New plots and parameter degeneracies in neutrino oscillations

It is shown that eightfold degeneracy in neutrino oscillations is easily seen by plotting constant probabilities in the $(\sin^22\theta_{13}, 1/s^2_{23})$ plane. Using this plot, we discuss how an additional long baseline measurement resolves degeneracies after the JPARC experiment measures the oscillation probabilities $P(\nu_\mu\to\nu_e)$ and $P(\bar{\nu}_\mu\to\bar{\nu}_e)$ at $|\Delta m^2_{31}|L/4E=\pi/2$. By measuring $P(\nu_\mu\to\nu_e)$ or $P(\bar{\nu}_\mu\to\bar{\nu}_e)$, the sgn($\Delta m_{31}^2$) ambiguity is resolved better at longer baselines and the $\delta\leftrightarrow\pi-\delta$ ambiguity is resolved better when $||\Delta m^2_{31}|L/4E-\pi/2|$ is larger. The $\theta_{23}$ ambiguity may be resolved as a byproduct if $||\Delta m^2_{31}|L/4E-\pi|$ is small and the CP phase $\delta$ turns out to satisfy $|\cos(\delta +|\Delta m^2_{31}|L/4E)|\sim1$. It is pointed out that the low energy option ($E\sim$1GeV) at the off-axis NuMI experiment may be useful in resolving these ambiguities. The $\nu_e\to\nu_\tau$ channel offers a promising possibility which may potentially resolve all the ambiguities.