The effective Δmee2 in matter

In this paper, we generalize the concept of an effective Delta m(ee)(2) for nu(e)/(nu) over bar (e) disappearance experiments, which has been extensively used by the short baseline reactor experiments, to include the effects of propagation through matter for longer baseline nu(e)/(nu) over bar (e) disappearance experiments. This generalization is a trivial, linear combination of the neutrino mass squared eigenvalues in matter and thus is not a simple extension of the usually vacuum expression, although, as it must, it reduces to the correct expression in the vacuum limit. We also demonstrated that the effective Delta m(ee)(2) in matter is very useful conceptually and numerically for understanding the form of the neutrino mass squared eigenstates in matter and hence for calculating the matter oscillation probabilities. Finally, we analytically estimate the precision of this two-flavor approach and numerically verify that it is precise at the subpercent level.