Experimental study of the $\gamma p\to \eta p$ reaction with the Crystal Ball detector at the Mainz Microtron (MAMI-C)

The $\gamma p\to \eta p$ reaction has been measured with the Crystal Ball and TAPS multiphoton spectrometers in the energy range from the production threshold of 707 MeV to 1.4 GeV ($1.49⩽W⩽1.87$ GeV). Bremsstrahlung photons produced by the 1.5-GeV electron beam of the Mainz Microtron MAMI-C and momentum analyzed by the Glasgow tagging spectrometer were used for the $\eta$-meson production. Our accumulation of $3.8\times {10}^6$ $\gamma p\to \eta p\to 3{\pi }^{0}p\to 6\gamma p$ events allows a detailed study of the reaction dynamics. The $\gamma p\to \eta p$ differential cross sections were determined for 120 energy bins and the full range of the production angles. Our data show a dip near $W=1680$ MeV in the total cross section caused by a substantial dip in $\eta$ production at forward angles. The data are compared to predictions of previous SAID and MAID partial-wave analyses and to the latest SAID and MAID fits that included our data.

Figure 1

(a) Tagger-hit-time distribution for the experimental $\gamma p\to \eta p\to 3{\pi }^{0}p$ events, where the two vertical lines define the region of prompt coincidences. (b) Detector acceptance for $\gamma p\to \eta p\to 3{\pi }^{0}p$ events as a function of the incident-photon energy, $E_{\gamma }$.

Figure 2

Spectra of the $3{\pi }^0$ invariant mass obtained from kinematic fitting to the $\gamma p\to 3{\pi }^{0}p$ hypothesis for the events with values of $E_{\gamma }$ between 1150 and 1200 MeV: (a) experimental spectrum after the subtraction of the random and empty-target backgrounds, (b) experimental events selected also as $\eta \to 3{\pi }^0$ candidates, (c) MC simulation for $\gamma p\to 3{\pi }^{0}p$, (d) events from the MC simulation for $\gamma p\to 3{\pi }^{0}p$ selected also as $\eta \to 3{\pi }^0$ candidates.

Figure 3

Cosine $\theta$ distributions in the c.m. frame of $\eta$ photoproduction at $E_{\gamma }=760$ MeV ($W=1519$ MeV): (a) experimental $\gamma p\to \eta p\to 3{\pi }^{0}p$ events, (b) MC simulation for the $\gamma p\to \eta p\to 3{\pi }^{0}p$ events, (c) results for the $\gamma p\to \eta p$ differential cross section compared to the prediction by SAID (solution E429) [16] (solid line).

Figure 4

Same as Fig. 3, but for $E_{\gamma }=1060$ MeV ($W=1694$ MeV).

Figure 5

Differential cross sections for $\gamma p\to \eta p$ as a function of $\cos \theta$, where $\theta$ is the production angle of $\eta$ in the c.m. frame. The present data (solid circles) are shown for four energy bins: (a) $E_{\gamma }=714.5\pm 2.1$, (b) $772.9\pm 2.1$, (c) $1026.8\pm 3.7$, and (d) $1376.2\pm 9.7$ MeV. Previous data are shown for experiments at MAMI-B [17] for $715.9\pm 5$ and $775.3\pm 5$ MeV (open triangles); CLAS-g1c [18] for $775\pm 25$, $1025\pm 25$, and $1375\pm 25$ MeV (open circles); CLAS-g11a [19] for $1384\pm 10$ MeV (open diamonds); GRAAL [20] for $714\pm 9$ and $1024\pm 9$ MeV (open diamonds with crosses); LNS [21] for $718.0\pm 10$ and $768.8\pm 10$ MeV (horizontal bars); CB-ELSA [22] for $774\pm 25$, $1025\pm 25$, and $1374\pm 25$ MeV (open squares); and CB-ELSA/TAPS [23] for $1025\pm 25$ and $1375\pm 25$ MeV (crosses). Plotted uncertainties are statistical only.

Figure 6

Total cross section for $\gamma p\to \eta p$ as a function of the c.m. energy. Uncertainties plotted for our data are statistical only. Notation of different data is the same as in Fig. 5.

Figure 7

Same as Fig. 6, but for narrower $W$ ranges: (a) from the threshold to the maximum of the total cross section and (b) around a shallow dip, $W=1680$ MeV.

Figure 8

Dominant Legendre coefficients from the fits to our differential cross sections. The coefficients are plotted as a function of the c.m. energy; $A_1$ is shown by solid circles, $A_2$ by open triangles, and $A_3$ by open circles.

Figure 9

Present differential cross sections (open circles) for $\gamma p\to \eta p$ as a function of $\theta$, the $\eta$ production angle in the c.m. frame, over the range of c.m. energies $W$ presently measured. The plotted uncertainties are statistical only. The curves denote SAID solution GE09 (solid line), SAID solution E429 (dashed line), $\eta$-MAID solution (dotted line), and Regge-MAID solution (dot-dashed line).

Figure 10

Fixed-angle excitation functions for $\gamma p\to \eta p$ as a function of the c.m. energy $W$ shown for eight values of the $\eta$ production angle and for the full angular range. Our data are shown by solid circles. The plotted uncertainties are statistical only. The notation of the PWA solutions is the same as in Fig. 9.

Figure 11

PWA predictions for the $\gamma p\to \eta p$ excitation function at the extreme (forward and backward) production angles of $\eta$, shown as a function of the c.m. energy $W$. Notation of the PWA predictions is the same as in Fig. 9.

Figure 12

Our total cross section (circles) for $\gamma p\to \eta p$ as a function of the $\eta$ momentum in the c.m. frame. The solid line shows the results of fitting our data to a sum of linear and cubic terms.

Figure 13

Modulus of the multipole amplitude $S_{11}$pE (${}_p{E}_{0+}^{1/2}$) for $\gamma p\to \eta p$ from the reaction threshold to $E_{\gamma }=1.4$ GeV. Notations for the amplitude curves are the same as in Fig. 9. The vertical arrows indicate $W_R$ (Breit-Wigner mass) and the horizontal bars show the full and partial width $\Gamma$ for ${\Gamma }_{\pi N}$ associated with the SAID solution SP06 for $\pi N$ [2].