Lepton Universality: Branching Ratios & Cross Sections

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SUMMARY

Lepton universality ensures that the couplings of tau particles to muons and electrons are identical, resulting in similar branching ratios (BRs) for their decays. Specifically, the branching ratios for tau decays into a tau neutrino, electron, and electron antineutrino is 17.82%, while the decay into a tau neutrino, muon, and muon antineutrino is 17.39%. The slight difference in these values arises from the phase space availability, as the heavier muon results in a smaller density of states in the cross section expression.

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JoePhysicsNut
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I'd just like to clarify something I read on Wikipedia:

"The branching ratio of the common purely leptonic tau decays are:

17.82% for decay into a tau neutrino, electron and electron antineutrino;
17.39% for decay into a tau neutrino, muon and muon antineutrino.

The similarity of values of the two branching ratios is a consequence of lepton universality."

Just to be clear, lepton universality insures the couplings of tau to mu and electron are identical, however, there is a slight difference between the BRs and cross sections due to the availability of phase space. BR_mu is slighly less than BR_el because the mu is heavier so the density of states term in the cross section expression is smaller. Is this correct?
 
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