Confidence in a neutrino mass hierarchy determination

In the next decade, a number of experiments will attempt to determine the neutrino mass hierarchy. Feasibility studies for such experiments generally determine the statistic (Δχ²)-bar . As the hierarchy is a discrete choice, Δχ² does not obey a one degree of freedom χ² distribution and so the number of σ's of sensitivity to the hierarchy is not the square root of (Δχ²)-bar . We present a simple Bayesian formula for the sensitivity to the hierarchy determination that can be expected from the median experiment as a function of (Δχ²)-bar