1. Elastic nucleon-pion scattering at $m_{\pi} \approx 200~{\rm MeV}$ from lattice QCD
- Author
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Bulava, John, Hanlon, Andrew D., Hörz, Ben, Morningstar, Colin, Nicholson, Amy, Romero-López, Fernando, Skinner, Sarah, Vranas, Pavlos, and Walker-Loud, André
- Subjects
expansion, effective range ,quark, mass ,partial wave ,scattering amplitude ,scattering ,lattice field theory ,Delta(1232) ,scattering amplitudes ,isospin ,lattice QCD ,error, statistical ,finite size ,scattering length ,excited state ,gauge field theory ,energy levels ,quark, flavor ,lattice - Abstract
Elastic nucleon-pion scattering amplitudes are computed using lattice QCD on a single ensemble of gauge field configurations with $N_f = 2+1$ dynamical quark flavors and $m_{\pi}$ = 200 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.
- Published
- 2022
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