Measuring tau neutrino appearance probability via unitarity

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