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 Γ_νν 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 m_t > 90 GeV). UA1 and UA2 measured the ratio

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 

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_W = σ_Z  = 3:1.

Transcribed Image Text:

Ow BR(W → eve) R 07BR(Z → ete-) ete Г(W — Iv) Гz aw R = Г(Z — 11) Ги oz