Two-loop $O(N_f{\alpha }_s^2)$ correction to the decay width of the Higgs boson to two massive fermions

Abstract

We present an analytical calculation of additional real or virtual radiation of the light fermion pair in the fermionic decay of the Higgs boson $H\to f_1{\bar{f}}_1$ for arbitrary ratios of the Higgs boson mass to the $f_1$ fermion mass. This result gives us a value of the $O(N_f{\alpha }_s^2)$ radiative correction to the inclusive decay rate $H\to f_1{\bar{f}}_1$. Using this result in the framework of the Brodsky-Mackenzie-Lepage scheme, we discuss the scale setting in the one-loop QCD correction to the decay width $H\to f_1{\bar{f}}_1$ for arbitrary relation between the Higgs boson and fermion masses.

Comments: Latex, 18 pages, 4 uuencoded figures, some misprints in formulas are corrected