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.
Categories: hep-ph hep-ex
