Helicity-dependent cross sections and double-polarization observable $E$ in $\eta$ photoproduction from quasifree protons and neutrons

Precise helicity-dependent cross sections and the double-polarization observable $E$ were measured for $\eta$ photoproduction from quasifree protons and neutrons bound in the deuteron. The $\eta \to 2\gamma$ and $\eta \to 3{\pi }^0\to 6\gamma$ decay modes were used to optimize the statistical quality of the data and to estimate systematic uncertainties. The measurement used the A2 detector setup at the tagged photon beam of the electron accelerator MAMI in Mainz. A longitudinally polarized deuterated butanol target was used in combination with a circularly polarized photon beam from bremsstrahlung of a longitudinally polarized electron beam. The reaction products were detected with the electromagnetic calorimeters Crystal Ball and TAPS, which covered 98% of the full solid angle. The results show that the narrow structure observed earlier in the unpolarized excitation function of $\eta$ photoproduction off the neutron appears only in reactions with antiparallel photon and nucleon spin (${\sigma }_{1/2}$). It is absent for reactions with parallel spin orientation (${\sigma }_{3/2}$) and thus very probably related to partial waves with total spin 1/2. The behavior of the angular distributions of the helicity-dependent cross sections was analyzed by fitting them withLegendre polynomials. The results are in good agreement with a model from the Bonn-Gatchina group, which uses an interference of $P_{11}$ and $S_{11}$ partial waves to explain the narrow structure.

Figure 1

Detector setup of the A2 experiment at MAMI.

Figure 2

Coplanarity spectra. The angular difference $\mathrm{\Delta }\varphi$ between the recoil nucleon and the $\eta$ meson for five different bins of incident photon energy. The spectra are integrated over the whole angular range and were filled right after the ${\chi }^2$ selection, the PSA and the invariant-mass cut were applied. The results for the deuterium target are shown in colors (red and blue solid circles) and the results for the deuterated butanol target are shown as open black circles. The MC line shape is shown as a solid black line. The dashed lines show the $2\sigma$ cut position determined from the simulation.

Figure 3

Missing mass $\mathrm{\Delta }M$ for five different bins of incident photon energy. The spectra are integrated over the whole angular range and were filled after the ${\chi }^2$ selection, the PSA, the coplanarity and the invariant-mass cut were applied. Shown are the results for the $\eta \to 2\gamma$ (first two rows) and $\eta \to 6\gamma$ decay (last two rows). The results for the deuterium target are shown in colors (red and blue solid circles) and the results for the deuterated butanol target are shown as open black circles. The cut position of $\pm 1.5\sigma$ is indicated by the dashed line.

Figure 4

Invariant mass for five bins of incident photon energy. The spectra are integrated over the whole angular range and were filled after all analysis cuts (PSA, coplanarity, missing mass) were applied. Shown are the results for the $\eta \to 2\gamma$ (first two rows) and $\eta \to 6\gamma$ decay (last two rows). The results for the deuterium target are shown in colors (red and blue solid circles) and the results for the deuterated butanol target are shown as open black circles. The result of the MC simulation is shown as solid black line. The cut positions are indicated as dashed lines.

Figure 5

Left-hand side: simulated response of the detection system to fixed values of $W$ (vertical dashed lines) for the $\eta \to 2\gamma$ and $\eta \to 6\gamma$ decays. Right-hand side: FWHM of the response as function of $W$.

Figure 6

Missing mass $\mathrm{\Delta }M$ for deuterated butanol for the difference, $N_{1/2}-N_{3/2}$, and the sum, $N_{1/2}+N_{3/2}$, of the two helicity states for the reaction on the proton (blue) and the neutron (red). The line shape of the simulation is shown as a black line. The influence of the carbon is clearly visible in the sum, whereas for the difference, the simulation and the experimental data are in agreement. The spectra are integrated over all incident photon energies and are thus dominated by the count rates from the $N\left(1535\right)1/2^{-}$ region.

Figure 7

Incident photon flux, i.e., count rate of scattered electrons times tagging efficiency for the measurement with the butanol target. Left-hand side: as function of photon energy measured with the tagging spectrometer. Right-hand side: as function of reconstructed $W$ after folding with Fermi motion.

Figure 8

Missing-mass contribution from the deuterium target (dashed green line), the contribution from the carbon target (dotted blue line), and the deuterated butanol distribution for ${\sigma }_{\mathrm{sum}}$ (black dots). The sum of the deuterium and the carbon is shown in red. The yields from the different targets were absolutely normalized with the target densities, the fluxes, and the detection efficiencies. Only the overall scale of the figures is in arbitrary units. A variable energy binning was used (mean value indicated) and only a selection of bins is shown here.

