Impact of matter effects on the unitarity test of lepton mixing

TL;DR

This paper explores how matter effects influence the testing of lepton mixing matrix unitarity in long baseline neutrino experiments, proposing methods to detect deviations from unitarity without assuming a specific parametrization.

Contribution

It introduces a novel approach to test lepton mixing matrix unitarity considering matter effects, using spectral data from experiments like T2HK and neutrino factories.

Findings

Spectral information can be used to extract mixing matrix elements without specific parametrization.

Energy spectra of CP-conjugate channels provide powerful tests of unitarity.

Matter effects are significant and must be considered in unitarity tests.

Abstract

Testing the unitarity of the lepton mixing matrix, in a manner analogous to the unitarity tests of the CKM matrix in the quark sector, is an important step toward probing physics beyond the standard three-generation framework. In long baseline neutrino oscillation experiments, the formula of the oscillation probabilities can be written as a sum of terms with various combinations of the mixing-matrix elements, and their coefficients depend differently on energy. By observing the spectral information of long baseline experiments such as T2HK and a future neutrino factory at J-PARC with a $\nu_e$ beam, the elements of the mixing matrix can be extracted without assuming a specific parametrization of the mixing matrix. We investigate how such an extraction method can be applied to neutrino oscillations by taking into account matter effects, and discuss how one can test unitarity of the mixing matrix in future long baseline experiments. As a concrete example, we examine the unitarity test by using a four-generation model, where we look at a quantity which should be vanishing in a unitary model. Among possible combinations of measurements, the most powerful test can be provided from the energy spectra of the CP-conjugate appearance channels $\nu_\mu \to \nu_e$ and $\bar{\nu}_\mu \to \bar{\nu}_e$ at T2HK, as well as from the T-conjugate pair $\nu_\mu \to \nu_e$ and $\nu_e \to \nu_\mu$ available at neutrino factories.