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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>0.4</a:mn><a:mi>σ</a:mi></a:math> if a one-loop correction of 2.0%—based on the Fermi coupling constant <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>G</c:mi><c:mi>μ</c:mi></c:msub></c:math> derived from measurements of muon lifetime—is included. The radiative corrections at one-loop level lead to resolving the neutrino mass ordering at <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>5</e:mn><e:mi>σ</e:mi></e:math> confidence level 4–9 days earlier than at tree level. In contrast, the sensitivity to leptonic <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>C</g:mi><g:mi>P</g:mi></g:math> 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.