Neutrino oscillations: measuring ${\theta }_{13}$ including its sign

Abstract

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

Comments: 5 pages, 5 figures