Commutators of lepton mass matrices,CPviolation, and matter effects in medium-baseline neutrino experiments

We introduce the commutators of lepton mass matrices to describe the phenomenon of lepton flavor mixing, and establish their relations to the effective Hamiltonians responsible for the propagation of neutrinos. The determinants of those commutators are invariant under matter effects, leading to an instructive relationship between the universal $\mathrm{CP}$-violating parameters in vacuum and in matter. In the scenario of low-energy (100 MeV $<~E<~1\mathrm{GeV})$ and medium-baseline (100 km $<~L<~400\mathrm{km})$ neutrino experiments, we illustrate the features of lepton flavor mixing and $\mathrm{CP}$ violation. The terrestrial matter effects on $\mathrm{CP}$- and T-violating asymmetries in ${\nu }_e\leftrightarrow {\nu }_{\mu }$ and ${\overline{\nu }}_e\leftrightarrow {\overline{\nu }}_{\mu }$ neutrino oscillations are also discussed. We demonstrate that a relatively pure signal of leptonic $\mathrm{CP}$ violation at the percent level can be established from such medium-baseline experiments with low-energy neutrino beams.