Measuring tau neutrino appearance probability via unitarity
We propose a {\em unitarity method} for determining $τ$ neutrino appearance probability $P(ν_μ \rightarrow ν_τ)$ in long-baseline (LBL) accelerator experiments and atmospheric neutrino observations. When simultaneous in situ measurements of $P(ν_μ \rightarrow ν_μ)$ and $P(ν_μ \rightarrow ν_{e})$ proceed, as is typical in the LBL experiments, one can use unitarity to "measure" $P(ν_μ \rightarrow ν_τ)$. A theorists' toy analysis for the model-independent determination of $P(ν_μ \rightarrow ν_μ)$ and $P(ν_μ \rightarrow ν_{e})$ is presented by using the NOvA data. It is shown in our analysis that $\lsim$5\% (8\%) measurement of $τ$ neutrino appearance probability in neutrino (antineutrino) mode is possible in the peak region $1.5 \lesssim E_ν\lesssim 2.5$ GeV. The $ν$SM-independent nature of determination of the probabilities is emphasized.