If there were more than three families, the Z would decay into more neutrino antineutrino channels. Given

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If there were more than three families, the Z would decay into more neutrino– antineutrino channels. Given the existing limits on the masses, however, the charged leptons and quark channels of the new families would be closed. Consequently, the Z width would increase by Γνν for every extra family. The total width of the W would not increase, because the third family channel W → t + b̅ is already closed (as was established in 1990 when CDF gave the limit mt > 90 GeV). UA1 and UA2 measured the ratio

Ow BR(W → eve) R 07BR(Z → ete-) ete


simply from the numbers of events observed in the two channels. Both theoretical and experimental systematic uncertainties cancel out in the ratio. Writing the ratio as 

Г(W — Iv) Гz aw R = Г(Z — 11) Ги oz


one sees that it increases with the number of neutrino types. The experimental upper limit established by joining the UA1 and UA2 data was R < 10.1 at 90% confidence level. Evaluate R for 3, 4 and 5 and establish an upper limit for the number of neutrinos. Take σ= σ = 3:1.

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