The impossibility of heavy neutrino dark matter in the Littlest Higgs Model with T-parity: constraints from direct search

We consider the Littlest Higgs Model with T-parity (LHT), in the parameter region where a heavy neutrino is the lightest T-odd particle (LTP). Having emphasized that this corresponds to a sizable region in the parameter space of the theory, we show that both the Cryogenic Dark Matter Search (CDMS) and Xenon10 experiments disallow the entire region where the masses of the new particles in LHT can lie within several TeV. Therefore, any observation of the signals of a heavy neutrino LTP is likely to seriously reopen the issue of cold dark matter in the universe.