Search for η mesic 3 He with the WASA-at-COSY facility in the pd → 3 He2 γ and pd → 3 He6 γ reactions

We report on the experimental search for the bound state of an η meson and 3 He nucleus performed using the WASA-at-COSY detector setup. In order to search for the η -mesic nucleus decay, the pd → 3 He2 γ and pd → 3 He6 γ channels have been analysed. These reactions manifest the direct decay of the η meson bound in a 3 He nucleus. This non-mesonic decay channel has been considered for the ﬁrst time. When taking into account only statistical errors, the obtained excitation functions reveal a slight indication for a possible bound state signal corresponding to a 3 He- η nucleus width (cid:4) above 20 MeV and binding energy B s between 0 and 15 MeV. However, the determined cross sections are consistent with zero in the range of the systematic uncertainty. Therefore, as ﬁnal result we estimate only the upper limit for the cross section of the η -mesic 3 He nucleus formation followed by the η meson decay which varies between 2 nb and 15 nb depending on possible bound state parameters.


Introduction
Strong attractive interactions between the η meson and nucleons mean that there is a chance to form η meson bound states in nuclei [1]. If discovered in experiments, these mesic nuclei would be a new state of matter bound just by the strong interaction without electromagnetic Coulomb effects playing a role. Strong interaction bound states are formed in a different way as compared to exotic atoms which involve binding of electrically charged mesons with nuclei. For the latter, negatively charged pions or kaons could replace an electron in an outer orbital in a standard atom and get bound in the atom due to the Coulomb interaction. The charged meson in such an excited state quickly undergoes transitions to the lower states until it is close enough to the nucleus and is either absorbed by the nucleus or lost in a nuclear reaction. For strong interactions, in contrast to the pion, the neutral η meson is special due to the strong attractive nature of this meson-nucleon interaction [1]. An off-shell η meson produced in nuclear reactions such as the pd → 3 He2γ and pd → 3 He6γ below the η production threshold may form a bound state with the nucleus within which it is produced. Thus the absence of the electromagnetic interaction and the attractive nature of the η-nucleon interaction, makes the case of the neutral η meson different from that of the pion or the kaon and opens the possibility for an exotic nucleus made up of the meson and nucleons. Early experiments with low statistics using photon [2,3], pion [4], proton [5] or deuteron [6][7][8][9] beams gave hints for possible η mesic bound states but no clear signal [10,11].
Here we present a new high statistics search for 3 He-η bound states with data from the WASA-at-COSY experiment. We focus on the two main neutral decay channels of the η meson: η → 2γ with branching ratio 39.41 ± 0.20% and η → 3π 0 → 6γ with branching ratio 31.54 ± 0.22% [12]. These processes constitute more than 70% of the η decays. The choice of neutral decay channels minimizes final state interactions involving charged particles. Concurrent measurement of the two channels increases the statis-tics and enables one to control systematic uncertainties in photons detection. The two-photon decay was previously suggested in [13] as a clean probe of the η in nuclear media.
Considering the η-nucleus interaction, bound states can be formed by the attractive interaction with finite level width corresponding to the finite lifetime of the state due to the absorptive interaction with the nucleus. The momentum distribution of the bound η meson determines the sum of the momenta of the emitted photons. Nuclear absorption and the additional η decay (disappearance) processes, reduces significantly the in-medium branching ratio of 2γ and 6γ decay channels [14].
η meson interactions with nucleons and nuclei are a topic of great experimental and theoretical interest. For recent reviews see [10,11,[15][16][17]. Possible η-nucleus binding energies are related to the η-nucleon optical potential and to the value of η-nucleon scattering length a ηN [18]. Phenomenological estimates for the real part of a ηN are typically between 0.2 and 1 fm depending on the model assumptions. η bound states in helium require a large η-nucleon scattering length with real part greater than about 0.7-1.1 fm [19][20][21]. Recent calculations in the framework of optical potential [22], multi-body calculations [20], and pionless effective field theory [19] suggest a possible 3 He-η bound state.
Modifications of meson properties are expected in medium. In studies of the transparency of nuclei to propagating mesons produced in photoproduction experiments one finds strong η absorption in nuclei [24]. For the η one finds weaker interaction with the nucleus. An effective mass shift for the η in medium has been observed by the CBELSA/TAPS Collaboration [25]. The η -nucleus optical potential V opt = V real + iW deduced from these photoproduction experiments with a carbon target is V real (ρ 0 ) = m * − m = −37 ± 10 ± 10 MeV and W (ρ 0 ) = −10 ± 2.5 MeV at nuclear matter density ρ 0 . This mass shift is very close to the prediction of the Quark Meson Coupling mode (QMC) with mixing angle -20 degrees [13,26], which also predicts a potential depth about -100 MeV for the η at ρ 0 . The η results are also consistent with scattering length estimates from COSY-11 [27] and Bonn [28]. Experimental search for η -nucleus bound states has also been performed with results reported in Ref. [29].
Hints for possible η helium bound states are inferred from the observation of strong interaction in the η helium system. One finds a sharp rise in the cross section at threshold for η production in both photoproduction from 3 He [2,30] and in the proton-deuteron reaction dp → 3 Heη [31]. These observations may hint at a reduced η effective mass in the nuclear medium.
Previous bound state searches at COSY have been focused on the reaction dd → 3 HeNπ [8,9]. Studies of the excitation function around the threshold for dd → 4 Heη did not reveal a structure that could be interpreted as a narrow mesic nucleus. Upper limits for the total cross sections for bound state production and decay in the processes dd → ( 4 He-η) bound → 3 Henπ 0 and dd → ( 4 He-η) bound → 3 Hepπ − were deduced to be about 5 nb and 10 nb for the nπ 0 and pπ − channels respectively [9]. The bound state production cross sections for pd → ( 3 He-η) bound [32] are expected to be more than 20 times larger than for dd → ( 4 He-η) bound [33].
In May 2014 the experiment searching for η mesic 3 He nuclei was performed at the COSY accelerator [34,35] in Jülich, Germany. The measurements were carried out using the WASA-at-COSY detector [36][37][38][39][40]. The mesic nuclei are supposed to be formed in proton-deuteron collisions. A ramped proton beam with beam momentum varying in the range from 1.426 to 1.635 GeV/c corresponding to 3 Heη excess energy range from −70 to 30 MeV and a pellet deuterium target [41] were used. The 3 He-η bound state was searched for in the pd → ( 3 He-η) bound → 3 He2γ and pd → ( 3 He-η) bound → 3 He6γ decay channels. These channels that manifest the direct decay of η bound in 3 He nucleus have been investigated for the first time. The existence of the bound 3 He-η state would manifest itself as a maximum or interference pattern in the excitation function for both of the studied reactions below the pd → 3 Heη reaction threshold.
For the normalization of the excitation functions, the integrated luminosity was determined as a function of the excess energy. The analysis is presented in the next section. Further on, the data selection and efficiency determination is described. The data analysis is followed by the interpretation of the achieved excitation functions in view of the possible signal from the η-mesic 3 He.

