Remarks upon the mass oscillation formulas

TL;DR

This paper critiques the standard derivation of neutrino mass oscillation formulas, highlighting an inconsistency that leads to a factor of two error, and proposes a clearer approach to resolve this ambiguity.

Contribution

It identifies and clarifies the source of the factor two discrepancy in mass oscillation formulas, proposing a simplified velocity-based scenario.

Findings

The standard $t o L$ approximation causes a factor of two error.

The inconsistency arises from assumptions about neutrino production.

A velocity scenario provides a consistent derivation.

Abstract

The standard formula for mass oscillations is often based upon the approximation $t \approx L$ and the hypotheses that neutrinos have been produced with a definite momentum $p$ or, alternatively, with definite energy $E$. This represents an inconsistent scenario and gives an unjustified reduction by a factor of two in the mass oscillation formulas. Such an ambiguity has been a matter of speculations and mistakes in discussing flavour oscillations. We present a series of results and show how the problem of the factor two in the oscillation length is not a consequence of gedanken experiments, i.e. oscillations in time. The common velocity scenario yields the maximum simplicity.