Matter effects of sterile neutrino in light of renormalization-group equations

The renormalization-group equation (RGE) approach to neutrino matter effects is further developed in this work. We derive a complete set of differential equations for effective mixing elements, masses and Jarlskog-like invariants in presence of a light sterile neutrino. The evolutions of mixing elements as well as Jarlskog-like invariants are obtained by numerically solving these differential equations. We calculate terrestrial matter effects in long-baseline (LBL) experiments, taking NOvA, T2K and DUNE as examples. In both three-flavor and four-flavor frameworks, electron-neutrino survival probabilities as well as the day-night asymmetry of solar neutrino are also evaluated as a further examination of the RGE approach.