Luminosity determination
Luminosity was determined based on the pd → 3 Heη and pd → ppn spectator reactions. The pd → 3 Heη reaction analysis allows one to estimate the integrated luminosity for 3 Heη excess energy Q 3 Heη above zero. The 3 He particles were registered in the forward detector [36] and identified using the E − E method based on energy losses in scintillator layers (see Fig. 1). The count of events originating from this reaction was obtained based on the 3 He missing mass spectra for each excess energy interval separately. An example spectrum is shown in Fig. 2. The reconstruction efficiency was calculated using Monte Carlo simulations taking into account the experimental data on cross sections and angular distributions [40,[42][43][44].
The pd → ppn spectator reaction analysis allows one to determine the integrated luminosity for the whole beam momentum range. As far as the target overlapping by the beam is changing during the acceleration cycle, the integrated luminosity value can change depending on the beam momentum. The registration efficiency for the pd → ppn spectator reaction was obtained with dedicated Monte Carlo simulations described in Refs. [45,46]. The distribution of relative proton-neutron motion inside the target deuteron was calculated based on the parametrisation of the Paris potential [47]. Data on the proton-proton elastic scattering cross section and the angular distribution [48] were used for simulating the quasi-elastic scattering in the framework of the spectator model. The calculated cross section was multiplied by the factor 0.96 to take into account the shading effect [49]. It is worth noting that above the η production threshold, the two estimates of luminosity are in agreement (based on the pd → ppn spectator and pd → 3 Heη reactions [45]). The total integrated luminosity was determined to be 2446 ± 3(stat.) ± 66(syst.) ± 4(norm.) nb −1 where the statistical, systematic and normalisation errors are indicated, respectively [45]. This is the largest statistics ever obtained for these experimental conditions.

The analysis of pd → ( 3 He-η) bound → 3 He2γ and pd → ( 3 He-η) bound → 3 He6γ reactions
As a first step, in order to establish the optimal selection criteria, Monte Carlo simulations for the pd → ( 3 He-η) bound → 3 He2γ  and pd → ( 3 He-η) bound → 3 He6γ reactions were performed in the framework of the spectator model with the assumption of an isotropic distribution of bound η meson decay products in its rest frame. The momentum of the η meson was simulated using the recent model [14] in which the 3 He-η relative momentum distribution was calculated by solving the Klein-Gordon equation assuming the potential of η-nucleus interaction based on Hiyama's density distribution in 3 He [50][51][52].
For the pd → ( 3 He-η) bound → 3 He2γ reaction analysis, the events containing a 3 He track in the forward detector and at least two photons in the central detector were selected. If there were more than two photons, the pair with the invariant mass closest to the η mass corrected by Q 3 Heη value was chosen. Then the restrictions on 3 He missing mass, γ -γ missing mass, and γ -γ invariant mass were applied using selection ranges based on the simulated distributions [45]. The excitation function obtained for the pd → 3 He2γ reaction is shown in the left panel of Fig. 3.
The signal from the bound state is expected for excess energies around or below zero. The increase of events above 10 MeV is due to the pd → 3 Heη reaction. It starts at 10 MeV because of a hole for the COSY beam in the geometrical acceptance of the WASA-at-COSY detector (see Fig. 4).
For the pd → ( 3 He-η) bound → 3 He6γ reaction analysis, the events containing a 3 He track in the forward detector and at least six photons in the central detector were selected. For each combination forming three pairs, to identify the η → 3π 0 → 6γ decay, the following quantity is calculated: where m γ (2i−1) γ 2i is the γ pair invariant mass and m π 0 is π 0 mass. The combination of six photons that minimises D was chosen. Then analogous to the 2γ case, the selection conditions on the 3 He missing mass, 6γ invariant mass, and 6γ missing mass were applied based on the simulated distributions [45]. The excitation function obtained for the pd → 3 He6γ reaction is shown in the right panel of Fig. 3.
The excitation curves have been normalised using the integrated luminosity values calculated based on the pd → ppn spectator reaction and the efficiency determined based on Monte Carlo simulations. The results for both studied reactions are shown in Fig. 5.

