Elastic nucleon-pion scattering at $m_{\pi }=200\mathrm{M}\mathrm{e}\mathrm{V}$ from lattice QCD

Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with $N_{\mathrm{f}}=2+1$ dynamical quark flavors and $m_{\pi }=200\mathrm{M}\mathrm{e}\mathrm{V}$. The $s$-wave scattering lengths with both total isospins $I=1\mathrm{/}2$ and $I=3\mathrm{/}2$ are inferred from the finite-volume spectrum below the inelastic threshold together with the $I=3\mathrm{/}2$ $p$-wave containing the $\mathrm{\Delta }(1232)$ 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 $I=3\mathrm{/}2$ scattering length with statistical errors below $5\mathrm{\%}$, while the $I=1\mathrm{/}2$ 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.