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 $\nu_{3}$ in the $\nu_{3}$ mass range between 50 and 150 meV/$c^{2}$ under the present constraints by the neutrino oscillation measurements. In the left--right symmetric model, the minimum lifetime of $\nu_{3}$ is predicted to be $1.5 \times 10^{17}$ years for $m_{3}$ of 50 meV/$c^{2}$. 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.