We investigate the relation between the $\eta \text{−}{}^3\mathrm{H}\mathrm{e}$ binding energy and width and the (complex) $\eta \text{−}{}^3\mathrm{H}\mathrm{e}$ scattering length. Following our systematic analysis of the $\eta \text{−}{}^3\mathrm{H}\mathrm{e}$ scattering length we set limits on the $\eta \text{−}{}^3\mathrm{H}\mathrm{e}$ binding. If bound states exist the binding energy (width) should not exceed $5\mathrm{MeV}$ $\left(10\mathrm{MeV}\right)$. In addition, we comment on a recently claimed observation of an $\eta$ mesic ${}^3\mathrm{H}\mathrm{e}$ quasibound state by the TAPS collaboration based on $\eta$ photoproduction data. Although our limits are in reasonable agreement with the values reported by this collaboration, our analysis of these data does not lead to a solid conclusion concerning the existence of an $\eta$-mesic bound state. More dedicated experiments are necessary for further clarification.

• Received 2 August 2004

DOI:https://doi.org/10.1103/PhysRevC.70.047001