$\gamma d\to {\pi }^{0}d$ reaction near the threshold of $\eta$ production

We consider the reaction $\gamma d\to {\pi }^{0}d$ in a wide energy range around and above the $\eta$-meson photoproduction threshold at backward c.m. angles of the outgoing pions. Our theoretical analysis is motivated by the recent measurements of the CLAS Collaboration at Jefferson Lab, where this kinematical region of the reaction has been thoroughly studied for the first time and an enhancement in the energy dependence of the differential cross section in the region of $E_{\gamma }~600\text{−}800\text{MeV}$ has been observed. Our preliminary and qualitative analysis, based on single- and double-scattering diagrams, shows that the observed structure can be explained by the contribution of the double-scattering diagram with intermediate production of the $\eta$ meson. The effect, to a considerable extent, is due to the contribution of the $N(1535)$ resonance to the amplitudes of subprocesses on the nucleons.

Figure 1

Feynman diagrams for the $\gamma d\to {\pi }^{0}d$ reaction: (a) single scattering and (b) double scattering.

Figure 2

Diagrams of meson photoproduction on the nucleon (resonance and VME contributions).

Figure 3

Diagrams of meson-nucleon binary reactions (resonance contributions).

Figure 4

(a) [(b)] Real [image] parts of the loop integral $A_{11}$ of the double-scattering diagram [Fig. 1b] in the “static” approximation with an intermediate $\eta$ meson in the reaction (1). The results are given for the values $z=\cos \theta =-0.55$. Solid (dashed) curves correspond to the results with the Bonn (Gaussian) s DWF.

Figure 5

(a) and (b) Results for Re$A_{11}$; (c) and (d) results for Im $A_{11}$; and (e) and (f) results for $\left|A_{11}\right|{}^2$ at $z=-0.55$ [(a), (c), and (e)] and $z=-0.85$ [(b), (d), and (f)] with the Gaussian s DWF. Solid (dashed) curves correspond to the “nonstatic” (“static”) case.

Figure 5g

(Continued.)

Figure 6

Differential cross sections of the reaction (1) vs photon laboratory energy $E_{\gamma }$ at several values of $z=\cos \theta$. Dashed (dotted) and solid curves show the contributions of single- (double-) scattering amplitudes and total amplitude, respectively. Dash-dotted curves correspond to the contributions of total amplitude without the $\omega$-exchange term. The results are obtained with energy-dependent total width of $N(1535)$. (a) $z=0$, (b) $z=-0.65$, and (c) $z=-0.85$.

Figure 7

The same as in Fig. 6 but the results are obtained with constant total width of $N(1535)$.