Are the Chiral Based $$\bar{\varvec{K}}\varvec{N}$$ K ¯ N Potentials Really Energy-Dependent?

It is shown, that the energy dependence of the chiral based $$\bar{K}N$$ potentials, responsible for the occurrence of two poles in the $$I=0$$ sector, is the consequence of applying the on-shell factorization introduced in Oset and Ramos (Nucl Phys A 635:99, 1998). When the dynamical equation is solved without this approximation, the T-matrix has only one pole in the energy region of the $$\Lambda (1405)$$ resonance.