Figure 9

Double-polarization observable $E$ as a function of the incident photon energy $E_{\gamma }$ for the proton (left) and the neutron (right). The experimental results are averaged over both decay channels $\eta \to 2\gamma$ and $\eta \to 6\gamma$. They are compared to Fermi-folded model results from the BnGa [38] and MAID [64] models. For better readability, the points from version 2 are shifted by $+5$ MeV with respect to version 1. The systematic uncertainties are indicated by the gray-shaded areas.

Figure 10

Angular distributions for the double-polarization observable $E$ for the recoil proton for bins of incident photon energy. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The Fermi-folded model predictions by BnGa [38] and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 11

Angular distributions for the double-polarization observable $E$ for the recoil neutron for bins of incident photon energy. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The Fermi-folded model predictions by BnGa [38] (model with interference of the $N\left(1535\right)$ and the $N\left(1650\right)$) and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 12

Double-polarization observable $E$ for the proton (left) and the neutron (right) shown as a function of the reconstructed c.m. energy. The results were averaged over both decay channels $\eta \to 2\gamma$ and $\eta \to 6\gamma$. The results are compared to model calculations by BnGa [38] (neutron model with interference of the $N\left(1535\right)$ and the $N\left(1650\right)$) and MAID [64]. For better visibility, the points from version 2 were shifted by $+5$ MeV with respect to version 1. The systematic uncertainties for analysis 1 are indicated by the gray-shaded areas.

Figure 13

Helicity-dependent cross sections ${\sigma }_{1/2}$ and ${\sigma }_{3/2}$ for the proton (left) and the neutron (right) as a function of the reconstructed c.m. energy. The results were averaged over both decay channels $\eta \to 2\gamma$ and $\eta \to 6\gamma$ and are compared to model calculations by BnGa [38] (neutron model with interference of the $N\left(1535\right)$ and the $N\left(1650\right)$) and MAID [64]. For better visibility, the points from version 2 and version 3 were shifted by $\pm 5$ MeV with respect to version 1. The systematic uncertainties for analysis 1 are indicated by the gray-shaded areas. For the proton, results are also shown (labeled “free”) when for version 1 of the analysis the unpolarized cross section ${\sigma }_0$ is taken from free-proton data [16].

Figure 14

Angular distributions for the helicity-dependent cross section ${\sigma }_{1/2}$ for the proton. The results are shown in the c.m. frame of the $\eta$ meson and the final-state nucleon. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The model predictions by BnGa [38] and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 15

Angular distributions for the helicity-dependent cross section ${\sigma }_{3/2}$ for the proton. The results are shown in the c.m. frame of the $\eta$ meson and the final-state nucleon. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The model predictions by BnGa [38] and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 16

Angular distributions for the helicity-dependent cross section ${\sigma }_{1/2}$ for the neutron. The results are shown in the c.m. frame of the $\eta$ meson and the final-state nucleon. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The model predictions by BnGa [38] and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 17

Angular distributions for the helicity-dependent cross section ${\sigma }_{3/2}$ for the neutron. The results are shown in the c.m. frame of the $\eta$ meson and the final-state nucleon. For better visibility, the points of version 2 (blue crosses) were shifted by $\mathrm{\Delta }cos\left({\theta }_{\eta }^{*}\right)=+0.05$ with respect to version 1 (green dots). The systematic uncertainties are indicated by the gray-shaded areas. The model predictions by BnGa [38] and MAID [64] are indicated as solid and dashed lines, respectively.

Figure 18

Legendre coefficients $A_0$–$A_3$ (rows) as defined in Eq. (11), which were extracted from version 1. First column: coefficients for the helicity-$1/2$ state (solid circles) for the reaction on the proton. Second column: coefficients for the helicity-$3/2$ state (open circles) for the reaction on the proton. Third and fourth columns: same for the reaction on the neutron. The experimental results (blue and red markers) are compared to the coefficients extracted from model predictions by MAID [64] (dashed green line) and BnGa [38]. Three different BnGa models predictions are shown for the neutron. BnGa (b): fit with a narrow $N\left(1685\right)$ resonance with positive $A_{1/2}$ coupling (dotted line). BnGa (c): fit with a narrow $N\left(1685\right)$ resonance with negative $A_{1/2}$ coupling (dash-dotted line). BnGa (a): fit without a narrow resonance (solid line). The position of the narrow structure at $W=1685$ MeV in the neutron cross section is indicated by a dashed vertical line.