The upper limit for the η mesic 3 He production cross section
The excitation curves obtained in the analysis (Fig. 5) did not reveal any resonance-like structures and the fit with linear functions results in χ 2 value < 1 when normalized to the number of degrees of freedom. This indicates that no strong signal from the bound 3 He-η state is observed.
Further on, for the quantitative estimates of the upper limits for the bound state production, a fit to the excitation curves with a linear function (for background) plus a Breit-Wigner function (for the signal) was performed. The fit was done for different combinations of the assumed η-mesic 3  For a given B s and pair, the following functions were fit simultaneously for the two studied reaction channels: Here σ , p 1 , p 2 , p 3 , and p 4 are the free fit parameters, P η→2γ and P η→6γ are the branching ratios for the η → 2γ and η → 6γ decays. Assuming that the ratio of branching ratios for the η → 2γ and η → 3π 0 decay channels for the bound η meson remain the same as in vacuum, the vacuum branching ratio values of P η→2γ = 0.3941 and P η→3π 0 →6γ = 0.3268 were used for performing the fit [12]. The function σ b (Q 3 Heη ) in the fit formulae represents a Breit-Wigner shape which for a given values of B s and reads: Example results of the fit are shown in Fig. 6. The figure shows results for the B s and values (indicated above the plots) for which The upper limit of the total cross section was determined based on the fit parameter uncertainty σ stat : where k is the statistical factor equal to 1.64 corresponding to 90% confidence level as given in PDG [12]). Fig. 7 shows the systematic limits (blue lines) in addition to the statistical uncertainties (green lines). Systematic errors were estimated by changing the parameters of all cuts applied in the data analysis, and changing the values of assumed potential parameters for the 3 He-η interaction that determines the Fermi momentum distribution for relative motion in the bound state. The highest contribution to the systematic error is connected with the background fit function. The uncertainty due to the fit of quadratic or linear function estimated as σ quad − σ lin varies from about 2 to 5 nb.
In the obtained excitation functions one can see a slight signal from the possible bound state for > 20 MeV and B s ∈ [0; 15] MeV corresponding to the optical potential parameters −100 < V 0 < −70 MeV and |W 0 | > 20 MeV in the model described in [14]. The result is also consistent with the QMC prediction of a potential depth about -100 MeV at nuclear matter density [13] and with the models in Refs. [19,20,22,23]. The allowed V 0 -W 0 area is however different to those deduced from the η- 4 He system [54] using the optical model of Ikeno et al. [53] where most of the model parameter space was excluded allowing values of the real and imaginary parts of the potential only between zero and about -60 MeV and -7 MeV respectively. However, the observed signal is within the range of the systematic uncertainty. Hence one cannot make definite conclusions whether η-mesic 3 He exists with the decay mechanism studied here.

Conclusions
The analysis of the pd → 3 He2γ and pd → 3 He6γ reactions has been performed in order to search for the existence of an η-mesic 3 He state. The analysis of the obtained excitation functions for the pd → 3 He2γ and pd → 3 He6γ reactions shows slight indication of the signal from the bound state for > 20 MeV and B s ∈ [0; 15] MeV. However, the observed indication is within the range of the systematic error which does not allow one to make a definite conclusion on a possible bound state formation.
The upper limit for the cross section of the bound state production varies between 2 and 15 nb depending on the bound state parameters. It is however important to stress that the determined upper limit concerns the production of the ( 3 He-η) bound state and its subsequent disintegration via decay of the η meson.
The branching ratio for the latter in the nuclear medium remains to be estimated theoretically.
This is the first result obtained for the direct decay of bound η meson. The upper limit is much lower than the limit of 70 nb for pd → ( 3 He-η) bound → 3 Heπ 0 reaction obtained by the COSY-11 Collaboration [55] and is comparable with the upper limits obtained for the dd → ( 4 He-η) bound → 3 Henπ 0 and dd → ( 4 He-η) bound → 3 Hepπ − reactions [9]. The much improved constraint will help tuning theoretical modelling of the η-nucleon and η-nucleus interactions.