Inclusive π+d→p(ηp) process and the ηn scattering length

The cross section of the inclusive process π+d→p(ηp) is calculated as a function of the ηp invariant mass when the detected proton is moving in the forward direction. The incident pion has a momentum of plab=898.47 MeV/c for which the ηp pair are left at rest in the laboratory system which allows one to study the effect of the ηp→ηp final-state interaction in the region of the N(1535)S11 resonance. The sensitivity of the inclusive cross section to different parametrizations of the ηN final-state interaction is discussed.