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.

arXiv comment10 pages, 8 figures; more contents added based on the referee's comments; accepted by Phys. Rev. D

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