What is $Δm^2_{ee}$ ?

Abstract

The current short baseline reactor experiments, Daya Bay and RENO (Double Chooz) have measured (or are capable of measuring) an effective $Δm^2$ 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 $Δm^2$ and argue that the simple, L/E independent, definition given by $Δm^2_{ee} \equiv \cos^2 θ_{12} Δm^2_{31}+ \sin^2 θ_{12} Δm^2_{32}$, i.e. "the $ν_e$ weighted average of $Δm^2_{31}$ and $Δm^2_{32}$," 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.

15 pages, 5 figures