Do massive neutrino states really exist?

Abstract

In neutrino physics, while massive states define neutrino masses, the flavor states participating in weak interactions are governed by an off-diagonal mass matrix. This work examines the complete form of this mass matrix, both for a two-flavor toy model and for the general three-flavor case under two distinct mass hierarchies. Using the Monte Carlo method, we estimate the mass matrix parameters and demonstrate how its structure governs the dependence of the interaction cross section on the mass hierarchy (normal vs inverted). This formalism enables the treatment of processes involving neutrino exchange through a non-diagonal propagator, corresponding to a quantum field theory description. Numerical estimates for a local charged-lepton interaction via virtual neutrino exchange yield a ratio of electron-antimuon (lepton flavor violating) to electron-positron cross sections on the order of $10^{-51}$. Furthermore, the cross section exhibits a fundamental dependence on the lightest neutrino mass, which differs drastically between the two hierarchies. For macroscopic processes, this propagator formalism reproduces the standard neutrino oscillation probability by operating directly with the non-diagonal mass matrix, thereby circumventing the wave-packet formalism and confirming the validity of this approach.