Relativistic treatment of the quasivirtual η N N state

We calculate ηd elastic scattering using a relativistic three-body model with separable interactions in order to study the position of the quasivirtual η N N state in the complex plane. The inputs of the model are the separable potentials of the NN and mN subsystems, where m is a meson (m = η, π, or σ). σ is not treated as a stable particle but as a ππ resonance so that we include its mass and width as deduced from the phase shift of the I = J = 0 resonance. In all cases, we find that the nearest pole corresponds to a quasivirtual state even if Re A_ηd is negative.