taken from [3] (open circles), [103] (solid circles), [104] (solid squares), and [105] (solid triangles). The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 12

Photon energy dependent differential cross sections of the $\gamma n\to {\pi }^{0}n$ reaction. Data are taken from [3] (solid triangles), [106] (solid stars), [104] (solid squares), and [105] (solid circles). The partial cross sections for $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}$, and $N\left(1720\right)P_{13}$ are indicated explicitly by different legends in the figure.

Figure 13

Total cross section as a function of the c.m. energy $W$ for the $\gamma n\to {\pi }^{0}n$ reaction. Data are taken from [3]. The results by switching off the contributions from $N\left(1650\right)S_{11}, \mathrm{\Delta }\left(1620\right)S_{31}$, and $t$ channel and the partial cross sections for $\mathrm{\Delta }\left(1232\right)P_{33}, N\left(1535\right)S_{11}, N\left(1520\right)D_{13}, N\left(1720\right)P_{13}$, and $u$ channel are indicated explicitly by different legends in the figure.

Figure 14

Cross section ratio ${\sigma }_n/{\sigma }_p$ between the reactions $\gamma n\to {\pi }^{0}n$ and $\gamma p\to {\pi }^{0}p$ as a function of the center-of-mass energy $W$. Data are taken from Ref. [3].

Figure 15

Beam asymmetry of the $\gamma n\to {\pi }^{0}n$ reaction as a function of scattering angle. Data are taken from [19]. The first and second numbers in each figure correspond to the photon energy $E_{\gamma }$ (MeV) and the $\pi N$ center-of-mass energy $W$ (MeV), respectively.

Figure 16

Photon energy dependent beam asymmetry of the $\gamma n\to {\pi }^{0}n$ reaction. Data are taken from [19]. The results by switching off the contributions from various partial waves are indicated explicitly by different legends in the figure.

Figure 17

Effects of $N\left(1650\right)S_{11}$ on the differential cross sections and the total cross section around its mass threshold. Data are taken from Ref. [3]. The solid and dashed curves are for the results with negative and positive $\gamma n$ couplings for $N\left(1650\right)S_{11}$, respectively.