Inferred 4.4 eV Upper Limits on the Muon- and Tau-Neutrino Masses

By combining experimental constraints from atmospheric and solar neutrino oscillations and the tritium beta decay endpoint, we infer upper limits of 4.4 eV on the $\nu_\mu$ and $\nu_\tau$ masses, if the universe consists of three neutrinos. For hierarchical mass spectra $m_3 \gg m_1, m_2$ or $m_3 \simeq m_2 \gg m_1$ we infer that $m_{\nu_\alpha} \lsim 0.08$ eV for $\alpha = e, \mu, \tau$. In a four neutrino universe, and assuming neutrino oscillations also account for the LSND experimental results, $m_{\nu_\alpha} \lsim 5.4$ eV. We also obtain lower limits on the masses.