Analytic treatment of neutrino oscillation and decay in matter

We analyze invisible decay of neutrinos in the presence of oscillation and matter eﬀects. The inclusion of decay can be accommodated by a non-Hermitian eﬀective Hamiltonian, with the Hermitian component giving rise to oscillations, and the anti-Hermitian component leading to the invisible decay of neutrinos. We consider the possibility that the oscillation and decay matrix may not commute; in fact, in matter, they will invariably become non-commuting. This would lead to a mismatch between the eﬀective mass eigenstates and the decay eigenstates. Employing a resummation of the Zassenhaus expansion, we develop a formalism for calculating the neutrino oscillation probabilities in the two-ﬂavor scenario. This technique can easily be extended to three ﬂavors.