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arXiv · 2208.03867

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

John Bulava·Andrew D. Hanlon·Ben Hörz·Colin Morningstar·Amy Nicholson·Fernando Romero-López·Sarah Skinner·Pavlos Vranas·André Walker-Loud
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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.

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John Bulava, Andrew D. Hanlon, Ben Hörz, Colin Morningstar, Amy Nicholson, Fernando Romero-López, Sarah Skinner, Pavlos Vranas, André Walker-Loud. 2022-08-08. Elastic nucleon-pion scattering at $m_{\pi} = 200~{\rm MeV}$ from lattice QCD. https://doi.org/10.1016/j.nuclphysb.2023.116105

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