An on-shell approach to neutrino oscillations

TL;DR

This paper introduces an on-shell amplitude approach to neutrino oscillations, deriving standard results and exploring potential beyond Standard Model effects without relying on Hamiltonian formalism.

Contribution

It presents a novel on-shell amplitude framework for neutrino oscillations, bypassing traditional Hamiltonian methods and enabling analysis of new physics effects.

Findings

Derivation of standard oscillation results from on-shell amplitudes

Method to incorporate matter effects without Hamiltonians

Extension to study beyond Standard Model contributions

Abstract

In the usual quantum field theoretical approach, neutrino oscillations are studied diagonalising either the mass or matter Hamiltonians. In this paper we analyse 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 PMNS matrix emerges. We then analyse 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.