On-shell approach to neutrino oscillations

In the usual quantum field theoretical approach, neutrino oscillations are studied diagonalizing either the mass or matter Hamiltonians. In this paper we analyze the problem from an on-shell amplitude perspective, where Lagrangians or Hamiltonians are not available. We start by studying in detail how flavor enters in the amplitudes and how the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix emerges. We then analyze the elastic amplitude of two neutrinos and two charged leptons that induce matter effects and propose a strategy to obtain the known results of the standard oscillation theory without Hamiltonians. Finally, we extend the previously proposed procedure and use the most general elastic 4-point amplitude to study beyond the Standard Model effects on oscillations.