Search for the $eta$ mesic $^3$He in the $pdrightarrow d p pi^{0}$ reaction with the WASA-at-COSY facility

The excitation function for the $pdrightarrow$ $d p pi^{0}$ reaction has been measured by WASA-at-COSY experiment with the aim of searching for $^{3}hspace{-0.03cm}mbox{He}$-$eta$ 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$^{*}$(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 $pdrightarrow$ $(^{3}hspace{-0.03cm}mbox{He}$-$eta)_{bound} rightarrow$ $d p pi^{0}$ process. It varies between 13 nb to 24 nb for the bound state with width in the range $Gamma in (5,50)$ MeV.