3  Tests of lepton universality

In the Standard Model, the partial widths of a heavier lepton L decaying to a lighter lepton ℓ are, neglecting neutrino masses and including radiative corrections [84],

where

We use r_γ^τ=1−43.2· 10⁻⁴ and r_γ^µ=1−42.4· 10⁻⁴ [84] and M_W from PDG 2011 [91] as usual.

Proper ratios of the above partial widths, corrected by the suitable above-illustrated factors to remove the dependencies from masses and radiative corrections, measure ratios of charged weak lepton coupling constants. Using the HFAG-Tau fit values where available and using PDG 2011 for the remaining quantities, we measure, accounting for the statistical correlations emerging from the HFAG-Tau fit:

Tau decays partial widths to hadrons compared to the same hadron decay to muons measure the tau-muon universality of charged weak couplings as follows:

where h = π or K and the radiative corrections are δ_π = (0.16 ± 0.14)% and δ_K = (0.90 ± 0.22)% [64]. Using the HFAG-Tau data and PDG 2011 we measure:

Similar tests could be performed with decays to electrons, however they are less precise because the hadron two body decays to electrons are helicity-suppressed. Averaging the three g_τ/g_µ ratios we obtain

accounting for statistical correlations. Table 8 reports the statistical correlation coefficients for the fitted coupling ratios:

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Table 8: Universality coupling ratios correlation coefficients (%)

( gτ/ge )	77
( gµ/ge )	-35	34
( gτ/gµ )π	49	50	2
( gτ/gµ )K	23	21	-2	14
	( gτ/gµ )	( gτ/ge )	( gµ/ge )	( gτ/gµ )π

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