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3.2. Evidence from the width of the Z

The experimental basis for the detection of the Z particle (carrier of the neutral weak interaction) is a large resonance in the electron-positron cross-section this reson around 93 GeV (the mass of the Z). The energy width of resonance is, according to the Heisenberg principle, related to the lifetime of this particle. And the lifetime is related to the number of channels (partial widths) in which the Z can decay.

Contrary to us, the Z knows how many families there are, and decays in all possible channels open to him. Hence the observed width of the resonance gives us a measure of the total number of families.

Numerically, the energy width of the Z computed taking into account the three families we already know turns out to be 2.63 GeV. Each unknown neutrino would contribute an addition of 180 MeV to the width. Comparison with the increasingly accurate observational data (LEP 1990) shows that the number of neutrino species is three to better than one percent.

There are some restrictions. The Z particle is a left-handed weak interacting particle. It cannot decay in righ-handed neutrinos (if they exist). Nor can it decay in particles of more than half of its mass (46 GeV). Its width would not reveal the existence of such hypothetical particles. Thus the Z decay does not probe exactly the same thing as BBN. However the particles probed by BBN are weighted according to the strength of their coupling constants. A right-handed neutrino, if it exists, would barely count for BBN as it would have decoupled at high temperature, probably before pion and muon annihilation. In this sense, the LEP number remains a best buy for BBN. As a result the best choice for g* is 9.75 and hence the n / p ratio can be considered as known.

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