Are the chiral based $\bar{K}N$ potentials really energy dependent?

TL;DR

This paper demonstrates that the perceived energy dependence of chiral-based ar{K}N potentials, linked to two poles in the I=0 sector, results from on-shell factorization, and removing this approximation reveals only one pole.

Contribution

It shows that the energy dependence in ar{K}N potentials is an artifact of on-shell factorization, challenging previous interpretations of the ar{K}N interaction.

Findings

Removing on-shell factorization yields a single ar{K}N pole.

The two-pole structure is due to an approximation, not an inherent property.

The results impact the understanding of the ar{K}N interaction and ar{K}N resonance models.

Abstract

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 [E. Oset, A. Ramos, Nucl. Phys. A 635(1998)99]. 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.