Unitarity test of lepton mixing via energy dependence of neutrino oscillation

A bstract We study the method to test the unitarity of the lepton mixing matrix by using only the long baseline neutrino oscillation experiments, such as the combination of the T2HK experiment and the one with the ν e beam from a future neutrino factory at J-PARC. Without a specific parametrization, one can directly extract the elements of the lepton mixing matrix by observing the energy dependence of the oscillation probabilities. A non-trivial test of the unitarity under the three-generation assumption can thus be made possible by examining the orthogonality in a similar manner to the unitarity triangle in the quark sector. As the first trial, we perform the analysis based on the simplified situation where the matter effects in the neutrino oscillation can be neglected. Under this simplified analysis, we demonstrate that a violation of unitarity in the 3 × 3 lepton mixing matrix can be observed, using a four-generation model as a concrete example of a non-unitary three-generation scenario. The statistically most significant measurement can be provided by the energy dependences of the combination of the CP conjugate modes, ν μ → ν e and $$ {\overline{\nu}}_{\mu}\to {\overline{\nu}}_e $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>μ</mml:mi> </mml:msub> <mml:mo>→</mml:mo> <mml:msub> <mml:mover> <mml:mi>ν</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mi>e</mml:mi> </mml:msub> </mml:math> , at T2HK and, independently, by the T conjugate modes, ν μ → ν e and ν e → ν μ , with the latter measured at the neutrino factory experiments.