Top Quark Mediated Higgs Boson Decay into Hadrons to Orderαs5

We present in analytic form the $O({\alpha }_s^5)$ correction to the $H\to gg$ partial width of the standard-model Higgs boson with an intermediate mass $M_H<2M_t$. Its knowledge is useful because the $O({\alpha }_s^4)$ correction is sizable (around 20%). For $M_H=120\mathrm{GeV}$, the resulting QCD correction factor reads $1+(215/12){\alpha }_s^{(5)}(M_H)/\pi +152.5[{\alpha }_s^{(5)}(M_H)/\pi {]}^2+381.5[{\alpha }_s^{(5)}(M_H)/\pi {]}^3\approx 1+0.65+0.20+0.02$. The new four-loop correction increases the total Higgs-boson hadronic width by a small amount of order 1‰ and stabilizes significantly the residual scale dependence.