LAUSR

We study neutral- and charged-current (anti)neutrino-induced dissociation of the deuteron at energies from threshold up to 150 MeV by employing potentials, as well as one- and two-body currents, derived in chiral effective field theory ($\ensuremath{\chi}\mathrm{EFT}$). We provide uncertainty estimates from $\ensuremath{\chi}\mathrm{EFT}$ truncations of the electroweak current, dependences on the $\ensuremath{\chi}\mathrm{EFT}$ cutoff, and variations in the pool of fit data used to fix the low-energy constants of $\ensuremath{\chi}\mathrm{EFT}$. At 100 MeV of incident (anti)neutrino energy, these uncertainties amount to about 2--3% and are smaller than the sensitivity of the cross sections to the single-nucleon axial form factor, which amounts to $5%$ if one varies the range of the nucleon axial radius within the bands determined by recent lattice quantum chromodynamics evaluations and phenomenological extractions. We conclude that a precise determination of the nucleon axial form factor is required for a high-precision calculation of the neutrino-deuteron cross sections at energies higher than 100 MeV. By matching our low-energy $\ensuremath{\chi}\mathrm{EFT}$ results to those of pionless effective field theory ($\overline{)\ensuremath{\pi}}\phantom{\rule{0.28em}{0ex}}\mathrm{EFT}$), we provide new constraints for the counterterm ${L}_{1,A}$ that parametrizes the strength of the axial two-body current in $\overline{)\ensuremath{\pi}}\phantom{\rule{0.28em}{0ex}}\mathrm{EFT}$. We obtain a value of $4.{9}_{\ensuremath{-}1.5}^{+1.9}\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{3}$ at renormalization scale set to pion mass, which is compatible with, albeit narrower than, previous experimental determinations, and comparable to a recent lattice quantum chromodynamics calculation.