Higgs-boson decay and the running mass

We calculate QED and quantum-chromodynamics (QCD) radiative corrections to the fermionic decays of the Higgs boson, $H\to l^{+}{l}^{-}$ and $H\to q\overline{q}$. A novel feature of the calculation is that renormalization introduces logarithms of the fermion mass into the total decay rate. The order-$\alpha$ QED corrections suppress the decay rate by a few percent. The order-${\alpha }_s$, QCD corrections to the hadronic decay rate for a heavy Higgs boson are large, and lowestorder perturbation theory is useful only for quantities in which the logarithms of the quark mass cancel, such as $\frac{\Gamma (H\to 2 \mathrm{jets})}{\Gamma (H\to \mathrm{hadrons})}$. We obtain reliable corrections to the decay rate $H\to q\overline{q}$ by summing the QCD corrections to all orders in the leading-logarithm approximation. The result has a simple interpretation in terms of the "running mass" of the renormalization group: The effective quark-Higgs-boson coupling is proportional to the running mass of the quark evaluated at the Higgs-boson mass.