Matter neutrino oscillations, an approximation in a parametrization-free framework

Neutrino oscillations are one of the most studied and successful phenomena since the establishment of the solar neutrino problem in late 1960's. In this work we discuss the exact expressions for the probability P_{\alpha\beta} in a constant density medium, in terms of the standard vacuum parameters and the medium density. Besides of being compact, these expressions are independent of any particular parametrization, which could be helpful in the application of unitary tests of the mixing matrix. In addition, we introduce a new approximation on P_{\alpha\beta} and compare it with the most commonly used, discussing their main differences.