Λ(1405) as a K¯N Feshbach resonance in the Skyrme model

Takashi Ezoe,Atsushi Hosaka

doi:10.1103/physrevd.102.014046

Abstract

We describe the Lambda(1405) hyperon as a Feshbach resonance of a bar-KN quasi-bound state coupled by a decaying channel of pi Sigma in the Skyrme model. A weakly bound bar-KN state is generated in the laboratory frame, while the Sigma hyperon as a strongly bound state of bar-KN in the intrinsic frame. We obtain a coupling of bar-KN and pi Sigma channels by computing a baryon matrix element of the axial current. This coupling enables the decay of the bar-KN bound state to pi-Sigma . It is shown that the Skyrme model supports the Lambda(1405) as a narrow Feshbach resonance.

Highlights

The negative parity state of the hyperon of the lowest mass, Λð1405Þ, has brought many discussions over half a century, because its properties are not explained by the standard quark model [1]
We describe the Λð1405Þ hyperon as a Feshbach resonance of a K N quasibound state coupled by a decaying channel of πΣ in the Skyrme model
In our previous publications [12,13], we have investigated the K N interaction in the Skyrme model using an analogous method to the bound state approach by Callan and Klebanov [22,23]

Summary

INTRODUCTION

The negative parity state of the hyperon of the lowest mass, Λð1405Þ, has brought many discussions over half a century, because its properties are not explained by the standard quark model [1]. A chiral model for the K N was developed, which predicted a less attractive interaction that is still sufficient to generate a loosely bound K N state with a mass spectrum of Λð1405Þ being consistent with experimental data [8] Setting the two parameters at suitable values, the pion decay constant and the Skyrme parameter, it has been shown that the Kfeels an attractive interaction from the nucleon and is bound with a binding energy of order 10 MeV, which is identified with Λð1405Þ Another interesting feature is that when the K N interaction is expressed in the form of a local potential, it exhibits an attractive pocket at medium distances supplemented by a repulsion at short distances. Details of technical issues in performing such a computation are developed

ACTIONS AND ANSATZ

COUPLING TO THE πΣ CHANNEL

The axial current

Baryon states

CALCULATION OF THE MATRIX ELEMENT

RESULTS AND DISCUSSIONS