  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 \mmev
and 150 \mmev 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 \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.
