Structure of the $\mathbf{\Lambda(1405)}$ from Hamiltonian effective field theory

TL;DR

This paper investigates the internal structure of the $ ext{Λ(1405)}$ resonance using Hamiltonian effective field theory, fitting to experimental scattering data and comparing finite-volume spectra to lattice QCD results, revealing the importance of a bare baryon component at high pion masses.

Contribution

It introduces a Hamiltonian effective field theory approach with momentum-dependent potentials to analyze the $ ext{Λ(1405)}$, including the effect of a bare baryon basis state, and compares results with experimental and lattice data.

Findings

Two complex poles for $ ext{Λ(1405)}$ are consistent with experimental data.

The bare baryon basis state is crucial for lattice QCD results at high pion masses.

Cross sections match experimental data across different model assumptions.

Abstract

The pole structure of the $\Lambda(1405)$ is examined by fitting the couplings of an underlying Hamiltonian effective field theory to cross sections of $K^- p$ scattering in the infinite-volume limit. Finite-volume spectra are then obtained from the theory, and compared to lattice QCD results for the mass of the $\Lambda(1405)$. Momentum-dependent, non-separable potentials motivated by the well-known Weinberg-Tomozawa terms are used, with SU(3) flavour symmetry broken in the couplings and masses. In addition, we examine the effect on the behaviour of the spectra from the inclusion of a bare triquark-like isospin-zero basis state. It is found that the cross sections are consistent with the experimental data with two complex poles for the $\Lambda(1405)$, regardless of whether a bare baryon basis state is introduced or not. However, it is apparent that the bare baryon is important for describing the results of lattice QCD at high pion masses.