Nucleon resonance production in the $\gamma p\to p\eta \varphi$ reaction

In this work, we perform a study of nucleon resonance production in the $\gamma p\to p\eta \varphi$ reaction within an effective Lagrangian approach. In our model, we consider the excitation of the $N^{*}\left(1535\right)$, $N^{*}\left(1650\right)$, $N^{*}\left(1710\right)$, and $N^{*}\left(1720\right)$ in the intermediate state and the background term. We find that this reaction is dominated by the excitation of the $N^{*}\left(1535\right)$ in the near threshold region. Especially, we study the possible role of the scalar meson exchange in this reaction. It is found that the $f_0\left(980\right)$ exchange may give a significant contribution and the parity asymmetry can be used to identify its role in this reaction.

Figure 1

Feynman diagrams for the $\gamma p\to \varphi \eta p$ reaction.

Figure 2

Total cross section vs. the beam energy $E_{\gamma }$ for the $\gamma p\to \varphi \eta p$ reaction without considering the $f_0$ exchange. The red-dashed, green-dotted, blue-dash-dotted, and pink-dash-dot-dotted lines represent the contribution of the $N^{*}\left(1535\right)$, $N^{*}\left(1650\right)$, $N^{*}\left(1710\right)$, and $N^{*}\left(1720\right)$, respectively. The gray-short-dashed line denotes the $t$-channel background contribution. Their sum is shown by the solid black line.

Figure 3

Individual contributions of various meson exchanges. The red-dashed, blue-dotted, and gray-dash-dotted lines indicate the contributions of the $\eta$, $\pi$ exchanges and background term, respectively. The shadow area represents the $f_0$ exchange contribution with ${\mathrm{\Lambda }}_{f_0}$ varying from 1.3 to 1.8 GeV.

Figure 4

Predictions for the $P_{\sigma }$ at $P_{\gamma }=3.0$ GeV. The black-solid, orange-dash-dot-dotted, and green-dash-dotted lines denote the results with ${\mathrm{\Lambda }}_{f_0}=1.8$, 1.5, and 1.3 GeV, respectively. The red-dashed line corresponds to the results using ${\mathrm{\Lambda }}_{f_0}=1.3$ GeV and a smaller mass of the $f_0$, i.e., $m_{f_0}=0.98$ GeV, in the calculation. The blue-dotted line indicates the result without considering the $f_0$ exchange contribution.