Effects of nucleon resonances on $\eta$ photoproduction off the neutron reexamined

We investigate $\eta$ photoproduction off the neutron target, i.e., $\gamma n\to \eta n$, employing an effective Lagrangian method combining with a Regge approach. As a background, we consider nucleon exchange in the $s$-channel diagram and $\rho$- and $\omega$-meson Regge trajectories in the $t$ channel. The role of nucleon resonances given in the Review of Particle Data Group in the range of $W\approx 1500–2100\mathrm{MeV}$ and the narrow nucleon resonance $N(1685,1/2^{+})$ is extensively studied. The numerical results of the total and differential cross sections, double polarization observable $E$, helicity-dependent cross sections ${\sigma }_{1/2}$, ${\sigma }_{3/2}$, and the Legendre coefficients of the angular distributions for ${\sigma }_{1/2}$, ${\sigma }_{3/2}$ are found to be in qualitative agreement with the recent A2 experimental data. The predictions of the beam asymmetry are also given.

Figure 1

Feynman diagrams for the $\gamma n\to \eta n$ reaction.

Figure 2

Total cross section for the $\gamma n\to \eta n$ reaction as a function of $W$. The left panel draws the numerical result of the present work. The dashed curve represents the background contributions from the nucleon, $\omega$-, and $\rho$-meson trajectories, whereas the dot-dashed curve draws the contribution of the nucleon resonances. The solid curve plots the total contribution and the dotted one the total contribution without the effect of the $N(1685,1/2^{+})$. The right panel depicts each contribution of the exchanged particles to the total cross section for the $\gamma n\to \eta n$. The legend in the box indicates each contribution in a different colored curve. The experimental data are taken from the A2 collaboration [10].

Figure 3

Differential cross sections for the $\gamma n\to \eta n$ as a function of $\cos \theta$ for each beam energy. The notations are the same as in the left panel of Fig. 2. The data are from the A2 collaboration (circle) [10] and CBELSA/TAPS collaboration (triangle) [5].

Figure 4

Double polarization observable $E$ for the $\gamma n\to \eta n$ as a function of $W$. The notations are the same as in the left panel of Fig. 2. The data are taken from the A2 collaboration [20].

Figure 5

Helicity-dependent total cross section for the $\gamma n\to \eta n$ as a function of $W$. The notations are the same as in the left panel of Fig. 2. The data are taken from the A2 collaboration [20].

Figure 6

Legendre coefficients ($A_i$) of the angular distributions of ${\sigma }_{1/2}$ (${\sigma }_{3/2}$) for the $\gamma n\to \eta n$ as a function of $W$ in the upper (lower) panels. The solid curves depict the corresponding $A_i$ with the narrow resonance $N(1685,1/2^{+})$, whereas the dotted ones draw those without it. The data are taken from the A2 collaboration [20].

Figure 7

Beam asymmetry for the $\gamma n\to \eta n$ as a function of $\cos \theta$.