Regge phenomenology in ${\pi }^0$ and $\eta$ photoproduction

The $\gamma N\to {\pi }^{0}N$ and $\gamma N\to \eta N$ reactions at photon beam energies above 4 GeV are investigated within Regge models. The models include $t$-channel exchanges of vector ($\rho$ and $\omega$) and axial-vector ($b_1$ and $h_1$) mesons. Moreover, Regge cuts of $\rho \mathbb{P},\rho f_2,\omega \mathbb{P}$, and $\omega f_2$ are investigated. A good description of differential cross sections and polarization observables at photon beam energies from 4 to 15 GeV can be achieved.

Figure 1

Kinematics for ${\pi }^0$ or $\eta$ photoproduction and frames for beam and target polarization.

Figure 2

$t$-channel contributions to $\eta$ photoproduction from single poles (a), Regge poles (b), and Regge cuts (c). An example for $\rho$ and $\omega$ meson exchange and $\mathbb{P}$ and $f_2$ mesons for rescattering of two Reggeons.

Figure 3

Regge trajectories: (a) $\rho$, black; $\omega$, red; $\varphi$, blue; $b_1$ and $h_1$, green; ${\rho }_2$ and ${\omega }_2$, magenta (dashed and dash-dotted magenta lines are ${\rho }_2$ and ${\omega }_2$ of Refs. [22, 23]); (b) $f_2$, red; $\mathbb{P}$, magenta; $\rho f_2$, black solid; $\omega f_2$, blue dashed; $\rho \mathbb{P}$, black solid; $\omega \mathbb{P}$, black dashed.

Figure 4

The differential cross sections of $\gamma p\to {\pi }^{0}p$ (a) and $\gamma p\to \eta p$ (b) reactions at $E_{\gamma }=6$ GeV. Experimental data are from Ref. [6] (a) and Ref. [3] (b). The solid line is a calculation with $\rho$ and $\omega$ exchange in the $t$ channel.

Figure 5

Differential cross sections for $\gamma p\to {\pi }^{0}p$. The solid red, dashed black, dash-dotted blue (coincide mostly with red curves), and dotted green lines are our Solutions I, II, III, and IV, respectively. Data are from SLAC [6] (black circles) and from DESY, [5] (red triangles) and [4] (blue squares).

Figure 6

Polarization observables $\mathrm{\Sigma },T$, and $P$ for $\gamma p\to {\pi }^{0}p$. The notation of the lines is the same as in Fig. 5. Data: SLAC [6] (black disks), GlueX-17 [7] (black open circles), Daresbury [32] (red triangles), DESY [33] (blue solid squares), CEA [34] (blue open squares).

Figure 7

Ratio of differential cross sections for ${\pi }^0$ photoproduction on neutrons and protons. The notation of the lines is the same as in Fig. 5. Data: DESY [35] (black circles), CEA [36] (red squares), and Cornell [37] (blue triangles).

Figure 8

Differential cross sections for $\gamma p\to \eta p$. The notation of the lines is the same as in Fig. 5. Data: DESY [3] (black disks), WLS [38] (red triangles), Daresbury [40] (blue solid squares), CEBAF Large Acceptnce Spectrometer (CLAS) [41] (black open circles), and CEA [42] (blue open squares).

Figure 9

Polarization observables $\mathrm{\Sigma }$ and $T$ for $\gamma p\to \eta p$. The notation of the lines is the same as in Fig. 5. Data: GlueX [7] (black open circles) and Daresbury: [40] (black disks) and [39] (blue squares).

Figure 10

Comparison of the polarization observables $T$ and $P$ at different photon beam energies for $\gamma p\to {\pi }^{0}p$ (top panels) and for $\gamma p\to \eta p$ (bottom panels). The solid red and black lines are our Solutions I and II for the target polarization $T$, and the dashed red and black lines are for the recoil polarization $P$, respectively.