observed correlated pairs were produced by bound or unbound intermediate etas.

After the works [@sokol99; @sokol00] gaining and using information on the decay products became mandatory for experiment planning and data analysis in all further searches for $\eta$-mesic nuclei.

In 2004 an evidence for the $\eta$-mesic nucleus $_\eta^3$He formed in the reaction + \^3[He]{} \_\^3[He]{} \^0 + p + X has been reported from Mainz [@pfeiffer04]. A resonance-like structure was observed in a contribution to the cross section from back-to-back $\pi^0p$ pairs found after a background subtraction. A later study [@pheron12] revealed, however, that the background has a rather complicated structure, so that the conclusions of Ref. [@pfeiffer04] cannot be confirmed. At the moment their statement is that the existence of the $\eta$-mesic nucleus $_\eta^3$He is not yet established.

One more attempt to find $\eta$-mesic nuclei by detecting their $\pi^-p$ decay products has recently been done at the JINR nuclotron [@afanasiev11]. The reaction studied was d + \^[12]{}[C]{} (\_[ ]{}\^[11]{}[Be]{} [  or  ]{} \_[ ]{}\^[11]{}[C]{}) + N\_1 + N\_2 \^- + p + X + N\_1 + N\_2. \[reac:Dubna\] The measured effective mass spectra of the correlated back-to-back $\pi^-p$ pairs show a presence of resonance-like peaks lying slightly below the 