Chiral unitary approach to \eta' N scattering at low energies

Abstract

We study the \eta' N interaction within a chiral unitary approach which includes \pi N, \eta N and related pseudoscalar meson-baryon coupled channels. Since the SU(3) singlet does not contribute to the standard interaction and the \eta' is mostly a singlet, the resulting scattering amplitude is very small and inconsistent with experimental estimations of the \eta' N scattering length. The additional consideration of vector meson-baryon states into the coupled channel scheme, via normal and anomalous couplings of pseudoscalar to vector mesons, enhances substantially the \eta' N amplitude. We also exploit the freedom of adding to the Lagrangian a new term, allowed by the symmetries of QCD, which couples baryons to the singlet meson of SU(3). Adjusting the unknown strength to the \eta' N scattering length, we obtain predictions for the elastic \eta' N --> \eta' N and inelastic \eta' N --> \eta N, \pi N, K\Lambda, K\Sigma\ cross sections at low \eta' energies, and discuss their significance.