Universality
The coupling of the leptons to gauge bosons are flavour-independent (i.e., the interactions between leptons and gauge bosons are the same for all leptons). This property is called lepton universality and has been tested in measurements of the tau and muon lifetimes and of Z boson partial decay widths, particularly at the Stanford Linear Collider (SLC) and Large Electron-Positron Collider (LEP) experiments.
The decay rate (Γ) of muons through the process μ− → e− + ν
e + ν
μ is approximately given by an expression of the form (see muon decay for more details)
where K1 is some constant, and GF is the Fermi coupling constant. The decay rate of tau particles through the process τ− → e− + ν
e + ν
τ is given by an expression of the same form
where K2 is some constant. Electron–muon universality implies that K1 = K2, and thus
This explains why the branching ratios for the electronic mode (17.85%) and muonic (17.36%) mode of tau decay are equal (within error).
Universality also accounts for the ratio of muon and tau lifetimes. The lifetime of a lepton (τl) is related to the decay rate by
where B(x → y) and Γ(x → y) denotes the branching ratios and the resonance width of the process x → y.
The ratio of tau and muon lifetime is thus given by
Using the values of the 2008 Review of Particle Physics for the branching ratios of muons and tau yields a lifetime ratio of ~1.29×10−7, comparable to the measured lifetime ratio of ~1.32×107. The difference is due to K1 and K2 not actually being constants; they depend on the mass of leptons.
Read more about this topic: Lepton