Effects of the Matter Potential at One-Loop Level on Neutrino Oscillations in Long-Baseline Experiments

In this work, we investigate in a quantitative way how much radiative corrections to the matter potential for neutrino oscillations can impact the sensitivity to neutrino mass ordering in long-baseline accelerator experiments. Using numerical simulations for the future experiment DUNE, we find that the statistical significance for excluding the incorrect mass ordering can be enhanced by about $0.4\sigma$ if a one-loop correction of $2.0\%$ -- based on the Fermi coupling constant $G^{}_\mu$ derived from measurements of muon lifetime -- is included. The radiative corrections at one-loop level lead to resolving the neutrino mass ordering at $5\sigma$ confidence level 4-9 days earlier than at tree level. In contrast, the sensitivity to leptonic CP violation in DUNE is essentially unchanged. Finally, we emphasize that one-loop corrections should be incorporated into analyses of future neutrino oscillation data in a consistent and systematic manner.