The $\gamma p\to p\eta \eta$ reaction in an effective Lagrangian model

In this paper, we investigate the $\gamma p\to p\eta \eta$ reaction within an effective Lagrangian approach and isobar model. We consider the contributions from the intermediate $N^{*}\left(1535\right)$, $N^{*}\left(1650\right)$, $N^{*}\left(1710\right)$, and $N^{*}\left(1720\right)$ isobars which finally decay to the $N\eta$ state. It is found that the excitation of the $N^{*}\left(1535\right)$ dominates this reaction close to threshold and $\rho$ meson exchange plays the most important role for the excitation of nucleon resonances. Therefore, this reaction offers a potentially good place to study the properties of nucleon resonances and their couplings to the $N\rho$ channel. Predictions for angular distributions and invariant mass spectra of final particles are also presented for future comparison with data.

Figure 1

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

Figure 2

Total cross section for the $\gamma p\to p\eta \eta$ reaction as a function of beam momentum within our model: (a) contribution from various nucleon resonances and mesonic term; (b) contribution from $\rho$ and $\omega$ exchanges.

Figure 3

Predictions of angular distribution, invariant mass spectrum, and Dalitz plot at $p_{\gamma }=1.89$ GeV. The solid line represents the full results and the dashed line represents the phase space distribution. $\theta$ denotes the angle of the outgoing particles relative to the incident beam direction in the center-of-mass frame.

Figure 4

Same as Fig. 3, but at $p_{\gamma }=2.5$ GeV.