Quasifree photoproduction of $\eta$ mesons off protons and neutrons

Differential and total cross sections for the quasifree reactions $\gamma p\to \eta p$ and $\gamma n\to \eta n$ have been determined at the MAMI-C electron accelerator by using a liquid deuterium target. Photons were produced via bremsstrahlung from the 1.5 GeV incident electron beam and energy tagged with the Glasgow photon tagger. Decay photons of the neutral decay modes $\eta \to 2\gamma$ and $\eta \to 3{\pi }^0\to 6\gamma$ and coincident recoil nucleons were detected in a combined setup of the Crystal Ball and the TAPS calorimeters. The $\eta$-production cross sections were measured in coincidence with recoil protons, recoil neutrons, and in an inclusive mode without a condition on recoil nucleons, which allowed a check of the internal consistency of the data. The effects from nuclear Fermi motion were removed by a kinematic reconstruction of the final-state invariant mass and possible nuclear effects on the quasifree cross section were investigated by a comparison of free and quasifree-proton data. The results, which represent a significant improvement in statistical quality compared to previous measurements, agree with the known neutron-to-proton cross-section ratio in the peak of the $S_{11}$(1535) resonance and confirm a peak in the neutron cross section, which is absent for the proton, at a center-of-mass energy $W=(1670\pm 5)$ MeV with an intrinsic width of $\Gamma \approx 30$ MeV.

Figure 1

Total cross section for $\gamma p\to \eta p$ averaged over data from Refs. [5, 6, 7, 8, 9, 10, 11, 12, 13]. Model curves are from MAID 1 [14], MAID 2 [15], SAID [13], and BnGn [16].

Figure 2

Diagram of the experimental setup created by the geant4 model. The Crystal Ball detector was cut along the x-axis to show the inner detectors and the target.

Figure 3

Tagger-calorimeter coincidence time spectra (sum of all channels). Left side shows timing between tagger and the Crystal Ball. Right side shows timing between tagger and TAPS. Hatched red areas show random background $(R_1$ and $R_2)$ and random coincidence $\left(C_R\right)$ windows. Hatched blue areas show true coincidence window $\left(C_T\right)$.

Figure 4

Typical invariant-mass spectra for two bins of incident photon energy $E_{\gamma }$ in the range of $\eta$ mesons for the $\eta \to 2\gamma$ and $\eta \to 3{\pi }^0$ decays in coincidence with recoil protons $p$, recoil neutrons $n$, and without any condition for recoil nucleons $\left(N\right)$. The indicated cuts (red lines) have been applied to the spectra discussed below.

Figure 5

$\eta \text{−}N$ coplanarity $\Delta \varphi$ used for the reaction identification. Top two rows show $\eta \to 2\gamma$ analyses. Bottom two rows show $\eta \to 3{\pi }^0$ analyses. Columns give bins of incident photon energy $E_{\gamma }$. Black squares are experimental data. Curves are simulations of pure signal (blue), all background contributions (dashed magenta, see text), and sum of signal and background (green). Red lines are cut markers.

Figure 6

Missing mass $\Delta m_X$ used for the reaction identification. Top three rows show $\eta \to 2\gamma$ analyses. Bottom three rows show $\eta \to 3{\pi }^0$ analyses. Columns give bins of incident photon energy $E_{\gamma }$. Black squares are experimental data. Curves are simulations of pure signal (blue), all background contributions (dashed magenta, see text), and sum of signal and background (green). Red lines are cut markers.

Figure 7

Pulse-shape analysis (PSA) distributions for particles detected in TAPS. Left column shows $\eta \to 2\gamma$ analyses. Right column shows $\eta \to 3{\pi }^0$ analyses. Top three rows show photon candidates in the inclusive and the two exclusive analyses. Bottom two rows show proton and neutron candidates in the exclusive analyses. Black lines are cut markers. Counts increase from violet to red.

Figure 8

Left side shows time-of-flight analysis (TOF) distributions for particles detected in TAPS. Left column shows $\eta \to 2\gamma$ analyses. Right column shows $\eta \to 3{\pi }^0$ analyses. Top three rows show photon candidates in the inclusive and the two exclusive analyses. Bottom two row show proton and neutron candidates in the exclusive analyses. Counts increase from violet to red. Right side shows $\Delta E\text{−}E$ distributions for protons: Left column shows $\eta \to 2\gamma$ analyses. Right column shows $\eta \to 3{\pi }^0$ analyses. First row shows protons in the CB (all events). Second row shows protons in the CB (accepted events). Third row shows protons in TAPS (all events). Fourth row shows protons in TAPS (accepted events). Counts increase from violet to red.

Figure 9

Cluster-size distributions in the $\gamma n\to \eta n\to 2\gamma n$ (solid red histograms) and the $\gamma n\to \eta n\to 3{\pi }^{0}n$ (dashed blue) analyses. Top row shows particles in the CB. Bottom row shows particles in TAPS. Left column shows photons. Right column shows neutrons.

