Experimental study of $\eta$ meson photoproduction reaction at MAMI

New data for the differential cross sections, polarization observables $T$, $F$, and $E$ in the reaction of $\eta$ photoproduction on proton from the threshold up to a center-of-mass energy of W=1.9 GeV are presented. The data were obtained with the Crystal-Ball/TAPS detector setup at the Glasgow tagged photon facility of the Mainz Microtron MAMI. The polarization measurements were made using a frozen-spin butanol target and circularly polarized photon beam. The results are compared to existing experimental data and different PWA predictions. The data solve a long-standing problem related the angular dependence of older $T$ data close to threshold. The unexpected relative phase motion between $s$- and $d$-wave amplitudes required by the old data is not confirmed. At higher energies, all model predictions fail to reproduce the new polarization data indicating a significant impact on our understanding of the underlying dynamics of $\eta$ meson photoproduction. Furthermore, we present a fit of the new data and existing data from GRAAL for $\Sigma$ asymmetry based on an expansion in terms of associated Legendre polynomials. A Legendre decomposition shows the sensitivity to small partial-wave contributions. The sensitivity of the Legendre coefficients to the nucleon resonance parameters is shown using the $\eta$MAID isobar model.


Introduction
The most baryon spectroscopy data have been obtained using πN scattering data. Pion photoproduction on nucleons is some additional tool for the investigation of the nucleon resonances, especially in case of small πN partial width. Compared to pion, η photoproduction has some additional advantages. First, the ηNN coupling is very small. For example, this value of g 2 ηNN /4π = 0.4 ± 0.2 was obtained in Ref. [1] in an analysis of the angular distributions of η photoproduction, that is by ∼ 30 times smaller than for pions. Second, because of the isoscalar nature of the η meson, only nucleon excitations with isospin I = 1/2 contribute to the γN → ηN reactions. Both these factors simplify the extraction of the nucleon resonance parameters.
The special feature of the γN → ηN reaction is the dominance of the E 0+ multipole amplitude, which is populated by the N * (1535)1/2 − and N * (1650)1/2 − resonances. An interference between these resonances successfully explained a narrow structure in the total cross section of η photoproduction off the neutron [2]. Experimental data for the total cross section of the γp → ηp reaction together with two PWA predictions are shown in Fig. 1. Partial resonance and non-resonance contributions to the total cross sections are shown in Fig. 2 as an example of the ηMAID predictions [5], [6]. The dominant role of the the N * (1535)1/2 − is illustrated in the left panel of the Fig. 2. Despite the fact that the Born terms give an insignificant contribution, a visible non-resonance background remains a e-mail: kashev@kph.uni-mainz.de due to ρ and ω exchange in the t-channel (black and green lines in the left panel for two version of the ηMAID predictions). Other possible resonance contributions lie below the background (right panel). Nevertheless these resonances can be identified by using the interference with the dominant E 0+ multipole amplitude in the polarization observables.
In this paper, new experimental data for the γp → ηp reaction will be presented together with preliminary results of the partial-wave analysis based on the Legendre fit to the data and the ηMAID isobar model.

Experimental setup and data analysis
The experiment was performed at the MAMI C accelerator in Mainz [7] using the Glasgow-Mainz tagged photon facility [8]. The quasi-monochromatic photon beam covered the energy range from 700 to 1450 MeV. The experimental setup is shown schematically in Fig. 3. The bremsstrahlung photons, produced by the electrons in a 10 μm copper radiator and collimated by a lead collimator, impinged on a target located in the center of the Crystal Ball detector [9]. This detector consists of 672 optically isolated NaI(Tl) crystals with a thickness of 15.7 radiation lengths covering 93% of the full solid angle. For chargedparticle identification a barrel of 24 scintillation counters (Particle Identification Detector [10]) surrounding the target was used. The forward angular range θ = 1 − 20 • is covered by the TAPS calorimeter [11]. TAPS consists of 384 hexagonally shaped BaF2 detectors, each of which  . Partial contributions to the total cross sections from different resonances, predicted by ηMAID isobar model [5] and non-resonance background for two ηMAID versions: bg [5] and bgRegg [6].
is 25 cm long, which corresponds to 12 radiation lengths. A 5-mm thick plastic scintillator in front of each module allows the identification of charged particles. The solid angle of the combined Crystal Ball and TAPS detection system is nearly 97% of 4π sr. More details on the energy and angular resolution of the CB and TAPS detector system are given in Ref. [12].
In the polarization measurements, a longitudinally polarized electron beam with an energy of 1557 MeV and a polarization degree of 80% was used. The longitudinal polarization of electrons is transferred to circular polarization of the photons during the bremsstrahlung process in a radiator. The degree of circular polarization depends on the photon energy and ranged from 65% at 700 MeV to 78% at 1450 MeV [13]. The experiment requires transversely (or longitudinally) polarized protons, which were provided by a frozenspin butanol (C 4 H 9 OH) target. A specially designed 3 He/ 4 He dilution refrigerator was built in order to maintain a temperature of 25 mK during the measurements. The target container, length 2 cm and diameter 2 cm, was filled with 2-mm diameter butanol spheres with a packing fraction (filling factor) of around 60%. The average proton polarization was 70% with relaxation times of around 2000 h. The target polarization was measured at the beginning and the end of each data taking period. In order to reduce the systematic errors, the direction of the target polarization vector was regularly reversed during the experiment. More details about the construction and operation of the target are given in Ref. [14].
The mesons were identified via the η → 2γ or η → 3π 0 → 6γ decays. Selections on the 2γ, or 6γ, invariant mass distributions and on the missing mass MM(γp, η), calculated from the initial state and the reconstructed η meson, allowed for a clean identification of the reaction. In order to subtract a background coming from quasi-free reactions on 12 C and 16 O nuclei of the butanol target, measurements on a pure carbon and a liquid hydrogen target were used. Figure 4 shows our preliminary results for differential cross sections together with various theoretical predictions [4,5,[15][16][17] for different bins in the incoming photon energy as a function of the η meson polar angle in the centerof-mass system, θ * η . The present data agree well with previous measurements, but are much more precise. The original data have a fine binning in energy, from 4 to 10 MeV, and span the full angular range. The data presented are EPJ Web of Conferences 01020-p.2 averages over larger energy bins to be use for Legendre fits (see below). All model predictions are in reasonable agreement with the data. Figures 5 and 6 show our results for T and F asymmetries [18] together with previous data for T [19]. The main inconsistencies with the existing data [19] are in the near threshold region. Here, our results do not confirm the observed nodal structure in the angular dependence of the T asymmetry and solve the long-standing question related to the relative phase between sand d-wave amplitudes. Our data do not require any additional phase shift beyond a Breit-Wigner parametrization of resonances. This important conclusion is corroborated by preliminary data from ELSA [20]. At higher energies, all existing theoretical predictions of both T and F are in poor agreement among themselves and with our experimental data, even though they describe the unpolarized differential cross sections well, see Fig. 4 . The new data will therefore have a significant impact on the partial-wave structure of all models.

