The Leptons

The six leptons are, generation one; electron (e$^{-}$) and electron-neutrino ( $\nu_{\rm e}$). Generation two; muon ($\mu^{-}$) and muon-neutrino ($\nu_{\mu}$). Generation three; tau ($\tau^{-}$) and tau-neutrino ( $\nu_{\tau}$). The corresponding anti-particles, positron, anti-muon and anti-tau, have the same mass as the particles and the opposite quantum numbers.

The fermions have half-integral spin so they may exist in two helicity states. However, the neutrinos only exist in left-handed states and anti-neutrinos in right-handed. For this to be possible, the neutrinos must be massless^1.2 and this is how they are described within the Standard Model.

The mass of the leptons increases with generation, the electron is the lightest ($\sim 0.51$ MeV) and tau the heaviest ($\sim 1.78$ GeV).

Figure 1.1: The muon decay process.

The massive leptons have charge $-1.9\times 10^{-19}$ Coulombs, but this is often denoted in terms of the positron charge, e, thus they are said to have charge -1 and the massive anti-leptons to have charge +1. The neutrinos have zero charge. The massive leptons in higher generations may decay into those from lower generations, for example, the dominant muon decay channel is $\mu^{-}\rightarrow{\rm e}^{-}\bar{\nu}_{\rm e}\nu_{\mu}$, as shown in figure 1.1. The main tau decay channels are shown below. (1.3) is known as the one prong hadronic decay and (1.4) is known as the three prong hadronic decay.

$$\tau^{-} \rightarrow \mu^{-}\bar{\nu}_{\mu}\nu_{\tau}$$ (1.1)

$$\tau^{-} \rightarrow {\rm e}^{-}\bar{\nu}_{\rm e}\nu_{\tau}$$ (1.2)

$$\tau^{-} \rightarrow \pi^{-}n\pi^{0}\nu_{\tau}$$ (1.3)

$$\tau^{-} \rightarrow \pi^{-}\pi^{-}\pi^{+}\nu_{\tau}$$ (1.4)