linguistic:voice_change
Universality

The coupling of leptons to all types of gauge boson are flavour-independent: The interaction between leptons and a gauge boson measures the same for each lepton. This property is called lepton universality and has been tested in measurements of the muon and tau 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 {\displaystyle \Gamma }) of muons through the process μ → e + ν + ν is approximately given by an expression of the form (see muon decay for more details)

where K is some constant, and G is the Fermi coupling constant. The decay rate of tau particles through the process τ → e + ν + ν is given by an expression of the same form

where K is some other constant. Muon–tauon universality implies that K ≈ K. On the other hand, electron–muon universality implies

The branching ratios for the electronic mode (17.82%) and muonic (17.39%) mode of tau decay are not equal due to the mass difference of the final state leptons.

Universality also accounts for the ratio of muon and tau lifetimes. The lifetime T ℓ {\displaystyle \mathrm {T} _{\ell }} of a lepton ℓ {\displaystyle \ell } (with ℓ {\displaystyle \ell } = " μ " or " τ ") is related to the decay rate by

where B (x → y) {\displaystyle \;{\mathcal {B}}(x\rightarrow y)\;} denotes the branching ratios and Γ (x → y) {\displaystyle \;\Gamma (x\rightarrow y)\;} denotes the resonance width of the process x → y , {\displaystyle \;x\rightarrow y~,} with x and y replaced by two different particles from " e " or " μ " or " τ ".

The ratio of tau and muon lifetime is thus given by

Using values from the 2008 Review of Particle Physics for the branching ratios of the muon and tau yields a lifetime ratio of ~ 1.29 × 10, comparable to the measured lifetime ratio of ~ 1.32 × 10. The difference is due to K and K not actually being constants: They depend slightly on the mass of leptons involved.

Recent tests of lepton universality in B meson decays, performed by the LHCb, BaBar, and Belle experiments, have shown consistent deviations from the Standard Model predictions. However the combined statistical and systematic significance is not yet high enough to claim an observation of new physics.

In July 2021 results on lepton universality have been published testing W decays, previous measurements by the LEP had given a slight imbalance but the new measurement by the ATLAS collaboration have twice the precision and give a ratio of B (W → τ − + ν τ) / B (W → μ − + ν μ) = 0.992 ± 0.013 {\displaystyle {\mathcal {B}}(W\rightarrow \tau ^{-}+\nu _{\tau })/{\mathcal {B}}(W\rightarrow \mu ^{-}+\nu _{\mu })=0.992\pm 0.013}, which agrees with the standard-model prediction of unity.