Astroparticle Physics

22 2 The Standard Model of Elementary Particleslight neutrinos (Fig. 2.1). This result was obtained fromthe measurement of the total Z decay width. According toHeisenberg’s uncertainty principle, the resolution of complementaryquantities is intrinsically limited by Planck’sconstant (h = 6.626 0693×10 −34 J s). The relation betweenthe complementary quantities of energy and time isE t ≥ ¯h/2 (¯h = h/2π) . (2.1)Fig. 2.1Determination of the number ofneutrino generations from Z decayThese decays can occur even if the charged leptons l x associatedwith the respective generation are too heavy to beproduced in Z decay. A large number of different light neu-trinos will consequently reduce the Z lifetime, thereby increasingits decay width. The exact measurement of the Zdecay width took place at the LEP storage ring (Large Electron–Positroncollider) in 1989, enabling the total numberof neutrino generations to be determined: there are exactlythree lepton generations with light neutrinos.The measurement of the primordial helium abundancehad already allowed physicists to derive a limit for the numberof neutrino generations. The nucleosynthesis in the earlyuniverse was essentially determined by the number of relativisticparticles, which were able to cool down the universeafter the Big Bang. At temperatures of ≈ 10 10 K, whichcorrespond to energies where nucleons start to bind in nuclei(≈ 1 MeV), these relativistic particles would have consistedof protons, neutrons, electrons, and neutrinos. If manydifferent neutrino flavours exist, a large amount of energywould have escaped from the original fireball, owing to thelow interaction probability of neutrinos. This has the consequencethat the temperature would have decreased quickly.A rapidly falling temperature means that the time taken forneutrons to reach nuclear binding energies would have beenvery short, and consequently they would have had very littletime to decay (lifetime τ n = 885.7 s). If there were manyneutrons that did not decay, they would have been able toform helium together with stable protons. The primordialhelium abundance is therefore an indicator of the numberneutrino generationsprimordialhelium abundancenucleosynthesisIf t = τ is the lifetime of the particle, relation (2.1) impliesthat the decay width E = Γ is larger when τ is shorter. Ifthere are many generations of light neutrinos, the Z particlecan decay into all these neutrinos,Z → ν x +¯ν x . (2.2)