First measurement of target and beam-target asymmetries in the $\gamma p\to {\pi }^0\eta p$ reaction

The first data on target and beam-target asymmetries for the $\gamma p\to {\pi }^0\eta p$ reaction at photon energies from 1050 up to 1450 MeV are presented. The measurements were performed using the Crystal Ball and TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The general assumption that the reaction is dominated by the $\mathrm{\Delta }3/2^{-}$ amplitude is confirmed. The data are in particular sensitive to small contributions from other partial waves.

Figure 1

Definition of the coordinate systems used in the present work. The azimuthal angle ${\varphi }_{23}^{*}$ is defined in the center-of-mass system (cm) system of particles 2 and 3 with the $z$ axis opposite to the momentum of particle 1 and $y$ axis parallel to $OY$. It is equal to the angle between the reaction plane $P_r$ and the decay plane $P_d$.

Figure 2

Diagrams representing the amplitude for the $\gamma N\to \pi \eta N$. The notations $\mathrm{\Delta }$ and $N^{*}$ are used for the resonances $\mathrm{\Delta }\left(1232\right)$ and $S_{11}\left(1535\right)$.

Figure 3

Experimental setup with the upper hemisphere of the Crystal Ball omitted to show the central region.

Figure 4

Event selection for final states with four photons: $M_{\gamma \gamma }$ vs $M_{\gamma \gamma }$ for all possible independent combinations of $\gamma \gamma$ pairs (three entries for each event).

Figure 5

Missing mass distributions corresponding to photon beam energies of (a) 1100 MeV and (b) 1400 MeV. The full black circles are obtained with butanol data. The green triangles and blue squares are hydrogen and carbon data scaled to fit the butanol data. The fit result, which is a sum of the hydrogen and carbon partial contributions, is shown by the open red circles.

Figure 6

Detection efficiency at fixed ${\mathrm{\Theta }}_{\pi }$ for two photon energy bins: $1100\pm 50$ MeV (solid blue line) and $1400\pm 50$ MeV (black dashed line). ${\mathrm{\Theta }}_{\eta }^{*}$ is the polar angle in the cm system of the $\left(\eta p\right)$ pair. Panels (a) and (c) show the efficiency at $cos{\mathrm{\Theta }}_{\pi }=-0.9\pm 0.1$, and (b) and (d) at $cos{\mathrm{\Theta }}_{\pi }=0.9\pm 0.1$.

Figure 7

Angular and invariant mass distributions for the target asymmetry $P_y$ of the $\gamma p\to {\pi }^0\eta p$ reaction for incident photon energies from 1050 to 1450 MeV. Our experimental results with statistical uncertainties are shown by filled circles. The solid curves show the prediction of the isobar model [5]. The dashed curves include only the $3/2^{-}$ partial wave. Predictions of the Bonn-Gatchina model [7] are shown by dashed-dotted curves. The energy labels on the left panels indicate the central energy of the four 100-MeV-wide photon energy bins.

Figure 8

Same as Fig. 7 for the beam-target asymmetry $P_x^{\odot }$. The red dotted line in the first column was obtained using Eq. (7).

Figure 9

The target asymmetry $P_x$ and beam-target asymmetry $P_y^{\odot }$ as functions of ${\varphi }_{\pi \eta }^{*}$. All notation is the same as in Fig. 7.