Do massive neutrino states really exist?

TL;DR

This work formulates a matrix-propagator framework for neutrinos by deriving an explicit Dirac propagator with a non-diagonal mass matrix and connecting it to the standard three-flavor PMNS parametrization. Using Monte Carlo sampling based on NuFIT 6.0 and T2K/NOvA results, it provides numerical estimates of the neutrino mass-matrix elements for normal and inverted hierarchies, highlighting distinct behavior of off-diagonal components and hints of fine-tuning in the IH case. In a two-flavor toy model, it shows that flavor-changing neutrino exchange in local processes is extremely suppressed (e.g., $d\\sigma\\sim 10^{-62}$ fbarn for off-diagonal terms, or a ratio ~ $10^{-51}$ to flavor-conserving channels), while macroscopic propagation reproduces the standard oscillation probability $P_{e\\to\\mu} \propto \sin^2(2\\theta)\\sin^2(\Delta m^2 L/(4E_{\\text{avg}}))$. The results validate a QFT approach with non-diagonal propagators that is consistent with conventional QM oscillations, provide explicit analytic expressions for the mass matrix in terms of mixing parameters and masses, and clarify hierarchy-dependent features that could inform future theoretical and phenomenological studies of neutrino flavor dynamics.

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.

Figures (13)

• Figure 1: analogue of the Mandelstam plane
• Figure 2: Plots of $\Re(m_{e\mu})$ for both neutrino mass hierarchies: normal hierarchy on the left and inverted hierarchy on the right, as a function of the lightest neutrino mass.
• Figure 3: Diagram of $l_{\alpha}^- l_{\beta}^+ \to W^+ W^-$ for t-channel.
• Figure 4: Plots of $\frac{d\sigma}{d\Omega}$ for both neutrino mass hierarchies: normal (left) and inverted (right), as a function of the lightest neutrino mass $m_1$ and $m_3$, respectively.
• Figure 5: Diagram of $l_{\alpha} W^+ \to l_{\beta} W^+$ for s-channel.