Higgs-boson decay and the running mass

TLDR: In this article, the decay rate of the Higgs boson was derived by summing the radiative corrections to all orders in the leading-logarithm approximation of the QED and quantum-chromodynamics (QCD) model.

Abstract: We calculate QED and quantum-chromodynamics (QCD) radiative corrections to the fermionic decays of the Higgs boson, $H\ensuremath{\rightarrow}{l}^{+}{l}^{\ensuremath{-}}$ and $H\ensuremath{\rightarrow}q\overline{q}$. A novel feature of the calculation is that renormalization introduces logarithms of the fermion mass into the total decay rate. The order-$\ensuremath{\alpha}$ QED corrections suppress the decay rate by a few percent. The order-${\ensuremath{\alpha}}_{s}$, 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 $\frac{\ensuremath{\Gamma}(H\ensuremath{\rightarrow}2 \mathrm{jets})}{\ensuremath{\Gamma}(H\ensuremath{\rightarrow}\mathrm{hadrons})}$. We obtain reliable corrections to the decay rate $H\ensuremath{\rightarrow}q\overline{q}$ 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.