What is $\Delta m^2_{ee}$ ?

TL;DR

This paper clarifies the definition of the effective neutrino mass-squared difference $oldsymbol{ ext{Δ}m^2_{ee}}$, proposing a simple, weighted average that improves consistency across short and medium baseline reactor neutrino experiments.

Contribution

The paper introduces a clear, simple definition of $ ext{Δ}m^2_{ee}$ as a weighted average of $ ext{Δ}m^2_{31}$ and $ ext{Δ}m^2_{32}$, enhancing experimental analysis consistency.

Findings

$ ext{Δ}m^2_{ee}$ is best defined as a weighted average of $ ext{Δ}m^2_{31}$ and $ ext{Δ}m^2_{32}$

The proposed definition is superior for current and future reactor neutrino experiments

The definition simplifies comparisons across different experimental setups

Abstract

The current short baseline reactor experiments, Daya Bay and RENO (Double Chooz) have measured (or are capable of measuring) an effective $\Delta m^2$ associated with the atmospheric oscillation scale of 0.5 km/MeV in electron anti-neutrino disappearance. In this paper, I compare and contrast the different definitions of such an effective $\Delta m^2$ and argue that the simple, L/E independent, definition given by $\Delta m^2_{ee} \equiv \cos^2 \theta_{12} \Delta m^2_{31}+ \sin^2 \theta_{12} \Delta m^2_{32}$, i.e. "the $\nu_e$ weighted average of $\Delta m^2_{31}$ and $\Delta m^2_{32}$," is superior to all other definitions and is useful for both short baseline experiments mentioned above and for the future medium baseline experiments JUNO and RENO 50.