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Search for Radiative Decays of Cosmic Background Neutrino using Cosmic Infrared Background Energy Spectrum

We propose to search for the neutrino radiative decay by fitting a photon energy spectrum of the cosmic infrared background to a sum of the photon energy spectrum from the neutrino radiative decay and a continuum. By comparing the present cosmic infrared background energy spectrum observed by AKARI and Spitzer to the photon energy spectrum expected from neutrino radiative decay with a maximum likelihood method, we obatined a lifetime lower limit of $3.1 \times 10^{12}$ to $3.8 \times 10^{12}$ years at 95% confidence level for the third generation neutrino $ν_3$ in the $ν_3$ mass range between 50 \mmev and 150 \mmev under the present constraints by the neutrino oscillation measurements. In the left-right symmetric model, the minimum lifetime of $ν_3$ is predicted to be $1.5 \times 10^{17}$ years for $m_3$ of 50 \mmev. We studied the feasibility of the observation of the neutrino radiative decay with a lifetime of $1.5 \times 10^{17}$ years, by measuring a continuous energy spectrum of the cosmic infrared background.