Search for the η -mesic bound states with the WASA-at-COSY detector

. The experiments dedicated to the search for η -mesic Helium were performed with high statistics using WASA detection setups installed at the COSY accelerator in the Research Center Juelich. The search for the η -mesic bound states is conducted via the measurement of the excitation function for selected decay channels of the He- η systems using unique ramped beam technique. This report presents recent status of the data analysis.

Measurements with the WASA-at-COSY detection setup dedicated to search for η-mesic 4 He nuclei were carried out twice (in 2008 and 2010) using the unique ramped beam technique which allows for the beam momentum to be changed slowly and continuously around the η production threshold in each of the acceleration cycles [1,4,47,49]. The advantage of this technique is the reduction of systematic uncertainties with respect to separate runs at fixed beam energies [4,38].
The search for 4 He-η bound states was carried out by studying the excitation functions for dd → 3 Hepπ − [1][2][3][4] and dd → 3 Henπ 0 [1][2][3] reactions near the 4 Heη production threshold. A detailed description of the data analysis and simulations leading to determination of the excitation functions is presented in the Refs [1,4]. Since the obtained excitation functions do not reveal any direct narrow structure below the η production threshold, which could be considered as a signature of the bound state, the upper limit of the total cross section for the η-mesic 4 He formation was determined at the 90% confidence level. For this purpose the excitation curves were fitted simultaneously using the Breit-Wigner function (signal) with a fixed binding energy and width combined with a second order polynomial (background) taking into account the isospin relation between nπ 0 and pπ − pairs.
In case of the dd → ( 4 He-η) bound → 3 Henπ 0 process, the upper limit was for the first time obtained experimentally and varies in the range from 2.5 to 3.5 nb. For the dd → ( 4 Heη) bound → 3 Hepπ − reaction we achieved a sensitivity of the cross section of about 6 nb [1] which is about four times better in comparison with the result obtained in the previous experiment [4]. The obtained upper limits as a function of the bound state width are presented for both of the studied reactions in Fig. 1.

Constraining the optical potential
Previously, the data analyses were carried out assuming that the signal from the bound state is described by a Breit-Wigner shape with fixed binding energy and width [1,4], since there were no theoretical predictions for the dd → ( 4 He-η) bound → 3 HeNπ reactions cross sections below the η production threshold. However, at present, a theoretical description of the cross sections in the excess energy range relevant to the η-mesic nuclear search was proposed in Ref. [8]. The authors used a phenomenological approach with an optical potential for the η-4 He interaction and determine the total cross sections for a broad range of real (V 0 ) and imaginary (W 0 ) parameters.  18 Fitting the theoretical spectra convoluted with the experimental resolution of the excess energy (example Fig. 2) to experimental data collected by WASA-at-COSY [1] brought the upper limit of the total cross section (CL=90%) for creation of η-mesic nuclei via the dd → 3 HeNπ process varying from about 5.2 nb to about 7.5 nb. A comparison of the determined upper limits with the cross sections obtained in Ref. [8] made it possible to put a constraint on the η-4 He optical potential parameters. As it is presented in Fig. 3, only extremely narrow and loosely bound states are allowed within the model [8]. A detailed description of performed studies interested reader can find in Ref. [2].  [8]. The light shaded area shows the region excluded by our analysis, while the dark shaded area denotes the systematic uncertainty of the σ CL=90% upp . The red line extends the allowed region based on a new estimate of errors (see text for details). Dots correspond to the optical potential parameters corresponding to the predicted η-mesic 4 He states. Figure is adopted from Ref. [2].  18 Experiments dedicated to the search for η-mesic 4 He in dd → 3 Henπ 0 and dd → 3 Hepπ − reactions performed with the WASA-at-COSY detection setup did not enable the observation of the resonance structure related to the bound state. However, the upper limits of the total cross sections for η-mesic nuclei formation and decay were determined to be of the order of a few nb [1,4]. Moreover, a comparison between the phenomenological model proposed in Ref. [8] and experimental data allowed, for the first time, to constrain the range of the η-4 He optical potential parameters [2].

Summary and perspectives
Recently, the WASA-at-COSY Collaboration has performed a promising experiment dedicated to the search for η-mesic 3 He in three different mechanisms: (i) absorption of the η meson by one of the nucleons, which subsequently decays into N * -π pair e.g.: pd → ( 3 He-η) bound → pppπ − , (ii) η -meson decay while it is still "orbiting" around a nucleus e.g.: pd → ( 3 He-η) bound → 3 He2γ reactions and (iii) η meson absorption by few nucleons e.g.: pd → ( 3 He-η) bound → ppn. The measurement with a high average luminosity (3·10 30 cm −2 s −1 ) allowed the collection of the largest data sample, in the world available up to now, for 3 He-η [53][54][55]. The analysis is still in progress and the estimated upper limit value for pd → 3 He2γ and pd → 3 He6γ channels is on the level of a few nanobarns.