Insight into the Narrow Structure in $\eta$ Photoproduction on the Neutron from Helicity-Dependent Cross Sections

The double polarization observable $E$ and the helicity dependent cross sections ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ were measured for $\eta$ photoproduction from quasifree protons and neutrons. The circularly polarized tagged photon beam of the A2 experiment at the Mainz MAMI accelerator was used in combination with a longitudinally polarized deuterated butanol target. The almost $4\pi$ detector setup of the Crystal Ball and TAPS is ideally suited to detect the recoil nucleons and the decay photons from $\eta \to 2\gamma$ and $\eta \to 3{\pi }^0$. The results show that the narrow structure previously observed in $\eta$ photoproduction from the neutron is only apparent in ${\sigma }_{1/2}$ and hence, most likely related to a spin-$1/2$ amplitude. Nucleon resonances that contribute to this partial wave in $\eta$ production are only $N1/2^{-}$ ($S_{11}$) and $N1/2^{+}$ ($P_{11}$). Furthermore, the extracted Legendre coefficients of the angular distributions for ${\sigma }_{1/2}$ are in good agreement with recent reaction model predictions assuming a narrow resonance in the $P_{11}$ wave as the origin of this structure.

Figure 1

Double polarization observable $E$ for $\gamma p\to p\eta$ (left-hand side) and $\gamma n\to n\eta$ (right-hand side). Gray shaded areas: systematic uncertainties. Curves: predictions from MAID (green, dashed) [32] and BnGa (model based on $S_{11}$ interference) [22] (black, solid line).

Figure 2

Excitation functions for ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ for five $\cos ({\theta }_{\eta }^{\star })$ bins [$\cos (\theta )$ ranges given in figure]. Top two rows: results for $\gamma p\to p\eta$ (blue squares). Bottom two rows: $\gamma n\to n\eta$ (red circles). Gray shaded areas: systematic uncertainties. Curves: model predictions from MAID (dashed green line) [32], BnGa(a) (model version with interference in $S_{11}$ wave, solid black line) [22], BnGa(b) (model with narrow $P_{11}$ resonance with positive $A_{1/2}$ coupling, dotted black line) [22], and BnGa(c) (narrow $P_{11}$ resonance with negative $A_{1/2}$ coupling, dash-dotted, black line) [22]. Right hand side: total cross sections.

Figure 3

Legendre coefficients of the angular distributions of ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ for the reaction $\gamma n\to n\eta$. Experimental results (red circles) and model predictions by MAID [32] and BnGa [22]. Same notation as in Fig. 2. The vertical dashed lines at $W=1685\mathrm{MeV}$ indicate the position of the narrow structure. The results for $A_0$, ${\sigma }_{3/2}$ are up-scaled by a factor of 5.