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9) i Other groups [201,202] obtain results from LSS that are fully compatible with the previous upper bounds on neutrino masses. Hannestad in Ref. [201] performs a full numerical likelihood analysis in a cosmological parameter space with the following free parameters (other than Ων ): Ωm , Ωb , h, n, the normalization of the CMB power spectrum Q and the optical depth to reionization τ . e. with zero curvature. This is by no means a drawback since there is little degeneracy between neutrino mass and curvature.

121] from the fit of the distribution d2 Γ/dEh dmh (Eh is the total energy of the pions in the laboratory system). In the case of neutrino mixing, information about the minimal (common) mass m1 of an almost degenerate neutrino mass spectrum can be obtained from such experiments. ) (τ − → nπ + ντ ) . 11) Thus, the experiments on the measurement of the muon momentum in the decays of pions and the d2 Γ/dEh dmh distribution in the decays of taus are much less sensitive to the absolute neutrino mass m1 than tritium experiments.

2 2mi eV mi × 1021 eV . 3) We see there is a resonant energy for each neutrino mass mi , and for this reason we have added the subscript νi to E R . The lowest value of EνRi corresponds to the highest neutrino mass. 4) where ΓZ is the Z width. 4) scatters off a relic neutrino, about 70% of the times gives ν ν¯ → Z → hadrons . 5) The hadrons form a highly collimated final state, since in the relic neutrino rest frame the Z particle has a Lorentz factor of γ ∼ 1011 . Provided the scattering takes place at a distance from Earth of less than 50 Mpc, attenuation is small and the produced particles 50 may induce air showers in the Earth atmosphere giving rise to the observed super-GZK events.

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