# How does one measure anti-neutrino flavor oscillation probabilities?

The Dirac $CP$ phase $\delta_{CP}$ in the $U_{PMNS}$ mixing matrix lead to the $CP$-violation in the Lepton sector. I think this can be tested by comparing neutrino flavour oscillation probabilities with anti-neutrino flavour oscillation probabilities. If only neutrinos are produced in Sun but not antineutrinos, how can one measure and compare two probabilities?

• Ideally you use an accelerator source of neutrinos (e.g. what HyperK and DUNE plan to use) and reverse the polarity of the 'horn' to choose neutrinos or antineutrinos. – dukwon Apr 13 '17 at 18:35

But so far the available data simply isn't precise enough to detect a difference between matter-type and antimatter-type neutrino oscillation parameters.. This is something that the community has been building up to for some time. I think the smart money right now is on NO$\nu$A, and if they have some unexpected problem DUNE will be along to lend a hand.
One of the interesting issues is that some of the data has good resolution in $\Delta m$ and poor resolution in $\theta$ and other data sets turn that around. If you combine them under the assumption of CP symmetry then you get a good overall result, but of course that won't tell you that if CP is violated. Here's a figure from a KamLAND paper showing how this works:
• But how would you know the solar mixing angle $\theta^{\bar{\nu}}_{12}$ for anti-neutrino flavor oscillation? – SRS Apr 13 '17 at 18:40