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

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 π = 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 ∆(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 scattering length is somewhat less precisely evaluated. Systematic errors due to excited states and the influence of higher partial waves are controlled, providing a step toward future computations down to physical light quark masses with multiple lattice spacings and volumes.

Form factor and model dependence in neutrino-nucleus cross section predictions

“…Excited-state effects involving N π states have been identified as a significant source of systematic uncertainty in LQCD cal-culations of axial form factors [28,30,34,[37][38][39]. More sophisticated analysis strategies employed in recent calculations [28,30,34], as well as variational methods used to study ππ [40][41][42][43][44], N π [45][46][47][48][49], and N N [50][51][52] scattering and N π transition form factors [39] that enable N π and other excited-state effects to be explicitly subtracted from future nucleon elastic form factor calculations, provide paths towards better quantifying and reducing these challenging systematic uncertainties. Although significant future progress is expected, LQCD calculations of nucleon axial form factors have progressed to a point where it is important to understand the phenomenological impact of current results and quantitatively establish what form factor precision is required to achieve the cross-section precision needs of current and future neutrino oscillation experiments [53][54][55].…”