  Silicon photomultipliers (SiPM) are solid state light detectors with
sensitivity to single photons. Their use in high energy physics experiments,
and in particular in ring imaging Cherenkov (RICH) detectors, is hindered by
their poor tolerance to radiation. At room temperature the large increase in
dark count rate makes single photon detection practically impossible already at
10$^{11}$ cm$^{-2}$ 1-MeV-equivalent neutron fluence. The neutron fluences
foreseen by many subdetectors to be operated at the high luminosity LHC range
up to 10$^{14}$ cm$^{-2}$ 1-MeV-equivalent. In this paper we present the
effects of such high neutron fluences on Hamamatsu and SensL SiPMs of different
cell size. The advantage of annealing at high temperature (up to 175
$^{\circ}$C) is discussed. We demonstrate that, after annealing, operation at
the single photon level with a SiPM irradiated up to 10$^{14}$ cm$^{-2}$
1-MeV-equivalent neutron fluence is possible at cryogenic temperature (77 K)
with a dark count rate below 1~kHz.
