The Nucleon Axial Form Factor from Averaging Lattice QCD Results

Flagship neutrino oscillation experiments depend on precise and accurate theoretical knowledge of neutrino-nucleon cross sections across a variety of energies and interaction mechanisms. Key ingredients to the amplitudes that make up these cross sections are parameterized form factors. The axial form factor describing a weak interaction with a nucleon is part of one of the primary neutrino-nucleon interaction mechanisms, quasielastic scattering, yet this form factor is uncertain and its precision is limited by the availability of data for a neutrino scattering with nucleons or small nuclear targets. Lattice Quantum Chromodynamics (LQCD) now offers another approach for obtaining mathematically rigorous constraints of the axial form factor from theoretical calculations with complete systematic error budgets. In this work, strategies for averaging LQCD results are explored, including both a random sampling of form factor values across momentum transfers as well as an averaging strategy based on analytic calculations of form factor derivatives. Fits to z expansion parameterizations are reported and compared against neutrino-hydrogen and neutrino-deuterium scattering data.