Elastic nucleon-pion scattering at $m_{\pi} = 200~{\rm MeV}$ from lattice QCD

TL;DR

This study computes elastic nucleon-pion scattering amplitudes using lattice QCD at a pion mass of 200 MeV, providing precise scattering lengths and demonstrating controlled systematic errors, paving the way for more realistic future calculations.

Contribution

First lattice QCD calculation of nucleon-pion scattering amplitudes at this pion mass with controlled systematic errors and detailed analysis of scattering parameters.

Findings

I=3/2 scattering length determined with <5% error

Effective range expansion describes amplitudes well

Systematic errors from excited states are controlled

Abstract

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with $N_{\rm f} = 2+1$ dynamical quark flavors and $m_{\pi} = 200~{\rm MeV}$. The $s$-wave scattering lengths with both total isospins $I=1/2$ and $I=3/2$ are inferred from the finite-volume spectrum below the inelastic threshold together with the $I=3/2$ $p$-wave containing the $\Delta(1232)$ resonance. The amplitudes are well-described by the effective range expansion with parameters constrained by fits to the finite-volume energy levels enabling a determination of the $I=3/2$ scattering length with statistical errors below $5\%$, while the $I = 1/2$ is somewhat less precise. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a pathway for future computations down to the physical light quark masses with multiple lattice spacings and physical volumes.