Search for $\eta$-mesic ${}^4$He with the WASA-at-COSY detector

An exclusive measurement of the excitation function for the $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction was performed at the Cooler Synchrotron COSY-Jülich with the WASA-at-COSY detection system. The data were taken during a slow acceleration of the beam from 2.185 to 2.400 GeV/$c$ crossing the kinematic threshold for the $\eta$-meson production in the $dd\to {}^4\mathrm{He}\eta$ reaction at 2.336 GeV/$c$. The corresponding excess energy with respect to the ${}^4$He-$\eta$ system varied from $-$51.4 to 22 MeV. The integrated luminosity in the experiment was determined using the $dd\to {}^3\mathrm{He}n$ reaction. The shape of the excitation function for the $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction was examined. No signal of the ${}^4$He-$\eta$ bound state was observed. An upper limit for the cross section for the bound state formation and decay in the process $dd\to {({}^4\mathrm{He}-\eta )}_{\mathrm{bound}}\to {}^3\mathrm{He}p{\pi }^{-}$ was determined on the 90$\%$ confidence level and it varies from 20 to 27 nb for the bound state width ranging from 5 to 35 MeV, respectively.

Figure 1

Experimental spectrum of the energy losses in the first two layers of the forward range hodoscope (FRH). The area used for ${}^3\text{He}$ identification is indicated by the red (solid) line. The empty area below 0.05 GeV in the Edep(FRH1) distribution is due to the preselection condition. The regions corresponding to protons, ${}^3\text{He}$, and ${}^4\text{He}$ are clearly visible.

Figure 2

Comparison of the Monte Carlo simulation (a) and the experimental spectrum (b) of the energy loss in the plastic scintillator barrel ($x$ axis) combined with the energy deposited in the electromagnetic calorimeter ($y$ axis). The green (light gray) and red (dark gray) curves represent the applied graphical condition to separate protons and pions.

Figure 3

(a) Distribution of the ${}^3$He momentum in the c.m. system simulated for the processes leading to the creation of the ${}^4$He-$\eta$ bound state: $dd\to {({}^4\mathrm{He}-\eta )}_{\mathrm{bound}}\to {}^3\mathrm{He}p{\pi }^{-}$ [red (gray) area] and of the phase-space $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction (black line). The simulation was done for a momentum of the deuteron beam of 2.307 GeV/$c$. The Fermi momentum parametrization was taken from Ref. [31]. (b) Experimental distribution of the ${}^3$He momentum in the c.m. system. In both plots the dashed line demarcates the signal-poor and the signal-rich regions. The decrease of the counts at 0.48 GeV/$c$ is due to the geometry of the border of the barrel and the endcaps of the scintillator barrel detector that was used in the $p$-${\pi }^{-}$ identification process. This region has no relevance in the next steps of the analysis.

Figure 4

Excitation function for the $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction for the signal-rich region corresponding to ${}^3$He momentum below 0.3 GeV/$c$ (a) and the signal-poor region with ${}^3$He momentum above 0.3 GeV/$c$ (b). The difference of the excitation functions for the signal-rich and signal-poor regions after the normalization to the second bin of $Q$ is shown in panel c. The black solid line represents a straight-line fit. The threshold of ${}^4$He-$\eta$ is marked by the vertical dashed line.

Figure 5

(a) Simulated distribution of the $p$-${\pi }^{-}$ opening angle in the c.m. system for the $dd\to {({}^4\mathrm{He}-\eta )}_{\mathrm{bound}}\to {}^3\mathrm{He}p{\pi }^{-}$ reaction (red histogram) and for the phase-space $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction [blue (solid) line]. (b) Experimental distribution of the $p$-${\pi }^{-}$ opening angle in the c.m. system. In both plots the red dashed line separates the signal-poor and the signal-rich regions.

Figure 6

Kinetic energy distribution of protons (a) and ${\pi }^{-}$ (b) in the c.m. frame obtained from experiment (points) and from the simulations of a signal reaction (lines). The red dashed line indicates the boundary of the applied selection criteria: $E{\mathrm{kin}}_p^{\mathrm{c}.\mathrm{m}.}<200$ MeV, $E{\mathrm{kin}}_{{\pi }^{-}}^{\mathrm{c}.\mathrm{m}.}\in (180,400)$ MeV. Please note that the ranges on the $x$ axes are different.

Figure 7

Geometrical acceptance (solid black squares), overall efficiency (open red circles), and luminosity (solid blue triangles) as a function of the excess energy. The right axis denotes the luminosity.

Figure 8

Experimental excitation function for the $dd\to {}^3\mathrm{He}p{\pi }^{-}$ reaction obtained after the normalization of the events selected in individual excess energy intervals by the corresponding integrated luminosities. The dotted and solid lines correspond to the second-order and the first-order polynomials fitted to the data.

Figure 9

Upper limit at 90$\%$ confidence level of the cross section for formation of the ${}^4$He-$\eta$ bound state and its decay via the $dd\to {({}^4\mathrm{He}-\eta )}_{\mathrm{bound}}\to {}^3\mathrm{He}p{\pi }^{-}$ reaction as a function of the width of the bound state. The binding energy was set to $E_{\mathrm{BE}}=-20$ MeV. The green area at the bottom represents the systematic uncertainties.