Astroparticle Physics

17.10 Chapter 10 367whereσ√hadr 0 – peak cross section,s – center-of-mass energy,Γ Z – total width of the Z,M Z – massofthe Z,δ rad – radiative correction.The peak cross section σhadr 0 for the process e+ e − → Z → hadrons is given byσhadr 0 = 12π Γ e + e −Γ hadrMZ2 ΓZ2 ,where Γ e + e − is the partial e+ e − width of the Z and Γ hadr the partial width for Z →hadrons.The total Z width can be written asΓ Z = Γ hadr + Γ e + e − + Γ µ + µ − + Γ τ + τ − + Γ inv ,where Γ inv describes the invisible decay of the Z into neutrino pairs (ν e ¯ν e , ν µ ¯ν µ , ν τ ¯ν τ ,and possibly other neutrino pairs from a suspected fourth neutrino family).Lepton universality is well established. Therefore,Γ Z = Γ hadr + 3Γ l ¯l + Γ inv .Γ inv= Γ Z− 3 − Γ hadr= Γ Z− 3 − R,(∗)Γ l ¯l Γ l ¯l Γ l ¯l Γ l ¯lwhere R is the usual ratioR = σ(e+ e − → hadrons)σ(e + e − → l + l − .)The experiment provides σhadr 0 , Γ Z,andM Z .The measurement of the peak cross section σhadr 0 and Γ Z together with M Z fixes theproduct Γ l ¯l Γ hadr.The measurement of the peak cross section for the process e + e − → Z → µ + µ − ,σµµ 0 = 12π Γ e + e − Γ µ + µ −MZ2 ΓZ2 ,determines Γ l ¯l , if lepton universality is assumed. Therefore, also Γ hadr is now known,so that Γ inv can be obtained from (∗).In the framework of the Standard Model the width ofZ → ν x ¯ν xis calculated to be ≈ 170 MeV. The LEP experiments resulted inΓ inv ≈ 500 MeVindicating very clearly that there are only 500/170 ≈ 3 neutrino generations.