Eur. Phys. J. C (2025) 85: 277
https://doi.org/10.1140/epjc/s10052-025-14006-2

Regular Article - Theoretical Physics

Deciphering $\mathrm{\Lambda }(1405)$ state via mass, compositeness and magnetic moment

Department of Physics, Faculty of Sciences, Ondokuz Mayis University, 55200, Samsun, Turkey

^a hmutuk@omu.edu.tr

Received: 9 December 2024
Accepted: 24 February 2025
Published online: 12 March 2025

Abstract

The $\mathrm{\Lambda }(1405)$ state has strangeness $S=-1$ and isospin $I=0$ with quantum number $J^P=1/2^{-}$. It is located just below the threshold of $\overline{K}N$. In this study, the internal structure of the $\mathrm{\Lambda }(1405)$ state is investigated based on meson-baryon molecular configuration using one-boson-exchange (OBE) model. We take into account various states ($K^{-}p$, $K^{0}n$, $K^{-}p-K^{0}n$, ${\pi }^{+}{\mathrm{\Sigma }}^{-}$, ${\pi }^{-}{\mathrm{\Sigma }}^{+}$, ${\pi }^0{\mathrm{\Sigma }}^0$, ${\pi }^{+}{\mathrm{\Sigma }}^{-}-{\pi }^{-}{\mathrm{\Sigma }}^{+}$, ${\pi }^{+}{\mathrm{\Sigma }}^{-}-{\pi }^0{\mathrm{\Sigma }}^0$ and ${\pi }^{-}{\mathrm{\Sigma }}^{+}-{\pi }^0{\mathrm{\Sigma }}^0$ and $\eta \mathrm{\Lambda }$) and calculate spectroscopic parameters such as mass and magnetic moment. Some of the predicted masses for the states in this work are below corresponding threshold. The predicted masses of $K^{-}p$, $K^{0}n$, and $K^{-}p-K^{0}n$ states are below $\overline{K}N$ threshold whereas predicted masses of ${\pi }^{+}{\mathrm{\Sigma }}^{-}$, ${\pi }^{-}{\mathrm{\Sigma }}^{+}$, ${\pi }^0{\mathrm{\Sigma }}^0$, ${\pi }^{+}{\mathrm{\Sigma }}^{-}-{\pi }^{-}{\mathrm{\Sigma }}^{+}$, ${\pi }^{+}{\mathrm{\Sigma }}^{-}-{\pi }^0{\mathrm{\Sigma }}^0$, and ${\pi }^{-}{\mathrm{\Sigma }}^{+}-{\pi }^0{\mathrm{\Sigma }}^0$ states are below $\pi \mathrm{\Sigma }$ threshold. These states may be bound state candidates. We obtain that all the states of this present work have sizes larger than the confinement scale, $(1/{\mathrm{\Lambda }}_{\text{QCD}}\sim 1\text{fm})$. We also study compositeness criterion for these states. Using compositeness criterion, we calculate scattering length $a_s$ and effective range $r_e$. The results reflect that the present states of this work have compositeness dominance, i.e., they are in molecular configuration. The magnetic moment results yield that the magnetic moment is mainly dominated by the corresponding baryon component. Our results of magnetic moments support $\overline{K}N$ molecular configuration for $\mathrm{\Lambda }(1405)$.