The Higgs boson's coupling to a fermion is measured to grow with that fermion's mass

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 Higgs boson's coupling to a fermion is measured to grow with that fermion's mass, and its branching ratio to bbˉb\bar b is 58%58\% compared with 0.23%0.23\% to γγ\gamma\gamma, because the bottom quark (mb=4.18 GeV/c2m_b=4.18\,\mathrm{GeV}/c^2) is the heaviest fermion light enough to appear in a two-body Higgs decay. Someone argues: "because the Higgs boson's coupling to the muon (mμ=105.7 MeV/c2m_\mu=105.7\,\mathrm{MeV}/c^2) and to the bottom quark are both fixed by the same mass-proportional rule, the Standard Model table explains why the bottom quark is about 4040 times heavier than the muon." ((a)) State the rule connecting a Higgs coupling to a fermion mass. ((b)) Evaluate the claim: does the rule predict the ratio mb/mμm_b/m_\mu, or does it take the two masses as separately measured inputs?

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