Construction of a local barK N-pi Sigma-pi Lambda potential and composition of the Lambda(1405)

TL;DR

This paper constructs a coupled-channel potential for Kbar N, pi Sigma, pi Lambda interactions based on chiral SU(3) dynamics, revealing the two-pole structure of Lambda(1405) and analyzing its composition.

Contribution

It introduces a local potential framework that explicitly includes the pi Sigma channel, improving the description of Lambda(1405) and its two-pole structure compared to previous models.

Findings

The high-mass pole of Lambda(1405) is dominated by Kbar N component.

The potential reproduces coupled-channel scattering amplitudes accurately.

The framework clarifies the compositeness of Lambda(1405).

Abstract

A Kbar N-pi Sigma-pi Lambda coupled-channel potential is constructed on the basis of chiral SU(3) dynamics. Several matching conditions are introduced to formulate an equivalent local potential that reproduces the coupled-channel scattering amplitudes resulting from chiral SU(3)_L times SU(3)_R meson-baryon effective field theory. In contrast to a previously constructed effective single-channel Kbar N potential, the explicit treatment of the pi Sigma channel yields a natural description of the low-mass pole as part of the two-pole structure of the Lambda(1405) resonance. The energy dependence of the potential can now be parametrized with a minimum of polynomial orders. To study the properties of the Lambda(1405) as a quantum-mechanical quasibound state, we derive the normalization condition of its wave function generated by the energy-dependent coupled-channel potential, using the Feshbach projection method. This framework provides an improved understanding of this system from the viewpoint of the compositeness of hadrons. With the properly normalized wave function, we demonstrate and confirm that the high-mass pole of the Lambda(1405) is dominated by the Kbar N component.