Figure 10

Invariant masses $m\left(2\gamma \right)$ and $m\left(3{\pi }^0\right)$ used for the identification of the $\eta$ mesons. Top three rows show $\eta \to 2\gamma$ analyses. Bottom three rows show $\eta \to 3{\pi }^0$ analyses. Columns show bins of incident photon energy $E_{\gamma }$. Black squares show experimental data. Blue curves show the simulation results.

Figure 11

Resolution of the $W$ reconstructions illustrated by the response curves of the kinematic reconstruction (solid curves) and the reconstruction via time-of-flight (dotted curves) at several discrete values of $W$ (dashed lines). The response curves were obtained from the $\gamma n\to \eta n\to 2\gamma n$ simulation.

Figure 12

Photon flux on the target for the May 2009 dataset. Left side shows measured photon flux as a function of $E_{\gamma }$. Right side shows flux as a function of $W$ obtained from folding with the deuteron Fermi momentum distribution.

Figure 13

Detection efficiencies as a function of $cos\left({\theta }_{\eta }^{*}\right)$ for the exclusive analyses for different bins of $W_{\mathrm{kin}}$. Solid curves show $\eta \to 2\gamma$ proton (blue) and neutron (red) analyses. Dashed curves show $\eta \to 3{\pi }^0$ proton (blue) and neutron (red) analyses.

Figure 14

Total cross sections as a function of the photon beam energy $E_{\gamma }$. (a) Comparison of the two $\eta$ decay analyses of the proton (blue diamonds and triangles), neutron (red stars and circles) and the inclusive analyses (black crosses and squares).(b) Comparison of the averaged proton (blue triangles) and neutron (red circles) results and of their sum (black crosses) to the inclusive data (black squares). Hatched areas are total systematic uncertainties of inclusive (black), proton (blue), and neutron (red) data.

Figure 15

Differential cross sections as a function of the photon beam energy $E_{\gamma }$ and $cos\left({\theta }_{\eta }^{*}\right)$. Blue triangles are exclusive proton. Red circles are exclusive neutron. Black crosses are sum of proton and neutron data. Black squares are inclusive data.

Figure 16

Total cross sections as a function of the final-state invariant mass $W_{\mathrm{kin}}=m\left(\eta N\right)$. Blue triangles are proton data. Red circles are neutron data scaled by $3/2$. Black stars are free-proton data from MAMI-C [13]. Hatched areas are total systematic uncertainties of proton (blue) and neutron (red) data.

Figure 17

Differential cross sections for $\gamma p\to \eta p$ as a function of the final-state invariant mass $W_{\mathrm{kin}}=m\left(\eta p\right)$ and $cos\left({\theta }_{\eta }^{*}\right)$. Filled blue triangles are exclusive proton. Open green triangles are quasifree data from CBELSA/TAPS [41]. Black stars are free-proton data from MAMI-C [13]. Black curves are Legendre fits to the present results. Hatched blue areas are total systematic uncertainties in the present work.

Figure 18

Differential cross sections for $\gamma n\to \eta n$ as a function of the final-state invariant mass $W_{\mathrm{kin}}=m\left(\eta n\right)$ and $cos\left({\theta }_{\eta }^{*}\right)$. Filled red circles are exclusive neutron. Open green circles are quasifree data from CBELSA/TAPS [41]. Open black squares are quasifree data from GRAAL [38]. Black curves are Legendre fits to the present results. Hatched red areas are total systematic uncertainties in the present work.

Figure 19

Phenomenological fits of the total $\gamma n\to \eta n$ cross sections as functions of $W_{\mathrm{kin}}$ and $W_{\mathrm{TOF}}$. Top row shows $\eta \to 2\gamma$ analyses. Bottom row shows $\eta \to 3{\pi }^0$ analyses. Columns from left to right: Kinematic $W$ reconstruction with standard (Kin. I) and more strict (Kin. II) cuts, time-of-flight $W$ reconstruction with standard (TOF I) and more strict (TOF II) cuts. Points are original data (filled red circles) and background -subtracted data (open black circles). The TOF data were scaled by a factor of four. Curves show total fit (solid black), $S_{11}$(1535) contribution (dashed black), integrated background Breit–Wigner (dotted black), and narrow BW (solid red).

Figure 20

Differential cross sections as a function of $W_{\mathrm{kin}}$ for different bins of $cos\left({\theta }_{\eta }^{*}\right)$. Points are original data (filled red circles) and background-subtracted data (open black circles). Curves are total fit (solid black), $S_{11}$(1535) contribution (dashed black), integrated background Breit–Wigner (dotted black), total background [$S_{11}$(1535) + broad BW, solid blue], and narrow BW (solid red).

Figure 21

Contributions from $S_{11}$ BW (open, black squares), background function (open blue triangles), and narrow BW (red dots) for different angular bins integrated over excitation energy. The most extreme angles have been omitted because of unstable fit results due to lack of statistics.

Figure 22

Comparison of Legendre coefficients $A_i$ extracted from fits of the differential cross sections: quasifree proton from this work (filled blue triangles) and CBELSA/TAPS [41] (open black triangles), quasifree neutron from this work (filled red circles) and CBELSA/TAPS (open black circles), and free-proton data from MAMI-C [13] (black stars). Solid lines are MAID model predictions [14]. Dashed vertical lines show markers at $W=1680$ MeV.