Regions of Applicability of Approximate Formulations of Neutrino Oscillations in Matter

We examine the reliability of the theoretical methods presently used for analysis and prediction of neutrino oscillation phenomena. Of particular interest are the limitations imposed by branch points when expansions in one of the small parameters of the Standard Neutrino Model (SNM) are made to obtain tractable results. Our evaluation compares the approximate oscillation probabilities for flavor-changing transitions in the $(\nu_e , \nu_\mu)$ sector to exact results obtained from of a recently-developed exact analytical representation of neutrino oscillations in matter within the SNM. From our numerical comparisons, we are able to identify regions where the existing approaches can be improved to take full advantage of the higher quality data expected at future neutrino facilities.