Effects of matter density variations on dominant oscillations in long baseline neutrino experiments

Variations around the average density and composition of the Earth mantle may affect long-baseline (anti)neutrino oscillations through matter effects. For baselines not exceeding a few thousand km, such effects are known to be very small, and can be practically regarded as fractional contributions to the theoretical uncertainties. We perturbatively derive compact expressions to evaluate such contributions in phenomenologically interesting scenarios with three or four neutrinos and a dominant mass scale.