Energy dependence of the $\bar{K}N$ interaction and the two-pole structure of the $\Lambda(1405)$ -- are they real?

Abstract

It is shown, that the energy dependence of the chiral based $\bar{K}N$ potentials, responsible for the ocurence of two poles in the $I=0$ sector is the consequence of applying the on-shell factorization approximation [1]. When the dynamical equation is solved without this approximation, the $T$-matrix has only one pole in the region of the $\Lambda(1405)$ resonance.