Neutrino-deuteron scattering: Uncertainty quantification and new $L_{1,A}$ constraints

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 ($\chi$EFT). We provide uncertainty estimates from $\chi$EFT truncations of the electroweak current, dependences on the $\chi$EFT cutoff and variations in the pool of fit data used to fix the low-energy constants of $\chi$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 $\chi$EFT results to those of pionless effective field theory ($\cancel{\pi}$EFT), we provide new constraints for the counterterm $L_{1,A}$ that parameterizes the strength of the axial two-body current in $\cancel{\pi}$EFT. We obtain a value of $4.9^{+1.9}_{-1.5}\mathrm{fm}^3$ 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.