Search for the $η$ mesic $^3$He in the $pd\rightarrow d p π^{0}$ reaction with the WASA-at-COSY facility

The excitation function for the $pd\rightarrow$ $d p π^{0}$ reaction has been measured by WASA-at-COSY experiment with the aim of searching for $^{3}\hspace{-0.03cm}\mbox{He}$-$η$ mesic nuclei. The measurement in the vicinity of $η$ meson production was performed using a ramped proton beam. The data analysis and interpretation was carried out with the assumption that the $η$-mesic Helium decays via the formation of an intermediate N$^{*}$(1535) resonance. No direct signal of the $η$-mesic nucleus is observed in the excitation function. We determine a new improved upper limit for the total cross section for the bound state production and decay in the $pd\rightarrow$ $(^{3}\hspace{-0.03cm}\mbox{He}$-$η)_{bound} \rightarrow$ $d p π^{0}$ process. It varies between 13 nb to 24 nb for the bound state with width in the range $Γ\in (5,50)$ MeV.