theta13

theta13, denoted by θ13, is one of the three mixing angles in the Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix that describes how neutrino flavor states mix with neutrino mass states. Along with θ12 and θ23, θ13 parameterizes the rotation between the electron flavor eigenstate and the third mass eigenstate. The size of θ13 determines the amplitude for electron neutrinos to participate in oscillations driven by the third mass eigenstate and, critically, enables CP violation in neutrino oscillations through the complex phase δCP.

Experimentally, θ13 is the smallest of the three mixing angles but is definitively nonzero. It was established by reactor neutrino experiments. In 2012–2013, Daya Bay, RENO, and Double Chooz measured a nonzero θ13, with sin^2(2θ13) about 0.085. This corresponds to θ13 ≈ 8.5–9.0 degrees (roughly 0.15 radians).

Significance: a nonzero θ13 allows experiments to probe CP violation in the lepton sector and to determine the neutrino mass ordering in combination with matter effects. In the standard three-neutrino framework, θ12 ≈ 33°, θ23 ≈ 42–49°, and θ13 ≈ 8–9°. θ13 is a key parameter for ongoing and future long-baseline and reactor experiments such as DUNE, Hyper-K, and JUNO, which aim to measure δCP more precisely and resolve the mass hierarchy.

Global fits currently constrain θ13 with percent-level precision, and the value is treated as well established.