Importance of chiral constraints for the pole content of the $\bar{K}N$ scattering amplitude

Abstract

We critically examine the $\bar{K}N$ coupled-channel approach presented in [1] and demonstrate that it violates constraints imposed by chiral symmetry of QCD. The origin of this violation can be traced back to the off-shell treatment of the chiral-effective vertices, in combination with the use of non-relativistic approximations and the chosen regularization scheme. We propose an improved version of the approach, which is directly given by a resummation of relativistic Feynman graphs of baryon chiral perturbation theory, and is in accord with the chiral symmetry constraint. Within this improved model, two poles are generated dynamically in the isoscalar $\pi\Sigma - \bar{K}N$ coupled channels sector, in contrast with the non-relativistic model of [1] in which only one such pole was reported.