Question

From the data on the partial and full decay width of Z⁰ boson show that the number of neutrino generations is 3 only.

Answer 1

If N_{ν i}s the number of neutrino types in the sequence ν_e, ν_μ, ν_τ and assuming that there are only three charged leptons e, μ and τ , the balance equation for the decay rate can be written as 

Γ_z(total) = Γ(Z⁰ → hadrons) + 3 Γ(Z⁰ → l⁺ l ⁻) + N_νΓ(Z⁰ → ν_l bar ν_l) 

The factor 3 is for the three charged leptons. Substituting the given data 

2.534 = 1.797 + 3 × 0.084 + 0.166N_ν 

and solving, we get N_ν = 2.92 or 3.