Hadronic Higgs Boson Decay to Orderαs4

Abstract

We present in analytic form the three-loop $O\left({\alpha }_s^2\right)$ correction to the $H\to \mathrm{gg}$ partial width of the standard-model Higgs boson with intermediate mass $M_H\ll {2M}_t$. Its knowledge is required because the $O\left({\alpha }_s\right)$ correction is so sizable that the theoretical prediction to this order is unlikely to be reliable. For $M_H=100\mathrm{}\mathrm{GeV}$, the resulting QCD correction factor reads $1+\left(215/12\right){\alpha }_s^{\left(5\right)}\left(M_H\right)/\pi +150.419\mathrm{}\left[{\alpha }_s^{\left(5\right)}\right(M_H)/\pi {]}^2\approx 1+0.66+0.21$. The new three-loop correction increases the Higgs boson hadronic width by an amount of order 1%.