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

Abstract

The cross section of the inclusive process ${\ensuremath{\pi}}^{+}d\ensuremath{\rightarrow}p(\ensuremath{\eta}p)$ is calculated as a function of the $\ensuremath{\eta}p$ invariant mass when the detected proton is moving in the forward direction. The incident pion has a momentum of ${p}_{\mathrm{lab}}=898.47$ MeV/$c$ for which the $\ensuremath{\eta}p$ pair are left at rest in the laboratory system which allows one to study the effect of the $\ensuremath{\eta}p\ensuremath{\rightarrow}\ensuremath{\eta}p$ 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 $\ensuremath{\eta}N$ final-state interaction is discussed.