Testing unitarity of the 3 × 3 neutrino mixing matrix in an atomic system

Abstract

Unitarity of the [Formula: see text] lepton flavor mixing matrix [Formula: see text] is unavoidably violated in a seesaw mechanism if its new heavy degrees of freedom are slightly mixed with the active neutrino flavors. We propose to use the atomic transition process [Formula: see text] (for [Formula: see text], [Formula: see text]), where [Formula: see text] and [Formula: see text] stand, respectively for the excited and ground levels of an atomic system, to probe or constrain the unitarity-violating effects of [Formula: see text]. We find that the photon spectrum of this transition will be distorted by the effects of [Formula: see text] and [Formula: see text] as compared with the [Formula: see text] case. We locate certain frequencies in the photon spectrum to minimize the degeneracy of effects of the unitarity violation and uncertainties of the flavor mixing parameters themselves. The requirements of a nominal experimental setup to test the unitarity of [Formula: see text] are briefly discussed.