Search for the $\eta$ mesic ${}^3$He in the $pd\to dp{\pi }^0$ reaction with the WASA-at-COSY facility

The excitation function for the $pd\to$ $dp{\pi }^0$ reaction has been measured by WASA-at-COSY experiment with the aim of searching for ${}^{3}He$-$\eta$ mesic nuclei. The measurement in the vicinity of $\eta$ meson production was performed using a ramped proton beam. The data analysis and interpretation was carried out with the assumption that the $\eta$-mesic Helium decays via the formation of an intermediate N${}^{\ast }$(1535) resonance. No direct signal of the $\eta$-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 $pd\to$ ${(}^{3}He$-$\eta {)}_{bound}\to$ $d p \pi^{0}$ process. It varies between 13 nb to 24 nb for the bound state with width in the range $\mathrm{\Gamma }\in (5,50)$ MeV.