Structure of $\Lambda$(1405) resonance and $\gamma{p}\rightarrow K^{+}+(\pi\Sigma)^{0}$ reaction

TL;DR

This paper investigates the structure of the $ ext{Lambda}(1405)$ resonance through three-body calculations of the $Kar{K}N$ system, analyzing $ ext{pi} ext{Sigma}$ mass spectra in reactions to determine the resonance's mass.

Contribution

It introduces a detailed three-body calculation approach using different $ar{K}N- ext{pi} ext{Sigma}$ potentials to study the $ ext{Lambda}(1405)$ resonance in specific reactions.

Findings

The $ ext{Lambda}(1405)$ resonance mass is approximately 1417 MeV/c².

Different potential models can reproduce the $ ext{Lambda}(1405)$ features in $ ext{pi} ext{Sigma}$ spectra.

The study demonstrates the feasibility of observing $ ext{Lambda}(1405)$ in the specified reaction.

Abstract

Three-body calculations of $K\bar{K}N$ system with quantum numbers $I=1/2$, $J^{\pi}=(\frac{1}{2})^{+}$ were performed. Using separable potentials for two-body interactions, we calculated the $\pi\Sigma$ mass spectra for the $(\bar{K}N)_{I=0}+K^{+}\rightarrow(\pi\Sigma)^{0}K^{+}$ reaction on the basis of three-body Alt-Grassberger-Sandhas equations in the momentum representation. In this regard, different types of $\bar{K}N-\pi\Sigma$ potentials based on phenomenological and chiral SU(3) approach are used. The possibility to observe the trace of $\Lambda(1405)$ resonance in $(\pi\Sigma)^{0}$ mass spectra was studied. Using the $\chi^{2}$ fitting, it was shown that the mass of $\Lambda$(1405) resonance is about 1417 $\mathrm{MeV}/c^{2}$.