Progress on Meson-Baryon Scattering

TL;DR

This paper reports progress in calculating meson-baryon scattering amplitudes using lattice QCD techniques, focusing on specific isospin channels and resonances, with preliminary results indicating successful extraction of relevant amplitudes.

Contribution

It introduces a lattice QCD approach employing the finite-volume Lüscher method and stochastic LapH to compute meson-baryon scattering amplitudes on a single ensemble with dynamical fermions.

Findings

Preliminary amplitudes for $I=1/2, 3/2$ $N ext{pi}$ channels including $ ext{Delta}(1232)$.

Results for the $I=0$ $S$-wave amplitude with strangeness relevant to $ ext{Lambda}(1405)$.

Demonstration of the feasibility of extracting scattering amplitudes using the described lattice techniques.

Abstract

Progress in computing various meson-baryon scattering amplitudes is presented on a single ensemble from the Coordinated Lattice Simulations (CLS) consortium with $m_\pi=200$ MeV and $N_f=2+1$ dynamical fermions. The finite-volume L\"uscher approach is employed to determine the lowest few partial waves from ground- and excited-state energies computed from correlation matrices rotated in a single pivot using a generalized eigenvector solution. This analysis requires evaluating matrices of correlation functions between single- and two-hadron interpolating operators which are projected onto definite spatial momenta and finite-volume irreducible representations. The stochastic LapH method is used to estimate all needed quark propagators. Preliminary results are presented for $I=\frac{1}{2}, \frac{3}{2}$ $N\pi$ amplitudes including the $\Delta(1232)$ resonance and the $I=0$ $S$-wave amplitude with unit strangeness relevant for the $\Lambda(1405)$.