New plots and parameter degeneracies in neutrino oscillations

Abstract

It is shown that eightfold degeneracy in neutrino oscillations is easily seen by plotting constant probabilities in the $(\sin^22θ_{13}, 1/s^2_{23})$ plane. Using this plot, we discuss how an additional long baseline measurement resolves degeneracies after the JPARC experiment measures the oscillation probabilities $P(ν_μ\toν_e)$ and $P(\barν_μ\to\barν_e)$ at $|Δm^2_{31}|L/4E=π/2$. By measuring $P(ν_μ\toν_e)$ or $P(\barν_μ\to\barν_e)$, the sgn($Δm_{31}^2$) ambiguity is resolved better at longer baselines and the $δ\leftrightarrowπ-δ$ ambiguity is resolved better when $||Δm^2_{31}|L/4E-π/2|$ is larger. The $θ_{23}$ ambiguity may be resolved as a byproduct if $||Δm^2_{31}|L/4E-π|$ is small and the CP phase $δ$ turns out to satisfy $|\cos(δ+|Δm^2_{31}|L/4E)|\sim1$. 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 $ν_e\toν_τ$ channel offers a promising possibility which may potentially resolve all the ambiguities.