Determination of the analysing power for the $\vec{p}p \rightarrow pp\eta$ reaction using WASA-at-COSY detector system

We report on the measurement of the analyzing power for the (vec)pp->ppeta reaction with beam momenta of 2026 MeV/c and 2188 MeV/c performed with the WASA-at-COSY detector at the Cooler Synchrotron COSY. The eta meson from the (vec)pp->ppeta reaction was identified by the techniques of missing mass and invariant mass. The angular distribution of the determined analyzing power strongly disagree with theoretical predictions. A comparison of the obtained Ay angular distribution with a series of associated Legendre polynomials revealed negligible contribution of the Sd partial wave at Q = 15 MeV. However, at Q = 72 MeV, a significant interference of the Ps and Pp partial waves was observed.


Introduction
The production mechanism of the η meson and meson-nucleon final state interaction for the pp → ppη reaction can be studied via measurements of the cross sections and analyzing power, A y (θ ). Up to now total and differential cross sections have been determined relatively precisely [1,2,3,4,5,6,7,8,9,10,11,12], however so far A y for the pp → ppη reaction has been determined with rather large uncertainties [13,14,15,16].
In November 2010 the high statistics sample of pp → ppη reaction has been collected using the azimuthally symmetric WASA-at-COSY detector [17]. Measurements were taken with two beam momenta of 2026 MeV/c and 2188 MeV/c, corresponding to 15 MeV and 72 MeV excess energies, respectively.
Based on elastic scattering of protons, the vertex position of the real experiment were measured with two independent methods [18]. The spin flipping technique of the beam has been used to control the effect caused by potential asymmetries in the detector. Monitoring of the beam polarization was based on the pp → pp reaction. The result shown stable polarization during whole experiment [19,20].

Analyzing power for the η meson
The determination of the analyzing power for the η meson was carried out separately for spin up and spin down modes, and for each spin orientation the analyzing power was determined identifying the η meson via two decay channels: η → γγ and η → 3π 0 .
After the identification of the final state particles the number of events corresponding to the pp → ppη reaction, have been determined for each angular bin N(θ η ,ϕ η ) separately. θ η and ϕ η denote respectively the polar and the azimuthal angle of the eta meson emission in the center of mass system. An example of the missing mass distribution for a chosen spin mode of the beam momentum 2188 MeV/c is shown in Figure 1.
The collected amount of the η events, about 400 000 events, significantly improves the statistical uncertainty of the analyzing power for the η meson compared to the previous COSY-11 experiments with about 2000 events only [13]. The systematic uncertainty was improved due to the axial symmetry of the WASA-at-COSY detector and its close to 4π acceptance which is by two orders of magnitude larger than the acceptance of the COSY-11 detector.
Assuming that p and d waves can occur for the η meson production, its analyzing power is given by: where ℑ(A Ps A * Pp ) is the imaginary part of the interference term between the Ps and Pp waves, and ℑ(A Ss A * Sd ) is the interference term between the Ss and Sd waves [21]. Our experimental results are shown in Figure 2 together with meson exchange model predictions. Figure 3 shows result obtained in this experiment with superimposed lines corresponding to the fit of the formula:   [22]. The solid line describes the vector meson model [23] and the dotted line describes the pseudoscalar model [24]. Please note that the data at Q = 72 MeV are compared with theoretical predictions for Q = 36 MeV, which is the largest Q for which such predictions are available.
where C 1 and C 2 are treated as free parameters of the fit. For Q = 72 MeV the angular dependence of dσ /dΩ was determined by the parametrization of the data from reference [10], and for Q = 15 MeV it was assumed to be constant as determined in the experiments of COSY 11 [8] and COSY-TOF collaborations [7]. One can see in Figure 3 that the associated Legendre polynomials of order m = 1 fully describe the existing data.
Thus, the analyzing power is zero for the beam momentum 2026 MeV/c, and there is no interference between A Ss and A Sd as well as between A Pp and A Ps amplitudes of the partial waves.

Results
The comparison of the angular dependence of the analyzing power for the pp → ppη reactions with the associated Legendre polynomials revealed that at Q=15 MeV there is no Ss − Sd and no Pp − Ps interference and that for the higher beam momentum 2188 MeV/c, the Sd partial wave contribution is small (consistent with zero within two standard deviations). On the other hand, the contribution of Ps−Pp interference is large which means that both of these partial waves contribute at Q = 72 MeV (see Figure 3).
The obtained angular dependence of the analyzing power agrees with the previous experiments, however it disagrees with the theoretical predictions based on the pseudoscalar or vector meson dominance models [23,24].