The measured boson branching ratios to leptons are

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Electroweak theory and the Standard Model · Electroweak theory and the Standard Model

Particle Physics, Ch The Standard Model as a table you can predict from

Problem

The measured W−W^- boson branching ratios to leptons are B(W−→e−νˉe)=10.7%\mathcal{B}(W^-\to e^-\bar\nu_e)=10.7\%, B(W−→μ−νˉμ)=10.6%\mathcal{B}(W^-\to\mu^-\bar\nu_\mu)=10.6\% and B(W−→τ−νˉτ)=11.4%\mathcal{B}(W^-\to\tau^-\bar\nu_\tau)=11.4\%. The electron, muon and tau masses are 0.511 MeV/c20.511\,\mathrm{MeV}/c^2, 105.7 MeV/c2105.7\,\mathrm{MeV}/c^2 and 1776.9 MeV/c21776.9\,\mathrm{MeV}/c^2 respectively, a span of a factor of about 34773477. Someone argues: "the Standard Model has nineteen free parameters, including all nine charged-fermion masses, so nothing stops it from being adjusted to fit any pattern of branching ratios at all; the near-equality of these three numbers, despite the huge spread in lepton mass, therefore says nothing about whether the theory is right." ((a)) Identify which single parameter among the nineteen fixes the strength of the WW-lepton vertex. ((b)) State whether the lepton masses enter that vertex, and explain whether the near-equal branching ratios are an adjustable fit or a genuine prediction.

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