threshold energy $m_\eta+m_N=1486$ MeV. However, a consistent interpretation of these peaks was not yet obtained.

To date the strongest evidence for the existence of $\eta$-mesic nuclei came from the precision COSY-GEM experiment [@budzanowski09]. Following ideas of the work [@hayano99] borrowed in turn from previous experience in studying deeply-bound pionic states in nuclei, the reaction p + \^[27]{} \^3[He]{} + \^[25]{}\_[ ]{}[Mg]{} \^3[He]{} + p + \^- + X \[reac:COSY-GEM\] of a recoilless formation of the $\eta$-mesic nuclei $^{25}_{~\eta}\rm
Mg$ was explored and the mass of this $\eta$-mesic nucleus was determined through precision missing-mass measurements in $(p,
{}^3{\rm He})$. A clear peak was found in the missing mass spectrum that corresponds to the binding energy $-13.13\pm 1.64$ MeV and the width $10.22\pm 2.98$ MeV of the formed $\eta$-mesic nucleus. An upper limit of $\approx 0.5$ nb was found for the cross section of the $\eta$-mesic nucleus formation.

Recently Haider and Liu argued [@haider10a; @haider10b] that the observed peak in (\[reac:COSY-GEM\]) is shifted down from the genuine binding energy of $\eta$ because of interference of the resonance and nonresonance mechanisms of the reaction (similar to those shown in Fig. \[diagrams-piN\]). This very interesting effect signifies that the genuine $\eta$ binding in ${}_{~\eta}^{25}{\rm 