Revisiting series expansions of neutrino oscillation and decay probabilities in matter

Abstract

We present analytic expressions for three-flavor neutrino oscillations in presence of invisible neutrino decay and matter effects. Using the well-known Cayley-Hamilton formalism, the leading-order terms are derived for oscillation probabilities in all major channels assuming the neutrino mass eigenstate $ν_3$ to decay. Our work extends and complements previous studies utilizing the Cayley-Hamilton theorem, providing the series expansions for $ν_e \rightarrow ν_e$, $ν_e \rightarrow ν_μ$, $ν_e \rightarrow ν_τ$, $ν_μ\rightarrow ν_μ$ and $ν_μ\rightarrow ν_τ$. The accuracy of the analytical formulas is investigated by comparing the results with numerically calculated probabilities. We also comment on the implications on unitarity violation.