Neutrino oscillations: measuring $θ_{13}$ including its sign

In neutrino phenomenology, terms in the oscillation probabilities linear in $\sin θ_{13}$ lead naturally to the question ``How can one measure $θ_{13}$ including its sign?'' Here we demonstrate analytically and with a simulation of neutrino data that ${\mathcal P}_{eμ}$ and ${\mathcal {P}_{μμ}$ at $L/E = 2π/Δ_{21}$ exhibit significant linear dependence on $θ_{13}$ in the limit of vacuum oscillations. Measurements at this particular value of $L/E$ can thus determine not only $θ_{13}$ but also its sign, if CP violation is small.

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