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

The cross section of the inclusive process pi(+) d -> p(eta p) is calculated as a function of the eta p 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 eta p pair are left at rest in the laboratory system which allows one to study the effect of the eta p -> eta p final-state interaction in the region of the N( 1535) S-11 resonance. The sensitivity of the inclusive cross section to different parametrizations of the eta N final-state interaction is discussed.