Neutrino oscillations and the effect of the finite lifetime of the neutrino source

TL;DR

This paper investigates how the finite lifetime of a neutrino source affects neutrino oscillation probabilities, deriving conditions for observable effects and analyzing their significance in experimental setups.

Contribution

It introduces a condition linking source lifetime to neutrino oscillations and studies the impact of finite source lifetime on oscillation probabilities under specific assumptions.

Findings

Finite source lifetime can modify neutrino oscillation probabilities.

In current accelerator experiments, the effect of source lifetime is negligible.

Certain experimental conditions can make source lifetime effects significant.

Abstract

We consider a neutrino source at rest and discuss a condition for the existence of neutrino oscillations which derives from the finite lifetime $\tau_S$ of the neutrino source particle. This condition is present if the neutrino source is a free particle such that its wave function is non-stationary. For a Gaussian wave function and with some simplifying assumptions, we study the modification of the usual oscillation probability stemming from $\tau_S$. In the present accelerator experiments the effect of $\tau_S$ can be neglected. We discuss some experimental situations where the source lifetime becomes relevant in the oscillation formula.