Testing unitarity of the $3\times 3$ neutrino mixing matrix in an atomic system

Abstract

Unitarity of the $3\times 3$ lepton flavor mixing matrix $V$ 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 $|\mathrm{e}⟩\to |\mathrm{g}⟩+\gamma +{\nu }_i^{}+{\overline{\nu }}_j^{}$ (for $i,j=1,2,3$), where $|\mathrm{e}⟩$ and $|\mathrm{g}⟩$ stand respectively for the excited and ground levels of an atomic system, to probe or constrain the unitarity-violating effects of $V$. We find that the photon spectrum of this transition will be distorted by the effects of $V{V}^{†}\ne 1$ and $V^{†}V\ne 1$ as compared with the $V{V}^{†}=V^{†}V=1$ 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 $V$ are briefly discussed.

Comments: 15 pages, 4 figures