2022/12/23 by Asli M. Abdullahi, Abdullahi, Asli, Stephen Parke +1 · 1 citation
Physics and Astronomy · #Astrophysics and Cosmic Phenomena #Dark Matter and Cosmic Phenomena #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Neutrino Physics Research
paper · pdf · doi:10.48550/arxiv.2212.12565
openalex publication_date 2022/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We revisit neutrino oscillations in constant matter density for a number of different scenarios: three flavors with the standard Wolfenstein matter potential, four flavors with standard matter potential and three flavors with non-standard matter potentials. To calculate the oscillation probabilities for these scenarios one must determine the eigenvalues and eigenvectors of the Hamiltonians. We use a method for calculating the eigenvalues that is well known, determination of the zeros of determinant of matrix (λI -H), where H is the Hamiltonian, I the identity matrix and λ is a scalar. To calculate the associated eigenvectors we use a method that is little known in the particle physics community, the calculation of the adjugate (transpose of the cofactor matrix) of the same matrix, (λI -H). This method can be applied to any Hamiltonian, but provides a very simple way to determine the eigenvectors for neutrino oscillation in matter, independent of the complexity of the matter potential. This method can be trivially automated using the Faddeev-LeVerrier algorithm for numerical calculations. For the above scenarios we derive a number of quantities that are invariant of the matter potential, many are new such as the generalization of the Naumov-Harrison-Scott identity for four or more flavors of neutrinos. We also show how these matter potential independent quantities become matter potential dependent when off-diagonal non-standard matter effects are included.