π+d→ηpp and the ηN scattering length

We show that for incident pion momentum plab=903MeV/c the cross section of π+d→ηpp with the η produced in the backward direction is very sensitive to the low-energy ηN amplitude. We conclude that the measurement of this reaction at these kinematic conditions will allow a better determination of the ηN scattering length, which is known with a large uncertainty and attracts intense experimental and theoretical interest. Our result strongly motivates performing this experiment in the K1.8BR beam line area at the J-PARC facility in Japan. The experiment will eventually provide new insight on the important quest for eta-mesic nucleus in hadronic physics.