Photoproduction of $\eta$ and ${\eta }^{\text{'}}$ mesons off protons

Total and differential cross sections for $\eta$ and ${\eta }^{\text{'}}$photoproduction off the proton have been determined with the CBELSA/TAPS detector for photon energies between $0.85$ and $2.55$ GeV. The $\eta$ mesons are detected in their two neutral decay modes, $\eta \to \gamma \gamma$ and $\eta \to 3{\pi }^0\to 6\gamma$, and for the first time, cover the full angular range in $\cos \hspace{0.5em}{\theta }_{c.m.}$ of the $\eta$ meson. These new $\eta$ photoproduction data are consistent with the earlier CB-ELSA results. The ${\eta }^{\text{'}}$ mesons are observed in their neutral decay to ${\pi }^0{\pi }^0\eta \to 6\gamma$ and also extend the coverage in angular range.

Figure 1

Experimental setup of CBELSA/TAPS in Bonn. The electron beam delivered by the accelerator ELSA enters from the left side.

Figure 2

(Top) Schematic drawing of the liquid hydrogen target, scintillating-fiber detector, and Crystal-Barrel and TAPS calorimeters. (Bottom) Front view of TAPS. The left side shows the logical segmentation for the LED-low trigger; the right side shows the logical segmentation for the LED-high trigger (see text for more details).

Figure 3

Distributions of confidence levels resulting from a 1C kinematic fit of a true data event sample with two photons in the final state to the hypothesis $\gamma p\to p\gamma \gamma$ (a) and a 4C fit of a six-photon event sample to the hypothesis $\gamma p\to p3{\pi }^0$ (b) for $E_{\gamma }\in [1600,1650]$ MeV. The insets show the same for Monte Carlo data. The strong rise near zero is from poorly reconstructed signal events. Examples of pull distributions for the azimuthal angle $\varphi$ of the final-state photons are shown for data (c) and for Monte Carlo events (d) for the kinematic fit to $\gamma p\to p3{\pi }^0$ integrated over the full kinematic range. The mean and $\sigma$ values are 0.0036 and 0.00078 as well as $\sigma =1.14$ and 1.03, respectively.

Figure 4

Time difference between photons in TAPS (mean value for all photons) and electrons in the tagger integrated over all events. A prompt coincidence is defined by $-3<\Delta t<3$ ns.

Figure 5

Invariant mass spectra (integrated over all photon energies) for the reactions $\gamma p\to p\gamma \gamma$ (left) and $\gamma p\to p{\pi }^0{\pi }^0{\pi }^0$ (center); confidence-level cuts were applied at ${10}^{-2}$ and at ${10}^{-3}$, respectively. In the two-photon decay mode, the ${\pi }^0$ and $\eta$ mesons are observed with very little background. The inset on the left shows the distribution using a logarithmic scale; the gap between 200 and 400 MeV/$c^2$ stems from a loose kinematic cut before kinematic fitting requiring the proton and the two-photon system to go back-to-back in the center-of-mass system. The invariant ${\pi }^0{\pi }^0\eta$ mass spectrum (right) shows a clear ${\eta }^{\text{'}}$ signal and an enhancement at 1250 MeV/$c^2$.

Figure 6

Invariant $\gamma \gamma$ mass spectra (integrated over all incoming photon energies) for the two reactions $\gamma p\to p{\pi }^0\eta \gamma \gamma$ (left) and $\gamma p\to p{\pi }^0{\pi }^0\gamma \gamma$ (right). The ${\pi }^0$ signal shows a double-peak structure because the “better” ${\pi }^0$ was found in the kinematic fit.

Figure 7

Ratio ${\Gamma }_{\eta \to 3{\pi }^0}/{\Gamma }_{\eta \to 2\gamma }$ for each ($E_{\gamma },\cos \hspace{0.5em}{\theta }_{\mathrm{c}.\mathrm{m}.}$) bin. The values are weighted with their squared inverse errors.

Figure 8

Differential cross sections for $\gamma p\to p\eta$ using the $\eta \to 2\gamma$ (▪) and $\eta \to 3{\pi }^0\to 6\gamma$ (▴) decay channels. Only statistical errors are assigned to the data points. In some bins, the acceptance for $\eta \to 3{\pi }^0$ is small ($<5\%$) and, thus, corresponding data points are not shown. The figure shows the excellent agreement of both reactions.

Figure 9

Differential cross sections for $\gamma p\to p\eta$ (▪) using the combined data set of $\eta \to 2\gamma$ and $\eta \to 3{\pi }^0\to 6\gamma$ events. For comparison, CB-ELSA data [8] are represented by (▴) and CLAS data by (★). The solid line shows our previous PWA solution [8] and the dashed line represents the SAID model [40]. The data points include statistical errors only; the total systematic error is given as error bands at the bottom of each plot.

Figure 10

Differential cross sections for the reaction $\gamma p\to p{\eta }^{\text{'}}$ (analyzed decay mode ${\eta }^{\text{'}}\to 2{\pi }^0\eta \to p6\gamma$) (▪) using 50-MeV-wide energy bins and $\cos \hspace{0.5em}{\theta }_{\mathrm{c}.\mathrm{m}.}^{{\eta }^{\text{'}}}$ bins of width 0.2. The data cover the full angular range; energies are given in MeV. For comparison, data are shown from SAPHIR [28] (★) and CLAS [29] (▴). The SAPHIR data are based on only 250 events and, thus, have large error bars. The dashed line represents the SAID model [40].

Figure 11

Differential cross sections for the reaction $\gamma p\to p{\eta }^{\text{'}}$ close to the reaction threshold (▪) determined for individual tagger channels using 5 $\cos \hspace{0.5em}{\theta }_{\mathrm{c}.\mathrm{m}.}^{{\eta }^{\text{'}}}$ bins of width 0.4. Energies in the plots are given in MeV. Although limited in statistics, all angular distributions appear to be flat indicating $s$-wave behavior of the reaction at the threshold.

Figure 12

Shown is the linear energy dependence of the squared total cross section, ${\sigma }_{\mathrm{tot}}^2$, for the reaction $\gamma p\to p{\eta }^{\text{'}}$ close to the reaction threshold of $E_{\mathrm{thres}}\approx 1447$ MeV.

Figure 13

Total $\gamma p\to p\eta$ cross section. The data points ($•$) are calculated by summation of the differential cross section; the gray line represents the result of our previous partial wave analysis.

Figure 14

Total $\eta \to \gamma \gamma$ yields per tagger channel number covering the energy range of the anomaly observed in the total $\eta$ cross section. The data point at 1.73 GeV/$c^2$ (see Fig. 13) is based on channels 421–426. No statistically significant enhancement can be seen in the excitation function.

Figure 15

Total $\gamma p\to p{\eta }^{\text{'}}$ cross section. The data points ($•$) are calculated by summation of the differential cross section.