The number of neutrino species

The authors review the methods used before the operation of the high energy Stanford and CERN $e^{+}{e}^{-}$ colliders to determine the number of neutrino species $N_{\nu }$, or an upper limit on this number, within the framework of the Standard Model of light stable neutrinos interacting according to the SU(2)×U(1) universal couplings. The astrophysical limit based on the neutrino burst from supernova 1987A is discussed first, followed by a discussion of the cosmological constraint based on the observed He/H abundance ratio. Finally, the particle physics methods based on single-photon production in $e^{+}{e}^{-}$ collisions, on the production of monojets in $p\overline{p}$ collisions, and on the determination of $N_{\nu }$ from the ratio of the $W\to l\overline{\nu }$ to $Z^0\to l\overline{l}$ partial cross sections in $p\overline{p}$ collisions are discussed. The various sources of uncertainty and the experimental backgrounds are presented, as well as an idea of what may be expected on this subject in the future. There is a remarkable agreement between the various methods, with central values for $N_{\nu }$ between 2 and 3 and with upper limits $N_{\nu }<6\mathrm{}$. Combining all determinations, the authors obtain a central value $N_{\nu }={2.1}_{-0.4\mathrm{}}^{+0.6\mathrm{}}$ for $m_{\mathrm{top}}=50\mathrm{}$ GeV/${\mathit{c}}^2$ and $N_{\nu }={2.0}_{-0.4\mathrm{}}^{+0.6\mathrm{}}$ if $m_{\mathrm{top}}\ge m_W$. The results are perfectly compatible with the a priori knowledge that at least three families of neutrinos should exist. The observed consistency between this a priori knowledge, the laboratory determinations of $N_{\nu }$, and determinations from SN 1987A and cosmology represent an astounding success for the Standard Model and for the current descriptions of stellar collapse and the Big-Bang primordial nucleosynthesis. These results, however, severely limit the number of additional families. Although the consistency is significantly worse, four families still provide a reasonable fit. In the framework of the Standard Model, a fifth light neutrino is, however, unlikely. A noted added in proof summarizes the results recently obtained at the Fermilab $\overline{p}p$ and the Stanford and CERN $e^{+}{e}^{-}$ colliders which confirm these conclusions.