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4  Universality improved B (τ → e ν ν) and Rhad

Following Ref. [63], we assume lepton universality to obtain a more precise experimental determination of B e = B (τ → eνeντ) using the tau branching fraction to muon and the tau lifetime, by averaging the B e direct measurement, the B e determination from assuming that gµ/ge = 1 hence (see also Section 3) B e = B µ· f(me2/mτ2)/f(mµ2/mτ2), and B e from assuming that gτ/gµ=1 hence B e = B (µ → e νe νµ)· (ττ/ τµ) · (mτ/mµ)5 · f(me2/mτ2)/f(me2/mµ2) · (δγτδWτ)/(δγµδWµ) where B (µ → e νe νµ) = 1. Accounting for statistical correlations, we obtain

     
  B euni = (17.839 ± 0.028)%.           

We use B euni to obtain the ratio

     
  Rhad = 
Γ(τ → hadrons)
Γ(τ→ eν
ν
)
 = 3.6279 ± 0.0094.
          

Here Γ(τ → hadrons) is obtained by summing all tau hadronic decay modes.


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