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

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.

Comments: 10 pages, 8 figures; more contents added based on the referee's comments; accepted by Phys. Rev. D