Legendre analysis
The full angular coverage of our new differential cross sections and polarization observables allow us to perform a quality fit with the Legendre series truncated to a maximum orbital angular momentum max : where P m n (cos Θ η ) are associated Legendre polynomials. The spin-dependent cross sections, T dσ/dΩ, Fdσ/dΩ, Edσ/dΩ, and Σdσ/dΩ were obtained by multiplying the corresponding asymmetries with our new differential cross sections. Besides the observables T and F, we used for the Legendre fit our preliminary data for the double polarization observable E (circularly polarized photon beam and longitudinally polirized target) and the photon beam asymmetry Σ (linerly polarized photon beam and unpolirized target) measured at the GRAAL facility [21]. Our preliminary data for the spin-dependent cross sections together with results of the Legendre fit with max = 3 are shown in Figs 7,8,9,10. The results for the Legendre coefficients are presented in Figs. 11 and 12 (black circles). The last coefficient, A 6 , depends only on f -wave contribution, A 5 is dominated by the an interference between d and f waves, A 4 includes d, f waves and an interference between p and f waves, and so on. The first coefficient, A σ 0 , includes all possible partial-wave amplitudes and reflects the magnitude of the total cross section. As expected the coefficient in a good agreement with the ηMAID prediction (red line). The coefficients A Σ n are also in reasonable agreement with the predictions, because the Σ asymmetry was included to the ηMAID fit.
The fact that deviations of the ηMAID prediction for the coefficients A σ 1 -A σ 5 (top raw in Fig. 11) are mach larger than for the differential cross sections themselves (see Fig. 4) prompted us to involve these coefficients instead the differential cross sections in the data base for obtaining a new solution of the ηMAID isobar model. Results of the ηMAID fit to the coefficients A σ 0 -A σ 6 (Solution 1) are shown in Fig. 11 as blue curves. Solution 1 significantly improved the description of the coefficients A σ 1 -A σ 6 , but ruined all others. Results of the ηMAID fit to the all coefficients, A σ n , A T n , A F n , A Σ n , (Solution 2) are shown in Fig. 12. This very preliminary solution is much better suited to describe the entire dataset, especially for the lowest coefficients, A 1 , A 2 . Probably involving additional resonances in the model will improve the situation with more high coefficients. Here we just demonstrated the impact of the new data for future partial-wave analyses. New ηMAID predictions based on Solution 2 for the observables T and F are shown in Fig. 13 (blue lines).

Summary
In summary, we have presented new experimental data for the target asymmetry T , the transverse beam-target observable F, preliminary data for the longitudinal beamtarget observable E and the differential cross sections for the γp → ηp reaction. All existing solutions from various partial-wave analyses fail to reproduce the new polarization data. A Legendre decomposition of the new results shows the sensitivity to small partial-wave contributions. We presented also results of the fit to the new data with the Legendre series truncated to a maximum orbital angular momentum max . Preliminary ηMAID fit to the obtained Legendre coefficients results a new solution which much better describes the new polarization data. Further improvement could be due to the addition of new resonances in the model, involving others polarization observables, extending energy region for the data.

EPJ Web of Conferences
Dark Matter, Hadron Physics and Fusion Physics 01020-p.7