Cosmic-Ray Neutrinos from the Decay of Long-Lived Particle and the
  Recent IceCube Result
  Motivated by the recent IceCube result, we study high energy cosmic-ray
neutrino flux from the decay of a long-lived particle. Because neutrinos are so
transparent, high energy neutrinos produced in the past may also contribute to
the present neutrino flux. We point out that the PeV neutrino events observed
by IceCube may originate in the decay of a particle much heavier than PeV if
its lifetime is shorter than the present cosmic time. It is shown that the mass
of the particle responsible for the IceCube event can be as large as $\sim
10^{10}\ {\rm GeV}$. We also discuss several possibilities to acquire
information about the lifetime of the long-lived particle.
