For three generations of leptons, the Pontecorvo–Maki–Nakagawa–Sakata matrix can be written as:
On the left are the neutrino fields participating in the weak interaction, and on the right is the PMNS matrix along with a vector of the neutrino fields diagonalizing the neutrino mass matrix. The PMNS matrix describes the probability of a neutrino of given flavor α to be found in mass eigenstate i. These probabilities are proportional to |Uαi|2.
Various parametrizations of this matrix exist, however due to the difficulties of detecting neutrinos, it is much more difficult to determine the individual coefficients than in the equivalent matrix for the quarks (the CKM matrix). The matrix is most commonly parameterized by three mixing angles (Θ12, Θ23 and Θ13) and a single phase. Experimentally, the mixing angles were established to be approximately Θ12=45 degrees, Θ23=34 degrees, and Θ13<4 degrees.
As a starting point, one recent particle physics course provided the following estimated values for the matrix (assuming the mixing angle Θ13=0, which is in good agreement with the experiment, and therefore no imaginary parameters in the matrix):